xref: /libCEED/rust/libceed-sys/c-src/interface/ceed-preconditioning.c (revision 249f8407d3193c39004e0d62898526a0457c663c)
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 
40   // Check if NULL qf passed in
41   if (!qf) return CEED_ERROR_SUCCESS;
42 
43   CeedDebug256(qf->ceed, 1, "---------- CeedOperator Fallback ----------\n");
44   CeedDebug(qf->ceed, "Creating fallback CeedQFunction\n");
45 
46   if (qf->source_path) {
47     size_t path_len = strlen(qf->source_path), name_len = strlen(qf->kernel_name);
48     CeedCall(CeedCalloc(path_len + name_len + 2, &source_path_with_name));
49     memcpy(source_path_with_name, qf->source_path, path_len);
50     memcpy(&source_path_with_name[path_len], ":", 1);
51     memcpy(&source_path_with_name[path_len + 1], qf->kernel_name, name_len);
52   } else {
53     CeedCall(CeedCalloc(1, &source_path_with_name));
54   }
55 
56   CeedCall(CeedQFunctionCreateInterior(fallback_ceed, qf->vec_length, qf->function, source_path_with_name, qf_fallback));
57   {
58     CeedQFunctionContext ctx;
59 
60     CeedCall(CeedQFunctionGetContext(qf, &ctx));
61     CeedCall(CeedQFunctionSetContext(*qf_fallback, ctx));
62   }
63   for (CeedInt i = 0; i < qf->num_input_fields; i++) {
64     CeedCall(CeedQFunctionAddInput(*qf_fallback, qf->input_fields[i]->field_name, qf->input_fields[i]->size, qf->input_fields[i]->eval_mode));
65   }
66   for (CeedInt i = 0; i < qf->num_output_fields; i++) {
67     CeedCall(CeedQFunctionAddOutput(*qf_fallback, qf->output_fields[i]->field_name, qf->output_fields[i]->size, qf->output_fields[i]->eval_mode));
68   }
69   CeedCall(CeedFree(&source_path_with_name));
70   return CEED_ERROR_SUCCESS;
71 }
72 
73 /**
74   @brief Duplicate a `CeedOperator` with a reference `Ceed` to fallback for advanced `CeedOperator` functionality
75 
76   @param[in,out] op `CeedOperator` to create fallback for
77 
78   @return An error code: 0 - success, otherwise - failure
79 
80   @ref Developer
81 **/
82 static int CeedOperatorCreateFallback(CeedOperator op) {
83   Ceed         ceed_fallback;
84   bool         is_composite;
85   CeedOperator op_fallback;
86 
87   // Check not already created
88   if (op->op_fallback) return CEED_ERROR_SUCCESS;
89 
90   // Fallback Ceed
91   CeedCall(CeedGetOperatorFallbackCeed(op->ceed, &ceed_fallback));
92   if (!ceed_fallback) return CEED_ERROR_SUCCESS;
93 
94   CeedDebug256(op->ceed, 1, "---------- CeedOperator Fallback ----------\n");
95   CeedDebug(op->ceed, "Creating fallback CeedOperator\n");
96 
97   // Clone Op
98   CeedCall(CeedOperatorIsComposite(op, &is_composite));
99   if (is_composite) {
100     CeedInt       num_suboperators;
101     CeedOperator *sub_operators;
102 
103     CeedCall(CeedCompositeOperatorCreate(ceed_fallback, &op_fallback));
104     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
105     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
106     for (CeedInt i = 0; i < num_suboperators; i++) {
107       CeedOperator op_sub_fallback;
108 
109       CeedCall(CeedOperatorGetFallback(sub_operators[i], &op_sub_fallback));
110       CeedCall(CeedCompositeOperatorAddSub(op_fallback, op_sub_fallback));
111     }
112   } else {
113     CeedQFunction qf_fallback = NULL, dqf_fallback = NULL, dqfT_fallback = NULL;
114 
115     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->qf, &qf_fallback));
116     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqf, &dqf_fallback));
117     CeedCall(CeedQFunctionCreateFallback(ceed_fallback, op->dqfT, &dqfT_fallback));
118     CeedCall(CeedOperatorCreate(ceed_fallback, qf_fallback, dqf_fallback, dqfT_fallback, &op_fallback));
119     for (CeedInt i = 0; i < op->qf->num_input_fields; i++) {
120       CeedCall(CeedOperatorSetField(op_fallback, op->input_fields[i]->field_name, op->input_fields[i]->elem_rstr, op->input_fields[i]->basis,
121                                     op->input_fields[i]->vec));
122     }
123     for (CeedInt i = 0; i < op->qf->num_output_fields; i++) {
124       CeedCall(CeedOperatorSetField(op_fallback, op->output_fields[i]->field_name, op->output_fields[i]->elem_rstr, op->output_fields[i]->basis,
125                                     op->output_fields[i]->vec));
126     }
127     CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op->qf_assembled, &op_fallback->qf_assembled));
128     // Cleanup
129     CeedCall(CeedQFunctionDestroy(&qf_fallback));
130     CeedCall(CeedQFunctionDestroy(&dqf_fallback));
131     CeedCall(CeedQFunctionDestroy(&dqfT_fallback));
132   }
133   CeedCall(CeedOperatorSetName(op_fallback, op->name));
134   CeedCall(CeedOperatorCheckReady(op_fallback));
135   // Note: No ref-counting here so we don't get caught in a reference loop.
136   //       The op holds the only reference to op_fallback and is responsible for deleting itself and op_fallback.
137   op->op_fallback                 = op_fallback;
138   op_fallback->op_fallback_parent = op;
139   return CEED_ERROR_SUCCESS;
140 }
141 
142 /**
143   @brief Core logic for assembling operator diagonal or point block diagonal
144 
145   @param[in]  op             `CeedOperator` to assemble point block diagonal
146   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
147   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
148   @param[out] assembled      `CeedVector` to store assembled diagonal
149 
150   @return An error code: 0 - success, otherwise - failure
151 
152   @ref Developer
153 **/
154 static inline int CeedSingleOperatorAssembleAddDiagonal_Core(CeedOperator op, CeedRequest *request, const bool is_point_block, CeedVector assembled) {
155   Ceed ceed;
156   bool is_composite;
157 
158   CeedCall(CeedOperatorGetCeed(op, &ceed));
159   CeedCall(CeedOperatorIsComposite(op, &is_composite));
160   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
161 
162   // Assemble QFunction
163   CeedInt             layout_qf[3];
164   const CeedScalar   *assembled_qf_array;
165   CeedVector          assembled_qf        = NULL;
166   CeedElemRestriction assembled_elem_rstr = NULL;
167 
168   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, request));
169   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
170   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
171   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
172 
173   // Get assembly data
174   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
175   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
176   CeedSize               **eval_mode_offsets_in, **eval_mode_offsets_out, num_output_components;
177   CeedBasis               *active_bases_in, *active_bases_out;
178   CeedElemRestriction     *active_elem_rstrs_in, *active_elem_rstrs_out;
179   CeedOperatorAssemblyData data;
180 
181   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
182   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, &eval_mode_offsets_in,
183                                                 &num_active_bases_out, &num_eval_modes_out, &eval_modes_out, &eval_mode_offsets_out,
184                                                 &num_output_components));
185   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, NULL, NULL, &active_bases_out, NULL));
186   CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, NULL, &active_elem_rstrs_in, NULL, &active_elem_rstrs_out));
187 
188   // Loop over all active bases (find matching input/output pairs)
189   for (CeedInt b = 0; b < CeedIntMin(num_active_bases_in, num_active_bases_out); b++) {
190     CeedInt             b_in, b_out, num_elem, num_nodes, num_qpts, num_comp;
191     bool                has_eval_none = false;
192     CeedScalar         *elem_diag_array, *identity = NULL;
193     CeedVector          elem_diag;
194     CeedElemRestriction diag_elem_rstr;
195 
196     if (num_active_bases_in <= num_active_bases_out) {
197       b_in = b;
198       for (b_out = 0; b_out < num_active_bases_out; b_out++) {
199         if (active_bases_in[b_in] == active_bases_out[b_out]) {
200           break;
201         }
202       }
203       if (b_out == num_active_bases_out) {
204         continue;
205       }  // No matching output basis found
206     } else {
207       b_out = b;
208       for (b_in = 0; b_in < num_active_bases_in; b_in++) {
209         if (active_bases_in[b_in] == active_bases_out[b_out]) {
210           break;
211         }
212       }
213       if (b_in == num_active_bases_in) {
214         continue;
215       }  // No matching output basis found
216     }
217     CeedCheck(active_elem_rstrs_in[b_in] == active_elem_rstrs_out[b_out], ceed, CEED_ERROR_UNSUPPORTED,
218               "Cannot assemble operator diagonal with different input and output active element restrictions");
219 
220     // Assemble point block diagonal restriction, if needed
221     if (is_point_block) {
222       CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstrs_in[b_in], &diag_elem_rstr));
223     } else {
224       CeedCall(CeedElemRestrictionCreateUnsignedCopy(active_elem_rstrs_in[b_in], &diag_elem_rstr));
225     }
226 
227     // Create diagonal vector
228     CeedCall(CeedElemRestrictionCreateVector(diag_elem_rstr, NULL, &elem_diag));
229 
230     // Assemble element operator diagonals
231     CeedCall(CeedVectorSetValue(elem_diag, 0.0));
232     CeedCall(CeedVectorGetArray(elem_diag, CEED_MEM_HOST, &elem_diag_array));
233     CeedCall(CeedElemRestrictionGetNumElements(diag_elem_rstr, &num_elem));
234     CeedCall(CeedBasisGetNumNodes(active_bases_in[b_in], &num_nodes));
235     CeedCall(CeedBasisGetNumComponents(active_bases_in[b_in], &num_comp));
236     if (active_bases_in[b_in] == CEED_BASIS_NONE) num_qpts = num_nodes;
237     else CeedCall(CeedBasisGetNumQuadraturePoints(active_bases_in[b_in], &num_qpts));
238 
239     // Construct identity matrix for basis if required
240     for (CeedInt i = 0; i < num_eval_modes_in[b_in]; i++) {
241       has_eval_none = has_eval_none || (eval_modes_in[b_in][i] == CEED_EVAL_NONE);
242     }
243     for (CeedInt i = 0; i < num_eval_modes_out[b_out]; i++) {
244       has_eval_none = has_eval_none || (eval_modes_out[b_out][i] == CEED_EVAL_NONE);
245     }
246     if (has_eval_none) {
247       CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
248       for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) identity[i * num_nodes + i] = 1.0;
249     }
250 
251     // Compute the diagonal of B^T D B
252     // Each element
253     for (CeedSize e = 0; e < num_elem; e++) {
254       // Each basis eval mode pair
255       CeedInt      d_out              = 0, q_comp_out;
256       CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
257 
258       for (CeedInt e_out = 0; e_out < num_eval_modes_out[b_out]; e_out++) {
259         CeedInt           d_in              = 0, q_comp_in;
260         const CeedScalar *B_t               = NULL;
261         CeedEvalMode      eval_mode_in_prev = CEED_EVAL_NONE;
262 
263         CeedCall(CeedOperatorGetBasisPointer(active_bases_out[b_out], eval_modes_out[b_out][e_out], identity, &B_t));
264         CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_out[b_out], eval_modes_out[b_out][e_out], &q_comp_out));
265         if (q_comp_out > 1) {
266           if (e_out == 0 || eval_modes_out[b_out][e_out] != eval_mode_out_prev) d_out = 0;
267           else B_t = &B_t[(++d_out) * num_qpts * num_nodes];
268         }
269         eval_mode_out_prev = eval_modes_out[b_out][e_out];
270 
271         for (CeedInt e_in = 0; e_in < num_eval_modes_in[b_in]; e_in++) {
272           const CeedScalar *B = NULL;
273 
274           CeedCall(CeedOperatorGetBasisPointer(active_bases_in[b_in], eval_modes_in[b_in][e_in], identity, &B));
275           CeedCall(CeedBasisGetNumQuadratureComponents(active_bases_in[b_in], eval_modes_in[b_in][e_in], &q_comp_in));
276           if (q_comp_in > 1) {
277             if (e_in == 0 || eval_modes_in[b_in][e_in] != eval_mode_in_prev) d_in = 0;
278             else B = &B[(++d_in) * num_qpts * num_nodes];
279           }
280           eval_mode_in_prev = eval_modes_in[b_in][e_in];
281 
282           // Each component
283           for (CeedInt c_out = 0; c_out < num_comp; c_out++) {
284             // Each qpt/node pair
285             for (CeedInt q = 0; q < num_qpts; q++) {
286               if (is_point_block) {
287                 // Point Block Diagonal
288                 for (CeedInt c_in = 0; c_in < num_comp; c_in++) {
289                   const CeedSize c_offset =
290                       (eval_mode_offsets_in[b_in][e_in] + c_in) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
291                   const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
292 
293                   for (CeedInt n = 0; n < num_nodes; n++) {
294                     elem_diag_array[((e * num_comp + c_out) * num_comp + c_in) * num_nodes + n] +=
295                         B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
296                   }
297                 }
298               } else {
299                 // Diagonal Only
300                 const CeedInt c_offset =
301                     (eval_mode_offsets_in[b_in][e_in] + c_out) * num_output_components + eval_mode_offsets_out[b_out][e_out] + c_out;
302                 const CeedScalar qf_value = assembled_qf_array[q * layout_qf[0] + c_offset * layout_qf[1] + e * layout_qf[2]];
303 
304                 for (CeedInt n = 0; n < num_nodes; n++) {
305                   elem_diag_array[(e * num_comp + c_out) * num_nodes + n] += B_t[q * num_nodes + n] * qf_value * B[q * num_nodes + n];
306                 }
307               }
308             }
309           }
310         }
311       }
312     }
313     CeedCall(CeedVectorRestoreArray(elem_diag, &elem_diag_array));
314 
315     // Assemble local operator diagonal
316     CeedCall(CeedElemRestrictionApply(diag_elem_rstr, CEED_TRANSPOSE, elem_diag, assembled, request));
317 
318     // Cleanup
319     CeedCall(CeedElemRestrictionDestroy(&diag_elem_rstr));
320     CeedCall(CeedVectorDestroy(&elem_diag));
321     CeedCall(CeedFree(&identity));
322   }
323   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
324   CeedCall(CeedVectorDestroy(&assembled_qf));
325   return CEED_ERROR_SUCCESS;
326 }
327 
328 /**
329   @brief Core logic for assembling composite operator diagonal
330 
331   @param[in]  op             `CeedOperator` to assemble point block diagonal
332   @param[in]  request        Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
333   @param[in]  is_point_block Boolean flag to assemble diagonal or point block diagonal
334   @param[out] assembled      `CeedVector` to store assembled diagonal
335 
336   @return An error code: 0 - success, otherwise - failure
337 
338   @ref Developer
339 **/
340 static inline int CeedCompositeOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedRequest *request, const bool is_point_block,
341                                                                  CeedVector assembled) {
342   CeedInt       num_sub;
343   CeedOperator *suboperators;
344 
345   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub));
346   CeedCall(CeedCompositeOperatorGetSubList(op, &suboperators));
347   for (CeedInt i = 0; i < num_sub; i++) {
348     if (is_point_block) {
349       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(suboperators[i], assembled, request));
350     } else {
351       CeedCall(CeedOperatorLinearAssembleAddDiagonal(suboperators[i], assembled, request));
352     }
353   }
354   return CEED_ERROR_SUCCESS;
355 }
356 
357 /**
358   @brief Build nonzero pattern for non-composite CeedOperator`.
359 
360   Users should generally use @ref CeedOperatorLinearAssembleSymbolic().
361 
362   @param[in]  op     `CeedOperator` to assemble nonzero pattern
363   @param[in]  offset Offset for number of entries
364   @param[out] rows   Row number for each entry
365   @param[out] cols   Column number for each entry
366 
367   @return An error code: 0 - success, otherwise - failure
368 
369   @ref Developer
370 **/
371 static int CeedSingleOperatorAssembleSymbolic(CeedOperator op, CeedInt offset, CeedInt *rows, CeedInt *cols) {
372   Ceed                ceed;
373   bool                is_composite;
374   CeedSize            num_nodes_in, num_nodes_out, count = 0;
375   CeedInt             num_elem_in, elem_size_in, num_comp_in, layout_er_in[3];
376   CeedInt             num_elem_out, elem_size_out, num_comp_out, layout_er_out[3], local_num_entries;
377   CeedScalar         *array;
378   const CeedScalar   *elem_dof_a_in, *elem_dof_a_out;
379   CeedVector          index_vec_in, index_vec_out, elem_dof_in, elem_dof_out;
380   CeedElemRestriction elem_rstr_in, elem_rstr_out, index_elem_rstr_in, index_elem_rstr_out;
381 
382   CeedCall(CeedOperatorGetCeed(op, &ceed));
383   CeedCall(CeedOperatorIsComposite(op, &is_composite));
384   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
385 
386   CeedCall(CeedOperatorGetActiveVectorLengths(op, &num_nodes_in, &num_nodes_out));
387   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
388   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
389   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
390   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
391   CeedCall(CeedElemRestrictionGetELayout(elem_rstr_in, layout_er_in));
392 
393   // Determine elem_dof relation for input
394   CeedCall(CeedVectorCreate(ceed, num_nodes_in, &index_vec_in));
395   CeedCall(CeedVectorGetArrayWrite(index_vec_in, CEED_MEM_HOST, &array));
396   for (CeedInt i = 0; i < num_nodes_in; i++) array[i] = i;
397   CeedCall(CeedVectorRestoreArray(index_vec_in, &array));
398   CeedCall(CeedVectorCreate(ceed, num_elem_in * elem_size_in * num_comp_in, &elem_dof_in));
399   CeedCall(CeedVectorSetValue(elem_dof_in, 0.0));
400   CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_in, &index_elem_rstr_in));
401   CeedCall(CeedElemRestrictionApply(index_elem_rstr_in, CEED_NOTRANSPOSE, index_vec_in, elem_dof_in, CEED_REQUEST_IMMEDIATE));
402   CeedCall(CeedVectorGetArrayRead(elem_dof_in, CEED_MEM_HOST, &elem_dof_a_in));
403   CeedCall(CeedVectorDestroy(&index_vec_in));
404   CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_in));
405 
406   if (elem_rstr_in != elem_rstr_out) {
407     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
408     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
409               "Active input and output operator restrictions must have the same number of elements");
410     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
411     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
412     CeedCall(CeedElemRestrictionGetELayout(elem_rstr_out, layout_er_out));
413 
414     // Determine elem_dof relation for output
415     CeedCall(CeedVectorCreate(ceed, num_nodes_out, &index_vec_out));
416     CeedCall(CeedVectorGetArrayWrite(index_vec_out, CEED_MEM_HOST, &array));
417     for (CeedInt i = 0; i < num_nodes_out; i++) array[i] = i;
418     CeedCall(CeedVectorRestoreArray(index_vec_out, &array));
419     CeedCall(CeedVectorCreate(ceed, num_elem_out * elem_size_out * num_comp_out, &elem_dof_out));
420     CeedCall(CeedVectorSetValue(elem_dof_out, 0.0));
421     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr_out, &index_elem_rstr_out));
422     CeedCall(CeedElemRestrictionApply(index_elem_rstr_out, CEED_NOTRANSPOSE, index_vec_out, elem_dof_out, CEED_REQUEST_IMMEDIATE));
423     CeedCall(CeedVectorGetArrayRead(elem_dof_out, CEED_MEM_HOST, &elem_dof_a_out));
424     CeedCall(CeedVectorDestroy(&index_vec_out));
425     CeedCall(CeedElemRestrictionDestroy(&index_elem_rstr_out));
426   } else {
427     num_elem_out     = num_elem_in;
428     elem_size_out    = elem_size_in;
429     num_comp_out     = num_comp_in;
430     layout_er_out[0] = layout_er_in[0];
431     layout_er_out[1] = layout_er_in[1];
432     layout_er_out[2] = layout_er_in[2];
433     elem_dof_a_out   = elem_dof_a_in;
434   }
435   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
436 
437   // Determine i, j locations for element matrices
438   for (CeedInt e = 0; e < num_elem_in; e++) {
439     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
440       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
441         for (CeedInt i = 0; i < elem_size_out; i++) {
442           for (CeedInt j = 0; j < elem_size_in; j++) {
443             const CeedInt elem_dof_index_row = i * layout_er_out[0] + comp_out * layout_er_out[1] + e * layout_er_out[2];
444             const CeedInt elem_dof_index_col = j * layout_er_in[0] + comp_in * layout_er_in[1] + e * layout_er_in[2];
445             const CeedInt row                = elem_dof_a_out[elem_dof_index_row];
446             const CeedInt col                = elem_dof_a_in[elem_dof_index_col];
447 
448             rows[offset + count] = row;
449             cols[offset + count] = col;
450             count++;
451           }
452         }
453       }
454     }
455   }
456   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing assembled entries");
457   CeedCall(CeedVectorRestoreArrayRead(elem_dof_in, &elem_dof_a_in));
458   CeedCall(CeedVectorDestroy(&elem_dof_in));
459   if (elem_rstr_in != elem_rstr_out) {
460     CeedCall(CeedVectorRestoreArrayRead(elem_dof_out, &elem_dof_a_out));
461     CeedCall(CeedVectorDestroy(&elem_dof_out));
462   }
463   return CEED_ERROR_SUCCESS;
464 }
465 
466 /**
467   @brief Assemble nonzero entries for non-composite `CeedOperator`.
468 
469   Users should generally use @ref CeedOperatorLinearAssemble().
470 
471   @param[in]  op     `CeedOperator` to assemble
472   @param[in]  offset Offset for number of entries
473   @param[out] values Values to assemble into matrix
474 
475   @return An error code: 0 - success, otherwise - failure
476 
477   @ref Developer
478 **/
479 static int CeedSingleOperatorAssemble(CeedOperator op, CeedInt offset, CeedVector values) {
480   Ceed ceed;
481   bool is_composite;
482 
483   CeedCall(CeedOperatorGetCeed(op, &ceed));
484   CeedCall(CeedOperatorIsComposite(op, &is_composite));
485   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
486 
487   // Early exit for empty operator
488   {
489     CeedInt num_elem = 0;
490 
491     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
492     if (num_elem == 0) return CEED_ERROR_SUCCESS;
493   }
494 
495   if (op->LinearAssembleSingle) {
496     // Backend version
497     CeedCall(op->LinearAssembleSingle(op, offset, values));
498     return CEED_ERROR_SUCCESS;
499   } else {
500     // Operator fallback
501     CeedOperator op_fallback;
502 
503     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
504     if (op_fallback) {
505       CeedCall(CeedSingleOperatorAssemble(op_fallback, offset, values));
506       return CEED_ERROR_SUCCESS;
507     }
508   }
509 
510   // Assemble QFunction
511   CeedInt             layout_qf[3];
512   const CeedScalar   *assembled_qf_array;
513   CeedVector          assembled_qf        = NULL;
514   CeedElemRestriction assembled_elem_rstr = NULL;
515 
516   CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled_qf, &assembled_elem_rstr, CEED_REQUEST_IMMEDIATE));
517   CeedCall(CeedElemRestrictionGetELayout(assembled_elem_rstr, layout_qf));
518   CeedCall(CeedElemRestrictionDestroy(&assembled_elem_rstr));
519   CeedCall(CeedVectorGetArrayRead(assembled_qf, CEED_MEM_HOST, &assembled_qf_array));
520 
521   // Get assembly data
522   CeedInt                  num_elem_in, elem_size_in, num_comp_in, num_qpts_in;
523   CeedInt                  num_elem_out, elem_size_out, num_comp_out, num_qpts_out, local_num_entries;
524   const CeedEvalMode     **eval_modes_in, **eval_modes_out;
525   CeedInt                  num_active_bases_in, *num_eval_modes_in, num_active_bases_out, *num_eval_modes_out;
526   CeedBasis               *active_bases_in, *active_bases_out, basis_in, basis_out;
527   const CeedScalar       **B_mats_in, **B_mats_out, *B_mat_in, *B_mat_out;
528   CeedElemRestriction      elem_rstr_in, elem_rstr_out;
529   CeedRestrictionType      elem_rstr_type_in, elem_rstr_type_out;
530   const bool              *elem_rstr_orients_in = NULL, *elem_rstr_orients_out = NULL;
531   const CeedInt8          *elem_rstr_curl_orients_in = NULL, *elem_rstr_curl_orients_out = NULL;
532   CeedOperatorAssemblyData data;
533 
534   CeedCall(CeedOperatorGetOperatorAssemblyData(op, &data));
535   CeedCall(CeedOperatorAssemblyDataGetEvalModes(data, &num_active_bases_in, &num_eval_modes_in, &eval_modes_in, NULL, &num_active_bases_out,
536                                                 &num_eval_modes_out, &eval_modes_out, NULL, NULL));
537 
538   CeedCheck(num_active_bases_in == num_active_bases_out && num_active_bases_in == 1, ceed, CEED_ERROR_UNSUPPORTED,
539             "Cannot assemble operator with multiple active bases");
540   CeedCheck(num_eval_modes_in[0] > 0 && num_eval_modes_out[0] > 0, ceed, CEED_ERROR_UNSUPPORTED, "Cannot assemble operator without inputs/outputs");
541 
542   CeedCall(CeedOperatorAssemblyDataGetBases(data, NULL, &active_bases_in, &B_mats_in, NULL, &active_bases_out, &B_mats_out));
543   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &elem_rstr_in, &elem_rstr_out));
544   basis_in  = active_bases_in[0];
545   basis_out = active_bases_out[0];
546   B_mat_in  = B_mats_in[0];
547   B_mat_out = B_mats_out[0];
548 
549   CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_in, &num_elem_in));
550   CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_in, &elem_size_in));
551   CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_in, &num_comp_in));
552   if (basis_in == CEED_BASIS_NONE) num_qpts_in = elem_size_in;
553   else CeedCall(CeedBasisGetNumQuadraturePoints(basis_in, &num_qpts_in));
554 
555   CeedCall(CeedElemRestrictionGetType(elem_rstr_in, &elem_rstr_type_in));
556   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
557     CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_orients_in));
558   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
559     CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_in, CEED_MEM_HOST, &elem_rstr_curl_orients_in));
560   }
561 
562   if (elem_rstr_in != elem_rstr_out) {
563     CeedCall(CeedElemRestrictionGetNumElements(elem_rstr_out, &num_elem_out));
564     CeedCheck(num_elem_in == num_elem_out, ceed, CEED_ERROR_UNSUPPORTED,
565               "Active input and output operator restrictions must have the same number of elements");
566     CeedCall(CeedElemRestrictionGetElementSize(elem_rstr_out, &elem_size_out));
567     CeedCall(CeedElemRestrictionGetNumComponents(elem_rstr_out, &num_comp_out));
568     if (basis_out == CEED_BASIS_NONE) num_qpts_out = elem_size_out;
569     else CeedCall(CeedBasisGetNumQuadraturePoints(basis_out, &num_qpts_out));
570     CeedCheck(num_qpts_in == num_qpts_out, ceed, CEED_ERROR_UNSUPPORTED,
571               "Active input and output bases must have the same number of quadrature points");
572 
573     CeedCall(CeedElemRestrictionGetType(elem_rstr_out, &elem_rstr_type_out));
574     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
575       CeedCall(CeedElemRestrictionGetOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_orients_out));
576     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
577       CeedCall(CeedElemRestrictionGetCurlOrientations(elem_rstr_out, CEED_MEM_HOST, &elem_rstr_curl_orients_out));
578     }
579   } else {
580     num_elem_out  = num_elem_in;
581     elem_size_out = elem_size_in;
582     num_comp_out  = num_comp_in;
583     num_qpts_out  = num_qpts_in;
584 
585     elem_rstr_orients_out      = elem_rstr_orients_in;
586     elem_rstr_curl_orients_out = elem_rstr_curl_orients_in;
587   }
588   local_num_entries = elem_size_out * num_comp_out * elem_size_in * num_comp_in * num_elem_in;
589 
590   // Loop over elements and put in data structure
591   // We store B_mat_in, B_mat_out, BTD, elem_mat in row-major order
592   CeedTensorContract contract;
593   CeedSize           count = 0;
594   CeedScalar        *vals, *BTD_mat = NULL, *elem_mat = NULL, *elem_mat_b = NULL;
595 
596   CeedCall(CeedBasisGetTensorContract(basis_in, &contract));
597   CeedCall(CeedCalloc(elem_size_out * num_qpts_in * num_eval_modes_in[0], &BTD_mat));
598   CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat));
599   if (elem_rstr_curl_orients_in || elem_rstr_curl_orients_out) CeedCall(CeedCalloc(elem_size_out * elem_size_in, &elem_mat_b));
600 
601   CeedCall(CeedVectorGetArray(values, CEED_MEM_HOST, &vals));
602   for (CeedSize e = 0; e < num_elem_in; e++) {
603     for (CeedInt comp_in = 0; comp_in < num_comp_in; comp_in++) {
604       for (CeedInt comp_out = 0; comp_out < num_comp_out; comp_out++) {
605         // Compute B^T*D
606         for (CeedSize n = 0; n < elem_size_out; n++) {
607           for (CeedSize q = 0; q < num_qpts_in; q++) {
608             for (CeedInt e_in = 0; e_in < num_eval_modes_in[0]; e_in++) {
609               const CeedSize btd_index = n * (num_qpts_in * num_eval_modes_in[0]) + q * num_eval_modes_in[0] + e_in;
610               CeedScalar     sum       = 0.0;
611 
612               for (CeedInt e_out = 0; e_out < num_eval_modes_out[0]; e_out++) {
613                 const CeedSize b_out_index     = (q * num_eval_modes_out[0] + e_out) * elem_size_out + n;
614                 const CeedSize eval_mode_index = ((e_in * num_comp_in + comp_in) * num_eval_modes_out[0] + e_out) * num_comp_out + comp_out;
615                 const CeedSize qf_index        = q * layout_qf[0] + eval_mode_index * layout_qf[1] + e * layout_qf[2];
616 
617                 sum += B_mat_out[b_out_index] * assembled_qf_array[qf_index];
618               }
619               BTD_mat[btd_index] = sum;
620             }
621           }
622         }
623 
624         // Form element matrix itself (for each block component)
625         if (contract) {
626           CeedCall(CeedTensorContractApply(contract, 1, num_qpts_in * num_eval_modes_in[0], elem_size_in, elem_size_out, BTD_mat, CEED_NOTRANSPOSE,
627                                            false, B_mat_in, elem_mat));
628         } else {
629           CeedCall(CeedMatrixMatrixMultiply(ceed, BTD_mat, B_mat_in, elem_mat, elem_size_out, elem_size_in, num_qpts_in * num_eval_modes_in[0]));
630         }
631 
632         // Transform the element matrix if required
633         if (elem_rstr_orients_out) {
634           const bool *elem_orients = &elem_rstr_orients_out[e * elem_size_out];
635 
636           for (CeedInt i = 0; i < elem_size_out; i++) {
637             const double orient = elem_orients[i] ? -1.0 : 1.0;
638 
639             for (CeedInt j = 0; j < elem_size_in; j++) {
640               elem_mat[i * elem_size_in + j] *= orient;
641             }
642           }
643         } else if (elem_rstr_curl_orients_out) {
644           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_out[e * 3 * elem_size_out];
645 
646           // T^T*(B^T*D*B)
647           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
648           for (CeedInt i = 0; i < elem_size_out; i++) {
649             for (CeedInt j = 0; j < elem_size_in; j++) {
650               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * i + 1] +
651                                                (i > 0 ? elem_mat_b[(i - 1) * elem_size_in + j] * elem_curl_orients[3 * i - 1] : 0.0) +
652                                                (i < elem_size_out - 1 ? elem_mat_b[(i + 1) * elem_size_in + j] * elem_curl_orients[3 * i + 3] : 0.0);
653             }
654           }
655         }
656         if (elem_rstr_orients_in) {
657           const bool *elem_orients = &elem_rstr_orients_in[e * elem_size_in];
658 
659           for (CeedInt i = 0; i < elem_size_out; i++) {
660             for (CeedInt j = 0; j < elem_size_in; j++) {
661               elem_mat[i * elem_size_in + j] *= elem_orients[j] ? -1.0 : 1.0;
662             }
663           }
664         } else if (elem_rstr_curl_orients_in) {
665           const CeedInt8 *elem_curl_orients = &elem_rstr_curl_orients_in[e * 3 * elem_size_in];
666 
667           // (B^T*D*B)*T
668           memcpy(elem_mat_b, elem_mat, elem_size_out * elem_size_in * sizeof(CeedScalar));
669           for (CeedInt i = 0; i < elem_size_out; i++) {
670             for (CeedInt j = 0; j < elem_size_in; j++) {
671               elem_mat[i * elem_size_in + j] = elem_mat_b[i * elem_size_in + j] * elem_curl_orients[3 * j + 1] +
672                                                (j > 0 ? elem_mat_b[i * elem_size_in + j - 1] * elem_curl_orients[3 * j - 1] : 0.0) +
673                                                (j < elem_size_in - 1 ? elem_mat_b[i * elem_size_in + j + 1] * elem_curl_orients[3 * j + 3] : 0.0);
674             }
675           }
676         }
677 
678         // Put element matrix in coordinate data structure
679         for (CeedInt i = 0; i < elem_size_out; i++) {
680           for (CeedInt j = 0; j < elem_size_in; j++) {
681             vals[offset + count] = elem_mat[i * elem_size_in + j];
682             count++;
683           }
684         }
685       }
686     }
687   }
688   CeedCheck(count == local_num_entries, ceed, CEED_ERROR_MAJOR, "Error computing entries");
689   CeedCall(CeedVectorRestoreArray(values, &vals));
690 
691   // Cleanup
692   CeedCall(CeedFree(&BTD_mat));
693   CeedCall(CeedFree(&elem_mat));
694   CeedCall(CeedFree(&elem_mat_b));
695   if (elem_rstr_type_in == CEED_RESTRICTION_ORIENTED) {
696     CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_in, &elem_rstr_orients_in));
697   } else if (elem_rstr_type_in == CEED_RESTRICTION_CURL_ORIENTED) {
698     CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_in, &elem_rstr_curl_orients_in));
699   }
700   if (elem_rstr_in != elem_rstr_out) {
701     if (elem_rstr_type_out == CEED_RESTRICTION_ORIENTED) {
702       CeedCall(CeedElemRestrictionRestoreOrientations(elem_rstr_out, &elem_rstr_orients_out));
703     } else if (elem_rstr_type_out == CEED_RESTRICTION_CURL_ORIENTED) {
704       CeedCall(CeedElemRestrictionRestoreCurlOrientations(elem_rstr_out, &elem_rstr_curl_orients_out));
705     }
706   }
707   CeedCall(CeedVectorRestoreArrayRead(assembled_qf, &assembled_qf_array));
708   CeedCall(CeedVectorDestroy(&assembled_qf));
709   return CEED_ERROR_SUCCESS;
710 }
711 
712 /**
713   @brief Count number of entries for assembled `CeedOperator`
714 
715   @param[in]  op          `CeedOperator` to assemble
716   @param[out] num_entries Number of entries in assembled representation
717 
718   @return An error code: 0 - success, otherwise - failure
719 
720   @ref Utility
721 **/
722 static int CeedSingleOperatorAssemblyCountEntries(CeedOperator op, CeedSize *num_entries) {
723   bool                is_composite;
724   CeedInt             num_elem_in, elem_size_in, num_comp_in, num_elem_out, elem_size_out, num_comp_out;
725   CeedElemRestriction rstr_in, rstr_out;
726 
727   CeedCall(CeedOperatorIsComposite(op, &is_composite));
728   CeedCheck(!is_composite, op->ceed, CEED_ERROR_UNSUPPORTED, "Composite operator not supported");
729 
730   CeedCall(CeedOperatorGetActiveElemRestrictions(op, &rstr_in, &rstr_out));
731   CeedCall(CeedElemRestrictionGetNumElements(rstr_in, &num_elem_in));
732   CeedCall(CeedElemRestrictionGetElementSize(rstr_in, &elem_size_in));
733   CeedCall(CeedElemRestrictionGetNumComponents(rstr_in, &num_comp_in));
734   if (rstr_in != rstr_out) {
735     CeedCall(CeedElemRestrictionGetNumElements(rstr_out, &num_elem_out));
736     CeedCheck(num_elem_in == num_elem_out, op->ceed, CEED_ERROR_UNSUPPORTED,
737               "Active input and output operator restrictions must have the same number of elements");
738     CeedCall(CeedElemRestrictionGetElementSize(rstr_out, &elem_size_out));
739     CeedCall(CeedElemRestrictionGetNumComponents(rstr_out, &num_comp_out));
740   } else {
741     num_elem_out  = num_elem_in;
742     elem_size_out = elem_size_in;
743     num_comp_out  = num_comp_in;
744   }
745   *num_entries = (CeedSize)elem_size_in * num_comp_in * elem_size_out * num_comp_out * num_elem_in;
746   return CEED_ERROR_SUCCESS;
747 }
748 
749 /**
750   @brief Common code for creating a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`
751 
752   @param[in]  op_fine      Fine grid `CeedOperator`
753   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
754   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
755   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
756   @param[in]  basis_c_to_f `CeedBasis` for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction operators
757   @param[out] op_coarse    Coarse grid `CeedOperator`
758   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
759   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
760 
761   @return An error code: 0 - success, otherwise - failure
762 
763   @ref Developer
764 **/
765 static int CeedSingleOperatorMultigridLevel(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
766                                             CeedBasis basis_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
767   bool                is_composite;
768   Ceed                ceed;
769   CeedInt             num_comp;
770   CeedVector          mult_vec         = NULL;
771   CeedElemRestriction rstr_p_mult_fine = NULL, rstr_fine = NULL;
772 
773   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
774 
775   // Check for composite operator
776   CeedCall(CeedOperatorIsComposite(op_fine, &is_composite));
777   CeedCheck(!is_composite, ceed, CEED_ERROR_UNSUPPORTED, "Automatic multigrid setup for composite operators not supported");
778 
779   // Coarse Grid
780   CeedCall(CeedOperatorCreate(ceed, op_fine->qf, op_fine->dqf, op_fine->dqfT, op_coarse));
781   // -- Clone input fields
782   for (CeedInt i = 0; i < op_fine->qf->num_input_fields; i++) {
783     if (op_fine->input_fields[i]->vec == CEED_VECTOR_ACTIVE) {
784       rstr_fine = op_fine->input_fields[i]->elem_rstr;
785       CeedCall(CeedOperatorSetField(*op_coarse, op_fine->input_fields[i]->field_name, rstr_coarse, basis_coarse, CEED_VECTOR_ACTIVE));
786     } else {
787       CeedCall(CeedOperatorSetField(*op_coarse, op_fine->input_fields[i]->field_name, op_fine->input_fields[i]->elem_rstr,
788                                     op_fine->input_fields[i]->basis, op_fine->input_fields[i]->vec));
789     }
790   }
791   // -- Clone output fields
792   for (CeedInt i = 0; i < op_fine->qf->num_output_fields; i++) {
793     if (op_fine->output_fields[i]->vec == CEED_VECTOR_ACTIVE) {
794       CeedCall(CeedOperatorSetField(*op_coarse, op_fine->output_fields[i]->field_name, rstr_coarse, basis_coarse, CEED_VECTOR_ACTIVE));
795     } else {
796       CeedCall(CeedOperatorSetField(*op_coarse, op_fine->output_fields[i]->field_name, op_fine->output_fields[i]->elem_rstr,
797                                     op_fine->output_fields[i]->basis, op_fine->output_fields[i]->vec));
798     }
799   }
800   // -- Clone QFunctionAssemblyData
801   CeedCall(CeedQFunctionAssemblyDataReferenceCopy(op_fine->qf_assembled, &(*op_coarse)->qf_assembled));
802 
803   // Multiplicity vector
804   if (op_restrict || op_prolong) {
805     CeedVector          mult_e_vec;
806     CeedRestrictionType rstr_type;
807 
808     CeedCall(CeedElemRestrictionGetType(rstr_fine, &rstr_type));
809     CeedCheck(rstr_type != CEED_RESTRICTION_CURL_ORIENTED, ceed, CEED_ERROR_UNSUPPORTED,
810               "Element restrictions created with CeedElemRestrictionCreateCurlOriented are not supported");
811     CeedCheck(p_mult_fine, ceed, CEED_ERROR_INCOMPATIBLE, "Prolongation or restriction operator creation requires fine grid multiplicity vector");
812     CeedCall(CeedElemRestrictionCreateUnsignedCopy(rstr_fine, &rstr_p_mult_fine));
813     CeedCall(CeedElemRestrictionCreateVector(rstr_fine, &mult_vec, &mult_e_vec));
814     CeedCall(CeedVectorSetValue(mult_e_vec, 0.0));
815     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_NOTRANSPOSE, p_mult_fine, mult_e_vec, CEED_REQUEST_IMMEDIATE));
816     CeedCall(CeedVectorSetValue(mult_vec, 0.0));
817     CeedCall(CeedElemRestrictionApply(rstr_p_mult_fine, CEED_TRANSPOSE, mult_e_vec, mult_vec, CEED_REQUEST_IMMEDIATE));
818     CeedCall(CeedVectorDestroy(&mult_e_vec));
819     CeedCall(CeedVectorReciprocal(mult_vec));
820   }
821 
822   // Clone name
823   bool   has_name = op_fine->name;
824   size_t name_len = op_fine->name ? strlen(op_fine->name) : 0;
825   CeedCall(CeedOperatorSetName(*op_coarse, op_fine->name));
826 
827   // Check that coarse to fine basis is provided if prolong/restrict operators are requested
828   CeedCheck(basis_c_to_f || (!op_restrict && !op_prolong), ceed, CEED_ERROR_INCOMPATIBLE,
829             "Prolongation or restriction operator creation requires coarse-to-fine basis");
830 
831   // Restriction/Prolongation Operators
832   CeedCall(CeedBasisGetNumComponents(basis_coarse, &num_comp));
833 
834   // Restriction
835   if (op_restrict) {
836     CeedInt             *num_comp_r_data;
837     CeedQFunctionContext ctx_r;
838     CeedQFunction        qf_restrict;
839 
840     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_restrict));
841     CeedCall(CeedCalloc(1, &num_comp_r_data));
842     num_comp_r_data[0] = num_comp;
843     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_r));
844     CeedCall(CeedQFunctionContextSetData(ctx_r, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_r_data), num_comp_r_data));
845     CeedCall(CeedQFunctionSetContext(qf_restrict, ctx_r));
846     CeedCall(CeedQFunctionContextDestroy(&ctx_r));
847     CeedCall(CeedQFunctionAddInput(qf_restrict, "input", num_comp, CEED_EVAL_NONE));
848     CeedCall(CeedQFunctionAddInput(qf_restrict, "scale", num_comp, CEED_EVAL_NONE));
849     CeedCall(CeedQFunctionAddOutput(qf_restrict, "output", num_comp, CEED_EVAL_INTERP));
850     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_restrict, num_comp));
851 
852     CeedCall(CeedOperatorCreate(ceed, qf_restrict, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_restrict));
853     CeedCall(CeedOperatorSetField(*op_restrict, "input", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
854     CeedCall(CeedOperatorSetField(*op_restrict, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
855     CeedCall(CeedOperatorSetField(*op_restrict, "output", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
856 
857     // Set name
858     char *restriction_name;
859 
860     CeedCall(CeedCalloc(17 + name_len, &restriction_name));
861     sprintf(restriction_name, "restriction%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
862     CeedCall(CeedOperatorSetName(*op_restrict, restriction_name));
863     CeedCall(CeedFree(&restriction_name));
864 
865     // Check
866     CeedCall(CeedOperatorCheckReady(*op_restrict));
867 
868     // Cleanup
869     CeedCall(CeedQFunctionDestroy(&qf_restrict));
870   }
871 
872   // Prolongation
873   if (op_prolong) {
874     CeedInt             *num_comp_p_data;
875     CeedQFunctionContext ctx_p;
876     CeedQFunction        qf_prolong;
877 
878     CeedCall(CeedQFunctionCreateInteriorByName(ceed, "Scale", &qf_prolong));
879     CeedCall(CeedCalloc(1, &num_comp_p_data));
880     num_comp_p_data[0] = num_comp;
881     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_p));
882     CeedCall(CeedQFunctionContextSetData(ctx_p, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_p_data), num_comp_p_data));
883     CeedCall(CeedQFunctionSetContext(qf_prolong, ctx_p));
884     CeedCall(CeedQFunctionContextDestroy(&ctx_p));
885     CeedCall(CeedQFunctionAddInput(qf_prolong, "input", num_comp, CEED_EVAL_INTERP));
886     CeedCall(CeedQFunctionAddInput(qf_prolong, "scale", num_comp, CEED_EVAL_NONE));
887     CeedCall(CeedQFunctionAddOutput(qf_prolong, "output", num_comp, CEED_EVAL_NONE));
888     CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_prolong, num_comp));
889 
890     CeedCall(CeedOperatorCreate(ceed, qf_prolong, CEED_QFUNCTION_NONE, CEED_QFUNCTION_NONE, op_prolong));
891     CeedCall(CeedOperatorSetField(*op_prolong, "input", rstr_coarse, basis_c_to_f, CEED_VECTOR_ACTIVE));
892     CeedCall(CeedOperatorSetField(*op_prolong, "scale", rstr_p_mult_fine, CEED_BASIS_NONE, mult_vec));
893     CeedCall(CeedOperatorSetField(*op_prolong, "output", rstr_fine, CEED_BASIS_NONE, CEED_VECTOR_ACTIVE));
894 
895     // Set name
896     char *prolongation_name;
897 
898     CeedCall(CeedCalloc(18 + name_len, &prolongation_name));
899     sprintf(prolongation_name, "prolongation%s%s", has_name ? " for " : "", has_name ? op_fine->name : "");
900     CeedCall(CeedOperatorSetName(*op_prolong, prolongation_name));
901     CeedCall(CeedFree(&prolongation_name));
902 
903     // Check
904     CeedCall(CeedOperatorCheckReady(*op_prolong));
905 
906     // Cleanup
907     CeedCall(CeedQFunctionDestroy(&qf_prolong));
908   }
909 
910   // Check
911   CeedCall(CeedOperatorCheckReady(*op_coarse));
912 
913   // Cleanup
914   CeedCall(CeedVectorDestroy(&mult_vec));
915   CeedCall(CeedElemRestrictionDestroy(&rstr_p_mult_fine));
916   CeedCall(CeedBasisDestroy(&basis_c_to_f));
917   return CEED_ERROR_SUCCESS;
918 }
919 
920 /**
921   @brief Build 1D mass matrix and Laplacian with perturbation
922 
923   @param[in]  interp_1d   Interpolation matrix in one dimension
924   @param[in]  grad_1d     Gradient matrix in one dimension
925   @param[in]  q_weight_1d Quadrature weights in one dimension
926   @param[in]  P_1d        Number of basis nodes in one dimension
927   @param[in]  Q_1d        Number of quadrature points in one dimension
928   @param[in]  dim         Dimension of basis
929   @param[out] mass        Assembled mass matrix in one dimension
930   @param[out] laplace     Assembled perturbed Laplacian in one dimension
931 
932   @return An error code: 0 - success, otherwise - failure
933 
934   @ref Developer
935 **/
936 CeedPragmaOptimizeOff
937 static int CeedBuildMassLaplace(const CeedScalar *interp_1d, const CeedScalar *grad_1d, const CeedScalar *q_weight_1d, CeedInt P_1d, CeedInt Q_1d,
938                                 CeedInt dim, CeedScalar *mass, CeedScalar *laplace) {
939   for (CeedInt i = 0; i < P_1d; i++) {
940     for (CeedInt j = 0; j < P_1d; j++) {
941       CeedScalar sum = 0.0;
942       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];
943       mass[i + j * P_1d] = sum;
944     }
945   }
946   // -- Laplacian
947   for (CeedInt i = 0; i < P_1d; i++) {
948     for (CeedInt j = 0; j < P_1d; j++) {
949       CeedScalar sum = 0.0;
950 
951       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];
952       laplace[i + j * P_1d] = sum;
953     }
954   }
955   CeedScalar perturbation = dim > 2 ? 1e-6 : 1e-4;
956   for (CeedInt i = 0; i < P_1d; i++) laplace[i + P_1d * i] += perturbation;
957   return CEED_ERROR_SUCCESS;
958 }
959 CeedPragmaOptimizeOn
960 
961 /// @}
962 
963 /// ----------------------------------------------------------------------------
964 /// CeedOperator Backend API
965 /// ----------------------------------------------------------------------------
966 /// @addtogroup CeedOperatorBackend
967 /// @{
968 
969 /**
970   @brief Select correct basis matrix pointer based on @ref CeedEvalMode
971 
972   @param[in]  basis     `CeedBasis` from which to get the basis matrix
973   @param[in]  eval_mode Current basis evaluation mode
974   @param[in]  identity  Pointer to identity matrix
975   @param[out] basis_ptr `CeedBasis` pointer to set
976 
977   @ref Backend
978 **/
979 int CeedOperatorGetBasisPointer(CeedBasis basis, CeedEvalMode eval_mode, const CeedScalar *identity, const CeedScalar **basis_ptr) {
980   switch (eval_mode) {
981     case CEED_EVAL_NONE:
982       *basis_ptr = identity;
983       break;
984     case CEED_EVAL_INTERP:
985       CeedCall(CeedBasisGetInterp(basis, basis_ptr));
986       break;
987     case CEED_EVAL_GRAD:
988       CeedCall(CeedBasisGetGrad(basis, basis_ptr));
989       break;
990     case CEED_EVAL_DIV:
991       CeedCall(CeedBasisGetDiv(basis, basis_ptr));
992       break;
993     case CEED_EVAL_CURL:
994       CeedCall(CeedBasisGetCurl(basis, basis_ptr));
995       break;
996     case CEED_EVAL_WEIGHT:
997       break;  // Caught by QF Assembly
998   }
999   assert(*basis_ptr != NULL);
1000   return CEED_ERROR_SUCCESS;
1001 }
1002 
1003 /**
1004   @brief Create point block restriction for active `CeedOperatorField`
1005 
1006   @param[in]  rstr             Original `CeedElemRestriction` for active field
1007   @param[out] point_block_rstr Address of the variable where the newly created `CeedElemRestriction` will be stored
1008 
1009   @return An error code: 0 - success, otherwise - failure
1010 
1011   @ref Backend
1012 **/
1013 int CeedOperatorCreateActivePointBlockRestriction(CeedElemRestriction rstr, CeedElemRestriction *point_block_rstr) {
1014   Ceed           ceed;
1015   CeedInt        num_elem, num_comp, shift, elem_size, comp_stride, *point_block_offsets;
1016   CeedSize       l_size;
1017   const CeedInt *offsets;
1018 
1019   CeedCall(CeedElemRestrictionGetCeed(rstr, &ceed));
1020   CeedCall(CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets));
1021 
1022   // Expand offsets
1023   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
1024   CeedCall(CeedElemRestrictionGetNumComponents(rstr, &num_comp));
1025   CeedCall(CeedElemRestrictionGetElementSize(rstr, &elem_size));
1026   CeedCall(CeedElemRestrictionGetCompStride(rstr, &comp_stride));
1027   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
1028   shift = num_comp;
1029   if (comp_stride != 1) shift *= num_comp;
1030   CeedCall(CeedCalloc(num_elem * elem_size, &point_block_offsets));
1031   for (CeedInt i = 0; i < num_elem * elem_size; i++) {
1032     point_block_offsets[i] = offsets[i] * shift;
1033   }
1034 
1035   // Create new restriction
1036   CeedCall(CeedElemRestrictionCreate(ceed, num_elem, elem_size, num_comp * num_comp, 1, l_size * num_comp, CEED_MEM_HOST, CEED_OWN_POINTER,
1037                                      point_block_offsets, point_block_rstr));
1038 
1039   // Cleanup
1040   CeedCall(CeedElemRestrictionRestoreOffsets(rstr, &offsets));
1041   return CEED_ERROR_SUCCESS;
1042 }
1043 
1044 /**
1045   @brief Create object holding `CeedQFunction` assembly data for `CeedOperator`
1046 
1047   @param[in]  ceed `Ceed` object used to create the `CeedQFunctionAssemblyData`
1048   @param[out] data Address of the variable where the newly created `CeedQFunctionAssemblyData` will be stored
1049 
1050   @return An error code: 0 - success, otherwise - failure
1051 
1052   @ref Backend
1053 **/
1054 int CeedQFunctionAssemblyDataCreate(Ceed ceed, CeedQFunctionAssemblyData *data) {
1055   CeedCall(CeedCalloc(1, data));
1056   (*data)->ref_count = 1;
1057   (*data)->ceed      = ceed;
1058   CeedCall(CeedReference(ceed));
1059   return CEED_ERROR_SUCCESS;
1060 }
1061 
1062 /**
1063   @brief Increment the reference counter for a `CeedQFunctionAssemblyData`
1064 
1065   @param[in,out] data `CeedQFunctionAssemblyData` to increment the reference counter
1066 
1067   @return An error code: 0 - success, otherwise - failure
1068 
1069   @ref Backend
1070 **/
1071 int CeedQFunctionAssemblyDataReference(CeedQFunctionAssemblyData data) {
1072   data->ref_count++;
1073   return CEED_ERROR_SUCCESS;
1074 }
1075 
1076 /**
1077   @brief Set re-use of `CeedQFunctionAssemblyData`
1078 
1079   @param[in,out] data       `CeedQFunctionAssemblyData` to mark for reuse
1080   @param[in]     reuse_data Boolean flag indicating data re-use
1081 
1082   @return An error code: 0 - success, otherwise - failure
1083 
1084   @ref Backend
1085 **/
1086 int CeedQFunctionAssemblyDataSetReuse(CeedQFunctionAssemblyData data, bool reuse_data) {
1087   data->reuse_data        = reuse_data;
1088   data->needs_data_update = true;
1089   return CEED_ERROR_SUCCESS;
1090 }
1091 
1092 /**
1093   @brief Mark `CeedQFunctionAssemblyData` as stale
1094 
1095   @param[in,out] data              `CeedQFunctionAssemblyData` to mark as stale
1096   @param[in]     needs_data_update Boolean flag indicating if update is needed or completed
1097 
1098   @return An error code: 0 - success, otherwise - failure
1099 
1100   @ref Backend
1101 **/
1102 int CeedQFunctionAssemblyDataSetUpdateNeeded(CeedQFunctionAssemblyData data, bool needs_data_update) {
1103   data->needs_data_update = needs_data_update;
1104   return CEED_ERROR_SUCCESS;
1105 }
1106 
1107 /**
1108   @brief Determine if `CeedQFunctionAssemblyData` needs update
1109 
1110   @param[in]  data             `CeedQFunctionAssemblyData` to mark as stale
1111   @param[out] is_update_needed Boolean flag indicating if re-assembly is required
1112 
1113   @return An error code: 0 - success, otherwise - failure
1114 
1115   @ref Backend
1116 **/
1117 int CeedQFunctionAssemblyDataIsUpdateNeeded(CeedQFunctionAssemblyData data, bool *is_update_needed) {
1118   *is_update_needed = !data->reuse_data || data->needs_data_update;
1119   return CEED_ERROR_SUCCESS;
1120 }
1121 
1122 /**
1123   @brief Copy the pointer to a `CeedQFunctionAssemblyData`.
1124 
1125   Both pointers should be destroyed with @ref CeedQFunctionAssemblyDataDestroy().
1126 
1127   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`.
1128         This `CeedQFunctionAssemblyData` will be destroyed if ` *data_copy` is the only reference to this `CeedQFunctionAssemblyData`.
1129 
1130   @param[in]     data      `CeedQFunctionAssemblyData` to copy reference to
1131   @param[in,out] data_copy Variable to store copied reference
1132 
1133   @return An error code: 0 - success, otherwise - failure
1134 
1135   @ref Backend
1136 **/
1137 int CeedQFunctionAssemblyDataReferenceCopy(CeedQFunctionAssemblyData data, CeedQFunctionAssemblyData *data_copy) {
1138   CeedCall(CeedQFunctionAssemblyDataReference(data));
1139   CeedCall(CeedQFunctionAssemblyDataDestroy(data_copy));
1140   *data_copy = data;
1141   return CEED_ERROR_SUCCESS;
1142 }
1143 
1144 /**
1145   @brief Get setup status for internal objects for `CeedQFunctionAssemblyData`
1146 
1147   @param[in]  data     `CeedQFunctionAssemblyData` to retrieve status
1148   @param[out] is_setup Boolean flag for setup status
1149 
1150   @return An error code: 0 - success, otherwise - failure
1151 
1152   @ref Backend
1153 **/
1154 int CeedQFunctionAssemblyDataIsSetup(CeedQFunctionAssemblyData data, bool *is_setup) {
1155   *is_setup = data->is_setup;
1156   return CEED_ERROR_SUCCESS;
1157 }
1158 
1159 /**
1160   @brief Set internal objects for `CeedQFunctionAssemblyData`
1161 
1162   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1163   @param[in]     vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1164   @param[in]     rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1165 
1166   @return An error code: 0 - success, otherwise - failure
1167 
1168   @ref Backend
1169 **/
1170 int CeedQFunctionAssemblyDataSetObjects(CeedQFunctionAssemblyData data, CeedVector vec, CeedElemRestriction rstr) {
1171   CeedCall(CeedVectorReferenceCopy(vec, &data->vec));
1172   CeedCall(CeedElemRestrictionReferenceCopy(rstr, &data->rstr));
1173 
1174   data->is_setup = true;
1175   return CEED_ERROR_SUCCESS;
1176 }
1177 
1178 /**
1179   @brief Get internal objects for `CeedQFunctionAssemblyData`
1180 
1181   @param[in,out] data `CeedQFunctionAssemblyData` to set objects
1182   @param[out]    vec  `CeedVector` to store assembled `CeedQFunction` at quadrature points
1183   @param[out]    rstr `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1184 
1185   @return An error code: 0 - success, otherwise - failure
1186 
1187   @ref Backend
1188 **/
1189 int CeedQFunctionAssemblyDataGetObjects(CeedQFunctionAssemblyData data, CeedVector *vec, CeedElemRestriction *rstr) {
1190   CeedCheck(data->is_setup, data->ceed, CEED_ERROR_INCOMPLETE, "Internal objects not set; must call CeedQFunctionAssemblyDataSetObjects first.");
1191 
1192   CeedCall(CeedVectorReferenceCopy(data->vec, vec));
1193   CeedCall(CeedElemRestrictionReferenceCopy(data->rstr, rstr));
1194   return CEED_ERROR_SUCCESS;
1195 }
1196 
1197 /**
1198   @brief Destroy `CeedQFunctionAssemblyData`
1199 
1200   @param[in,out] data  `CeedQFunctionAssemblyData` to destroy
1201 
1202   @return An error code: 0 - success, otherwise - failure
1203 
1204   @ref Backend
1205 **/
1206 int CeedQFunctionAssemblyDataDestroy(CeedQFunctionAssemblyData *data) {
1207   if (!*data || --(*data)->ref_count > 0) {
1208     *data = NULL;
1209     return CEED_ERROR_SUCCESS;
1210   }
1211   CeedCall(CeedDestroy(&(*data)->ceed));
1212   CeedCall(CeedVectorDestroy(&(*data)->vec));
1213   CeedCall(CeedElemRestrictionDestroy(&(*data)->rstr));
1214 
1215   CeedCall(CeedFree(data));
1216   return CEED_ERROR_SUCCESS;
1217 }
1218 
1219 /**
1220   @brief Get `CeedOperatorAssemblyData`
1221 
1222   @param[in]  op   `CeedOperator` to assemble
1223   @param[out] data `CeedQFunctionAssemblyData`
1224 
1225   @return An error code: 0 - success, otherwise - failure
1226 
1227   @ref Backend
1228 **/
1229 int CeedOperatorGetOperatorAssemblyData(CeedOperator op, CeedOperatorAssemblyData *data) {
1230   if (!op->op_assembled) {
1231     CeedOperatorAssemblyData data;
1232 
1233     CeedCall(CeedOperatorAssemblyDataCreate(op->ceed, op, &data));
1234     op->op_assembled = data;
1235   }
1236   *data = op->op_assembled;
1237   return CEED_ERROR_SUCCESS;
1238 }
1239 
1240 /**
1241   @brief Create object holding `CeedOperator` assembly data.
1242 
1243   The `CeedOperatorAssemblyData` holds an array with references to every active `CeedBasis` used in the `CeedOperator`.
1244   An array with references to the corresponding active `CeedElemRestriction` is also stored.
1245   For each active `CeedBasis, the `CeedOperatorAssemblyData` holds an array of all input and output @ref CeedEvalMode for this `CeedBasis`.
1246   The `CeedOperatorAssemblyData` holds an array of offsets for indexing into the assembled `CeedQFunction` arrays to the row representing each @ref CeedEvalMode.
1247   The number of input columns across all active bases for the assembled `CeedQFunction` is also stored.
1248   Lastly, the `CeedOperatorAssembly` data holds assembled matrices representing the full action of the `CeedBasis` for all @ref CeedEvalMode.
1249 
1250   @param[in]  ceed `Ceed` object used to create the `CeedOperatorAssemblyData`
1251   @param[in]  op   `CeedOperator` to be assembled
1252   @param[out] data Address of the variable where the newly created `CeedOperatorAssemblyData` will be stored
1253 
1254   @return An error code: 0 - success, otherwise - failure
1255 
1256   @ref Backend
1257 **/
1258 int CeedOperatorAssemblyDataCreate(Ceed ceed, CeedOperator op, CeedOperatorAssemblyData *data) {
1259   CeedInt             num_active_bases_in = 0, num_active_bases_out = 0, offset = 0;
1260   CeedInt             num_input_fields, *num_eval_modes_in = NULL, num_output_fields, *num_eval_modes_out = NULL;
1261   CeedSize          **eval_mode_offsets_in = NULL, **eval_mode_offsets_out = NULL;
1262   CeedEvalMode      **eval_modes_in = NULL, **eval_modes_out = NULL;
1263   CeedQFunctionField *qf_fields;
1264   CeedQFunction       qf;
1265   CeedOperatorField  *op_fields;
1266   bool                is_composite;
1267 
1268   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1269   CeedCheck(!is_composite, ceed, CEED_ERROR_INCOMPATIBLE, "Can only create CeedOperator assembly data for non-composite operators.");
1270 
1271   // Allocate
1272   CeedCall(CeedCalloc(1, data));
1273   (*data)->ceed = ceed;
1274   CeedCall(CeedReference(ceed));
1275 
1276   // Build OperatorAssembly data
1277   CeedCall(CeedOperatorGetQFunction(op, &qf));
1278 
1279   // Determine active input basis
1280   CeedCall(CeedQFunctionGetFields(qf, &num_input_fields, &qf_fields, NULL, NULL));
1281   CeedCall(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
1282   for (CeedInt i = 0; i < num_input_fields; i++) {
1283     CeedVector vec;
1284 
1285     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1286     if (vec == CEED_VECTOR_ACTIVE) {
1287       CeedInt      index = -1, num_comp, q_comp;
1288       CeedEvalMode eval_mode;
1289       CeedBasis    basis_in = NULL;
1290 
1291       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_in));
1292       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1293       CeedCall(CeedBasisGetNumComponents(basis_in, &num_comp));
1294       CeedCall(CeedBasisGetNumQuadratureComponents(basis_in, eval_mode, &q_comp));
1295       for (CeedInt i = 0; i < num_active_bases_in; i++) {
1296         if ((*data)->active_bases_in[i] == basis_in) index = i;
1297       }
1298       if (index == -1) {
1299         CeedElemRestriction elem_rstr_in;
1300 
1301         index = num_active_bases_in;
1302         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_bases_in));
1303         (*data)->active_bases_in[num_active_bases_in] = NULL;
1304         CeedCall(CeedBasisReferenceCopy(basis_in, &(*data)->active_bases_in[num_active_bases_in]));
1305         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->active_elem_rstrs_in));
1306         (*data)->active_elem_rstrs_in[num_active_bases_in] = NULL;
1307         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_in));
1308         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_in, &(*data)->active_elem_rstrs_in[num_active_bases_in]));
1309         CeedCall(CeedRealloc(num_active_bases_in + 1, &num_eval_modes_in));
1310         num_eval_modes_in[index] = 0;
1311         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_modes_in));
1312         eval_modes_in[index] = NULL;
1313         CeedCall(CeedRealloc(num_active_bases_in + 1, &eval_mode_offsets_in));
1314         eval_mode_offsets_in[index] = NULL;
1315         CeedCall(CeedRealloc(num_active_bases_in + 1, &(*data)->assembled_bases_in));
1316         (*data)->assembled_bases_in[index] = NULL;
1317         num_active_bases_in++;
1318       }
1319       if (eval_mode != CEED_EVAL_WEIGHT) {
1320         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1321         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_modes_in[index]));
1322         CeedCall(CeedRealloc(num_eval_modes_in[index] + q_comp, &eval_mode_offsets_in[index]));
1323         for (CeedInt d = 0; d < q_comp; d++) {
1324           eval_modes_in[index][num_eval_modes_in[index] + d]        = eval_mode;
1325           eval_mode_offsets_in[index][num_eval_modes_in[index] + d] = offset;
1326           offset += num_comp;
1327         }
1328         num_eval_modes_in[index] += q_comp;
1329       }
1330     }
1331   }
1332 
1333   // Determine active output basis
1334   CeedCall(CeedQFunctionGetFields(qf, NULL, NULL, &num_output_fields, &qf_fields));
1335   CeedCall(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
1336   offset = 0;
1337   for (CeedInt i = 0; i < num_output_fields; i++) {
1338     CeedVector vec;
1339 
1340     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
1341     if (vec == CEED_VECTOR_ACTIVE) {
1342       CeedInt      index = -1, num_comp, q_comp;
1343       CeedEvalMode eval_mode;
1344       CeedBasis    basis_out = NULL;
1345 
1346       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis_out));
1347       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
1348       CeedCall(CeedBasisGetNumComponents(basis_out, &num_comp));
1349       CeedCall(CeedBasisGetNumQuadratureComponents(basis_out, eval_mode, &q_comp));
1350       for (CeedInt i = 0; i < num_active_bases_out; i++) {
1351         if ((*data)->active_bases_out[i] == basis_out) index = i;
1352       }
1353       if (index == -1) {
1354         CeedElemRestriction elem_rstr_out;
1355 
1356         index = num_active_bases_out;
1357         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_bases_out));
1358         (*data)->active_bases_out[num_active_bases_out] = NULL;
1359         CeedCall(CeedBasisReferenceCopy(basis_out, &(*data)->active_bases_out[num_active_bases_out]));
1360         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->active_elem_rstrs_out));
1361         (*data)->active_elem_rstrs_out[num_active_bases_out] = NULL;
1362         CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr_out));
1363         CeedCall(CeedElemRestrictionReferenceCopy(elem_rstr_out, &(*data)->active_elem_rstrs_out[num_active_bases_out]));
1364         CeedCall(CeedRealloc(num_active_bases_out + 1, &num_eval_modes_out));
1365         num_eval_modes_out[index] = 0;
1366         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_modes_out));
1367         eval_modes_out[index] = NULL;
1368         CeedCall(CeedRealloc(num_active_bases_out + 1, &eval_mode_offsets_out));
1369         eval_mode_offsets_out[index] = NULL;
1370         CeedCall(CeedRealloc(num_active_bases_out + 1, &(*data)->assembled_bases_out));
1371         (*data)->assembled_bases_out[index] = NULL;
1372         num_active_bases_out++;
1373       }
1374       if (eval_mode != CEED_EVAL_WEIGHT) {
1375         // q_comp = 1 if CEED_EVAL_NONE, CEED_EVAL_WEIGHT caught by QF Assembly
1376         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_modes_out[index]));
1377         CeedCall(CeedRealloc(num_eval_modes_out[index] + q_comp, &eval_mode_offsets_out[index]));
1378         for (CeedInt d = 0; d < q_comp; d++) {
1379           eval_modes_out[index][num_eval_modes_out[index] + d]        = eval_mode;
1380           eval_mode_offsets_out[index][num_eval_modes_out[index] + d] = offset;
1381           offset += num_comp;
1382         }
1383         num_eval_modes_out[index] += q_comp;
1384       }
1385     }
1386   }
1387   (*data)->num_active_bases_in   = num_active_bases_in;
1388   (*data)->num_eval_modes_in     = num_eval_modes_in;
1389   (*data)->eval_modes_in         = eval_modes_in;
1390   (*data)->eval_mode_offsets_in  = eval_mode_offsets_in;
1391   (*data)->num_active_bases_out  = num_active_bases_out;
1392   (*data)->num_eval_modes_out    = num_eval_modes_out;
1393   (*data)->eval_modes_out        = eval_modes_out;
1394   (*data)->eval_mode_offsets_out = eval_mode_offsets_out;
1395   (*data)->num_output_components = offset;
1396   return CEED_ERROR_SUCCESS;
1397 }
1398 
1399 /**
1400   @brief Get `CeedOperator` @ref CeedEvalMode for assembly.
1401 
1402   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1403 
1404   @param[in]  data                  `CeedOperatorAssemblyData`
1405   @param[out] num_active_bases_in   Total number of active bases for input
1406   @param[out] num_eval_modes_in     Pointer to hold array of numbers of input @ref CeedEvalMode, or `NULL`.
1407                                       `eval_modes_in[0]` holds an array of eval modes for the first active `CeedBasis`.
1408   @param[out] eval_modes_in         Pointer to hold arrays of input @ref CeedEvalMode, or `NULL`
1409   @param[out] eval_mode_offsets_in  Pointer to hold arrays of input offsets at each quadrature point
1410   @param[out] num_active_bases_out  Total number of active bases for output
1411   @param[out] num_eval_modes_out    Pointer to hold array of numbers of output @ref CeedEvalMode, or `NULL`
1412   @param[out] eval_modes_out        Pointer to hold arrays of output @ref CeedEvalMode, or `NULL`
1413   @param[out] eval_mode_offsets_out Pointer to hold arrays of output offsets at each quadrature point
1414   @param[out] num_output_components The number of columns in the assembled `CeedQFunction` matrix for each quadrature point, including contributions of all active bases
1415 
1416   @return An error code: 0 - success, otherwise - failure
1417 
1418   @ref Backend
1419 **/
1420 int CeedOperatorAssemblyDataGetEvalModes(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedInt **num_eval_modes_in,
1421                                          const CeedEvalMode ***eval_modes_in, CeedSize ***eval_mode_offsets_in, CeedInt *num_active_bases_out,
1422                                          CeedInt **num_eval_modes_out, const CeedEvalMode ***eval_modes_out, CeedSize ***eval_mode_offsets_out,
1423                                          CeedSize *num_output_components) {
1424   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1425   if (num_eval_modes_in) *num_eval_modes_in = data->num_eval_modes_in;
1426   if (eval_modes_in) *eval_modes_in = (const CeedEvalMode **)data->eval_modes_in;
1427   if (eval_mode_offsets_in) *eval_mode_offsets_in = data->eval_mode_offsets_in;
1428   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1429   if (num_eval_modes_out) *num_eval_modes_out = data->num_eval_modes_out;
1430   if (eval_modes_out) *eval_modes_out = (const CeedEvalMode **)data->eval_modes_out;
1431   if (eval_mode_offsets_out) *eval_mode_offsets_out = data->eval_mode_offsets_out;
1432   if (num_output_components) *num_output_components = data->num_output_components;
1433   return CEED_ERROR_SUCCESS;
1434 }
1435 
1436 /**
1437   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1438 
1439   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1440 
1441   @param[in]  data                 `CeedOperatorAssemblyData`
1442   @param[out] num_active_bases_in  Number of active input bases, or `NULL`
1443   @param[out] active_bases_in      Pointer to hold active input `CeedBasis`, or `NULL`
1444   @param[out] assembled_bases_in   Pointer to hold assembled active input `B` , or `NULL`
1445   @param[out] num_active_bases_out Number of active output bases, or `NULL`
1446   @param[out] active_bases_out     Pointer to hold active output `CeedBasis`, or `NULL`
1447   @param[out] assembled_bases_out  Pointer to hold assembled active output `B` , or `NULL`
1448 
1449   @return An error code: 0 - success, otherwise - failure
1450 
1451   @ref Backend
1452 **/
1453 int CeedOperatorAssemblyDataGetBases(CeedOperatorAssemblyData data, CeedInt *num_active_bases_in, CeedBasis **active_bases_in,
1454                                      const CeedScalar ***assembled_bases_in, CeedInt *num_active_bases_out, CeedBasis **active_bases_out,
1455                                      const CeedScalar ***assembled_bases_out) {
1456   // Assemble B_in, B_out if needed
1457   if (assembled_bases_in && !data->assembled_bases_in[0]) {
1458     CeedInt num_qpts;
1459 
1460     if (data->active_bases_in[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[0], &num_qpts));
1461     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_in[0], &num_qpts));
1462     for (CeedInt b = 0; b < data->num_active_bases_in; b++) {
1463       bool        has_eval_none = false;
1464       CeedInt     num_nodes;
1465       CeedScalar *B_in = NULL, *identity = NULL;
1466 
1467       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_in[b], &num_nodes));
1468       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_in[b], &B_in));
1469 
1470       for (CeedInt i = 0; i < data->num_eval_modes_in[b]; i++) {
1471         has_eval_none = has_eval_none || (data->eval_modes_in[b][i] == CEED_EVAL_NONE);
1472       }
1473       if (has_eval_none) {
1474         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1475         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1476           identity[i * num_nodes + i] = 1.0;
1477         }
1478       }
1479 
1480       for (CeedInt q = 0; q < num_qpts; q++) {
1481         for (CeedInt n = 0; n < num_nodes; n++) {
1482           CeedInt      d_in              = 0, q_comp_in;
1483           CeedEvalMode eval_mode_in_prev = CEED_EVAL_NONE;
1484 
1485           for (CeedInt e_in = 0; e_in < data->num_eval_modes_in[b]; e_in++) {
1486             const CeedInt     qq = data->num_eval_modes_in[b] * q;
1487             const CeedScalar *B  = NULL;
1488 
1489             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_in[b], data->eval_modes_in[b][e_in], identity, &B));
1490             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_in[b], data->eval_modes_in[b][e_in], &q_comp_in));
1491             if (q_comp_in > 1) {
1492               if (e_in == 0 || data->eval_modes_in[b][e_in] != eval_mode_in_prev) d_in = 0;
1493               else B = &B[(++d_in) * num_qpts * num_nodes];
1494             }
1495             eval_mode_in_prev                 = data->eval_modes_in[b][e_in];
1496             B_in[(qq + e_in) * num_nodes + n] = B[q * num_nodes + n];
1497           }
1498         }
1499       }
1500       if (identity) CeedCall(CeedFree(&identity));
1501       data->assembled_bases_in[b] = B_in;
1502     }
1503   }
1504 
1505   if (assembled_bases_out && !data->assembled_bases_out[0]) {
1506     CeedInt num_qpts;
1507 
1508     if (data->active_bases_out[0] == CEED_BASIS_NONE) CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[0], &num_qpts));
1509     else CeedCall(CeedBasisGetNumQuadraturePoints(data->active_bases_out[0], &num_qpts));
1510     for (CeedInt b = 0; b < data->num_active_bases_out; b++) {
1511       bool        has_eval_none = false;
1512       CeedInt     num_nodes;
1513       CeedScalar *B_out = NULL, *identity = NULL;
1514 
1515       CeedCall(CeedElemRestrictionGetElementSize(data->active_elem_rstrs_out[b], &num_nodes));
1516       CeedCall(CeedCalloc(num_qpts * num_nodes * data->num_eval_modes_out[b], &B_out));
1517 
1518       for (CeedInt i = 0; i < data->num_eval_modes_out[b]; i++) {
1519         has_eval_none = has_eval_none || (data->eval_modes_out[b][i] == CEED_EVAL_NONE);
1520       }
1521       if (has_eval_none) {
1522         CeedCall(CeedCalloc(num_qpts * num_nodes, &identity));
1523         for (CeedInt i = 0; i < (num_nodes < num_qpts ? num_nodes : num_qpts); i++) {
1524           identity[i * num_nodes + i] = 1.0;
1525         }
1526       }
1527 
1528       for (CeedInt q = 0; q < num_qpts; q++) {
1529         for (CeedInt n = 0; n < num_nodes; n++) {
1530           CeedInt      d_out              = 0, q_comp_out;
1531           CeedEvalMode eval_mode_out_prev = CEED_EVAL_NONE;
1532 
1533           for (CeedInt e_out = 0; e_out < data->num_eval_modes_out[b]; e_out++) {
1534             const CeedInt     qq = data->num_eval_modes_out[b] * q;
1535             const CeedScalar *B  = NULL;
1536 
1537             CeedCall(CeedOperatorGetBasisPointer(data->active_bases_out[b], data->eval_modes_out[b][e_out], identity, &B));
1538             CeedCall(CeedBasisGetNumQuadratureComponents(data->active_bases_out[b], data->eval_modes_out[b][e_out], &q_comp_out));
1539             if (q_comp_out > 1) {
1540               if (e_out == 0 || data->eval_modes_out[b][e_out] != eval_mode_out_prev) d_out = 0;
1541               else B = &B[(++d_out) * num_qpts * num_nodes];
1542             }
1543             eval_mode_out_prev                  = data->eval_modes_out[b][e_out];
1544             B_out[(qq + e_out) * num_nodes + n] = B[q * num_nodes + n];
1545           }
1546         }
1547       }
1548       if (identity) CeedCall(CeedFree(&identity));
1549       data->assembled_bases_out[b] = B_out;
1550     }
1551   }
1552 
1553   // Pass out assembled data
1554   if (num_active_bases_in) *num_active_bases_in = data->num_active_bases_in;
1555   if (active_bases_in) *active_bases_in = data->active_bases_in;
1556   if (assembled_bases_in) *assembled_bases_in = (const CeedScalar **)data->assembled_bases_in;
1557   if (num_active_bases_out) *num_active_bases_out = data->num_active_bases_out;
1558   if (active_bases_out) *active_bases_out = data->active_bases_out;
1559   if (assembled_bases_out) *assembled_bases_out = (const CeedScalar **)data->assembled_bases_out;
1560   return CEED_ERROR_SUCCESS;
1561 }
1562 
1563 /**
1564   @brief Get `CeedOperator` `CeedBasis` data for assembly.
1565 
1566   Note: See @ref CeedOperatorAssemblyDataCreate() for a full description of the data stored in this object.
1567 
1568   @param[in]  data                      `CeedOperatorAssemblyData`
1569   @param[out] num_active_elem_rstrs_in  Number of active input element restrictions, or `NULL`
1570   @param[out] active_elem_rstrs_in      Pointer to hold active input `CeedElemRestriction`, or `NULL`
1571   @param[out] num_active_elem_rstrs_out Number of active output element restrictions, or `NULL`
1572   @param[out] active_elem_rstrs_out     Pointer to hold active output `CeedElemRestriction`, or `NULL`
1573 
1574   @return An error code: 0 - success, otherwise - failure
1575 
1576   @ref Backend
1577 **/
1578 int CeedOperatorAssemblyDataGetElemRestrictions(CeedOperatorAssemblyData data, CeedInt *num_active_elem_rstrs_in,
1579                                                 CeedElemRestriction **active_elem_rstrs_in, CeedInt *num_active_elem_rstrs_out,
1580                                                 CeedElemRestriction **active_elem_rstrs_out) {
1581   if (num_active_elem_rstrs_in) *num_active_elem_rstrs_in = data->num_active_bases_in;
1582   if (active_elem_rstrs_in) *active_elem_rstrs_in = data->active_elem_rstrs_in;
1583   if (num_active_elem_rstrs_out) *num_active_elem_rstrs_out = data->num_active_bases_out;
1584   if (active_elem_rstrs_out) *active_elem_rstrs_out = data->active_elem_rstrs_out;
1585   return CEED_ERROR_SUCCESS;
1586 }
1587 
1588 /**
1589   @brief Destroy `CeedOperatorAssemblyData`
1590 
1591   @param[in,out] data `CeedOperatorAssemblyData` to destroy
1592 
1593   @return An error code: 0 - success, otherwise - failure
1594 
1595   @ref Backend
1596 **/
1597 int CeedOperatorAssemblyDataDestroy(CeedOperatorAssemblyData *data) {
1598   if (!*data) {
1599     *data = NULL;
1600     return CEED_ERROR_SUCCESS;
1601   }
1602   CeedCall(CeedDestroy(&(*data)->ceed));
1603   for (CeedInt b = 0; b < (*data)->num_active_bases_in; b++) {
1604     CeedCall(CeedBasisDestroy(&(*data)->active_bases_in[b]));
1605     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_in[b]));
1606     CeedCall(CeedFree(&(*data)->eval_modes_in[b]));
1607     CeedCall(CeedFree(&(*data)->eval_mode_offsets_in[b]));
1608     CeedCall(CeedFree(&(*data)->assembled_bases_in[b]));
1609   }
1610   for (CeedInt b = 0; b < (*data)->num_active_bases_out; b++) {
1611     CeedCall(CeedBasisDestroy(&(*data)->active_bases_out[b]));
1612     CeedCall(CeedElemRestrictionDestroy(&(*data)->active_elem_rstrs_out[b]));
1613     CeedCall(CeedFree(&(*data)->eval_modes_out[b]));
1614     CeedCall(CeedFree(&(*data)->eval_mode_offsets_out[b]));
1615     CeedCall(CeedFree(&(*data)->assembled_bases_out[b]));
1616   }
1617   CeedCall(CeedFree(&(*data)->active_bases_in));
1618   CeedCall(CeedFree(&(*data)->active_bases_out));
1619   CeedCall(CeedFree(&(*data)->active_elem_rstrs_in));
1620   CeedCall(CeedFree(&(*data)->active_elem_rstrs_out));
1621   CeedCall(CeedFree(&(*data)->num_eval_modes_in));
1622   CeedCall(CeedFree(&(*data)->num_eval_modes_out));
1623   CeedCall(CeedFree(&(*data)->eval_modes_in));
1624   CeedCall(CeedFree(&(*data)->eval_modes_out));
1625   CeedCall(CeedFree(&(*data)->eval_mode_offsets_in));
1626   CeedCall(CeedFree(&(*data)->eval_mode_offsets_out));
1627   CeedCall(CeedFree(&(*data)->assembled_bases_in));
1628   CeedCall(CeedFree(&(*data)->assembled_bases_out));
1629 
1630   CeedCall(CeedFree(data));
1631   return CEED_ERROR_SUCCESS;
1632 }
1633 
1634 /**
1635   @brief Retrieve fallback `CeedOperator` with a reference `Ceed` for advanced `CeedOperator` functionality
1636 
1637   @param[in]  op          `CeedOperator` to retrieve fallback for
1638   @param[out] op_fallback Fallback `CeedOperator`
1639 
1640   @return An error code: 0 - success, otherwise - failure
1641 
1642   @ref Backend
1643 **/
1644 int CeedOperatorGetFallback(CeedOperator op, CeedOperator *op_fallback) {
1645   // Create if needed
1646   if (!op->op_fallback) CeedCall(CeedOperatorCreateFallback(op));
1647   if (op->op_fallback) {
1648     bool is_debug;
1649 
1650     CeedCall(CeedIsDebug(op->ceed, &is_debug));
1651     if (is_debug) {
1652       Ceed        ceed, ceed_fallback;
1653       const char *resource, *resource_fallback;
1654 
1655       CeedCall(CeedOperatorGetCeed(op, &ceed));
1656       CeedCall(CeedGetOperatorFallbackCeed(ceed, &ceed_fallback));
1657       CeedCall(CeedGetResource(ceed, &resource));
1658       CeedCall(CeedGetResource(ceed_fallback, &resource_fallback));
1659 
1660       CeedDebug256(ceed, CEED_DEBUG_COLOR_SUCCESS, "---------- CeedOperator Fallback ----------\n");
1661       CeedDebug(ceed, "Falling back from %s operator at address %p to %s operator at address %p\n", resource, op, resource_fallback, op->op_fallback);
1662     }
1663   }
1664   *op_fallback = op->op_fallback;
1665   return CEED_ERROR_SUCCESS;
1666 }
1667 
1668 /**
1669   @brief Get the parent `CeedOperator` for a fallback `CeedOperator`
1670 
1671   @param[in]  op     `CeedOperator` context
1672   @param[out] parent Variable to store parent `CeedOperator` context
1673 
1674   @return An error code: 0 - success, otherwise - failure
1675 
1676   @ref Backend
1677 **/
1678 int CeedOperatorGetFallbackParent(CeedOperator op, CeedOperator *parent) {
1679   *parent = op->op_fallback_parent ? op->op_fallback_parent : NULL;
1680   return CEED_ERROR_SUCCESS;
1681 }
1682 
1683 /**
1684   @brief Get the `Ceed` context of the parent `CeedOperator` for a fallback `CeedOperator`
1685 
1686   @param[in]  op     `CeedOperator` context
1687   @param[out] parent Variable to store parent `Ceed` context
1688 
1689   @return An error code: 0 - success, otherwise - failure
1690 
1691   @ref Backend
1692 **/
1693 int CeedOperatorGetFallbackParentCeed(CeedOperator op, Ceed *parent) {
1694   *parent = op->op_fallback_parent ? op->op_fallback_parent->ceed : op->ceed;
1695   return CEED_ERROR_SUCCESS;
1696 }
1697 
1698 /// @}
1699 
1700 /// ----------------------------------------------------------------------------
1701 /// CeedOperator Public API
1702 /// ----------------------------------------------------------------------------
1703 /// @addtogroup CeedOperatorUser
1704 /// @{
1705 
1706 /**
1707   @brief Assemble a linear `CeedQFunction` associated with a `CeedOperator`.
1708 
1709   This returns a `CeedVector` containing a matrix at each quadrature point providing the action of the `CeedQFunction` associated with the `CeedOperator`.
1710   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.
1711 
1712   Inputs and outputs are in the order provided by the user when adding `CeedOperator` fields.
1713   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]`.
1714 
1715   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1716 
1717   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1718   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1719   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1720   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1721 
1722   @return An error code: 0 - success, otherwise - failure
1723 
1724   @ref User
1725 **/
1726 int CeedOperatorLinearAssembleQFunction(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1727   CeedCall(CeedOperatorCheckReady(op));
1728 
1729   if (op->LinearAssembleQFunction) {
1730     // Backend version
1731     CeedCall(op->LinearAssembleQFunction(op, assembled, rstr, request));
1732   } else {
1733     // Operator fallback
1734     CeedOperator op_fallback;
1735 
1736     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1737     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunction(op_fallback, assembled, rstr, request));
1738     else return CeedError(op->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunction");
1739   }
1740   return CEED_ERROR_SUCCESS;
1741 }
1742 
1743 /**
1744   @brief Assemble `CeedQFunction` and store result internally.
1745 
1746   Return copied references of stored data to the caller.
1747   Caller is responsible for ownership and destruction of the copied references.
1748   See also @ref CeedOperatorLinearAssembleQFunction().
1749 
1750   Note: If the value of `assembled` or `rstr` passed to this function are non-`NULL` , then it is assumed that they hold valid pointers.
1751         These objects will be destroyed if `*assembled` or `*rstr` is the only reference to the object.
1752 
1753   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1754   @param[out] assembled `CeedVector` to store assembled `CeedQFunction` at quadrature points
1755   @param[out] rstr      `CeedElemRestriction` for `CeedVector` containing assembled `CeedQFunction`
1756   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1757 
1758   @return An error code: 0 - success, otherwise - failure
1759 
1760   @ref User
1761 **/
1762 int CeedOperatorLinearAssembleQFunctionBuildOrUpdate(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1763   int (*LinearAssembleQFunctionUpdate)(CeedOperator, CeedVector, CeedElemRestriction, CeedRequest *) = NULL;
1764   CeedOperator op_assemble                                                                           = NULL;
1765   CeedOperator op_fallback_parent                                                                    = NULL;
1766 
1767   CeedCall(CeedOperatorCheckReady(op));
1768 
1769   // Determine if fallback parent or operator has implementation
1770   CeedCall(CeedOperatorGetFallbackParent(op, &op_fallback_parent));
1771   if (op_fallback_parent && op_fallback_parent->LinearAssembleQFunctionUpdate) {
1772     // -- Backend version for op fallback parent is faster, if it exists
1773     LinearAssembleQFunctionUpdate = op_fallback_parent->LinearAssembleQFunctionUpdate;
1774     op_assemble                   = op_fallback_parent;
1775   } else if (op->LinearAssembleQFunctionUpdate) {
1776     // -- Backend version for op
1777     LinearAssembleQFunctionUpdate = op->LinearAssembleQFunctionUpdate;
1778     op_assemble                   = op;
1779   }
1780 
1781   // Assemble QFunction
1782   if (LinearAssembleQFunctionUpdate) {
1783     // Backend or fallback parent version
1784     bool                qf_assembled_is_setup;
1785     CeedVector          assembled_vec  = NULL;
1786     CeedElemRestriction assembled_rstr = NULL;
1787 
1788     CeedCall(CeedQFunctionAssemblyDataIsSetup(op->qf_assembled, &qf_assembled_is_setup));
1789     if (qf_assembled_is_setup) {
1790       bool update_needed;
1791 
1792       CeedCall(CeedQFunctionAssemblyDataGetObjects(op->qf_assembled, &assembled_vec, &assembled_rstr));
1793       CeedCall(CeedQFunctionAssemblyDataIsUpdateNeeded(op->qf_assembled, &update_needed));
1794       if (update_needed) CeedCall(LinearAssembleQFunctionUpdate(op_assemble, assembled_vec, assembled_rstr, request));
1795     } else {
1796       CeedCall(CeedOperatorLinearAssembleQFunction(op_assemble, &assembled_vec, &assembled_rstr, request));
1797       CeedCall(CeedQFunctionAssemblyDataSetObjects(op->qf_assembled, assembled_vec, assembled_rstr));
1798     }
1799     CeedCall(CeedQFunctionAssemblyDataSetUpdateNeeded(op->qf_assembled, false));
1800 
1801     // Copy reference from internally held copy
1802     CeedCall(CeedVectorReferenceCopy(assembled_vec, assembled));
1803     CeedCall(CeedElemRestrictionReferenceCopy(assembled_rstr, rstr));
1804     CeedCall(CeedVectorDestroy(&assembled_vec));
1805     CeedCall(CeedElemRestrictionDestroy(&assembled_rstr));
1806   } else {
1807     // Operator fallback
1808     CeedOperator op_fallback;
1809 
1810     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1811     if (op_fallback) CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op_fallback, assembled, rstr, request));
1812     else return CeedError(op->ceed, CEED_ERROR_UNSUPPORTED, "Backend does not support CeedOperatorLinearAssembleQFunctionUpdate");
1813   }
1814   return CEED_ERROR_SUCCESS;
1815 }
1816 
1817 /**
1818   @brief Assemble the diagonal of a square linear `CeedOperator`
1819 
1820   This overwrites a `CeedVector` with the diagonal of a linear `CeedOperator`.
1821 
1822   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1823 
1824   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1825 
1826   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1827   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1828   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1829 
1830   @return An error code: 0 - success, otherwise - failure
1831 
1832   @ref User
1833 **/
1834 int CeedOperatorLinearAssembleDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1835   bool     is_composite;
1836   CeedSize input_size = 0, output_size = 0;
1837 
1838   CeedCall(CeedOperatorCheckReady(op));
1839   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1840 
1841   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1842   CeedCheck(input_size == output_size, op->ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1843 
1844   // Early exit for empty operator
1845   if (!is_composite) {
1846     CeedInt num_elem = 0;
1847 
1848     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1849     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1850   }
1851 
1852   if (op->LinearAssembleDiagonal) {
1853     // Backend version
1854     CeedCall(op->LinearAssembleDiagonal(op, assembled, request));
1855     return CEED_ERROR_SUCCESS;
1856   } else if (op->LinearAssembleAddDiagonal) {
1857     // Backend version with zeroing first
1858     CeedCall(CeedVectorSetValue(assembled, 0.0));
1859     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1860     return CEED_ERROR_SUCCESS;
1861   } else {
1862     // Operator fallback
1863     CeedOperator op_fallback;
1864 
1865     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1866     if (op_fallback) {
1867       CeedCall(CeedOperatorLinearAssembleDiagonal(op_fallback, assembled, request));
1868       return CEED_ERROR_SUCCESS;
1869     }
1870   }
1871   // Default interface implementation
1872   CeedCall(CeedVectorSetValue(assembled, 0.0));
1873   CeedCall(CeedOperatorLinearAssembleAddDiagonal(op, assembled, request));
1874   return CEED_ERROR_SUCCESS;
1875 }
1876 
1877 /**
1878   @brief Assemble the diagonal of a square linear `CeedOperator`.
1879 
1880   This sums into a `CeedVector` the diagonal of a linear `CeedOperator`.
1881 
1882   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
1883 
1884   Note: Calling this function asserts that setup is complete and sets the CeedOperator as immutable.
1885 
1886   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
1887   @param[out] assembled `CeedVector` to store assembled `CeedOperator` diagonal
1888   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
1889 
1890   @return An error code: 0 - success, otherwise - failure
1891 
1892   @ref User
1893 **/
1894 int CeedOperatorLinearAssembleAddDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1895   bool     is_composite;
1896   CeedSize input_size = 0, output_size = 0;
1897 
1898   CeedCall(CeedOperatorCheckReady(op));
1899   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1900 
1901   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1902   CeedCheck(input_size == output_size, op->ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1903 
1904   // Early exit for empty operator
1905   if (!is_composite) {
1906     CeedInt num_elem = 0;
1907 
1908     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
1909     if (num_elem == 0) return CEED_ERROR_SUCCESS;
1910   }
1911 
1912   if (op->LinearAssembleAddDiagonal) {
1913     // Backend version
1914     CeedCall(op->LinearAssembleAddDiagonal(op, assembled, request));
1915     return CEED_ERROR_SUCCESS;
1916   } else {
1917     // Operator fallback
1918     CeedOperator op_fallback;
1919 
1920     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
1921     if (op_fallback) {
1922       CeedCall(CeedOperatorLinearAssembleAddDiagonal(op_fallback, assembled, request));
1923       return CEED_ERROR_SUCCESS;
1924     }
1925   }
1926   // Default interface implementation
1927   if (is_composite) {
1928     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, false, assembled));
1929   } else {
1930     CeedCall(CeedSingleOperatorAssembleAddDiagonal_Core(op, request, false, assembled));
1931   }
1932   return CEED_ERROR_SUCCESS;
1933 }
1934 
1935 /**
1936    @brief Fully assemble the point-block diagonal pattern of a linear `CeedOperator`.
1937 
1938    Expected to be used in conjunction with @ref CeedOperatorLinearAssemblePointBlockDiagonal().
1939 
1940    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)`.
1941    Note that the `(i, j)` pairs are unique.
1942    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemblePointBlockDiagonal() provides the values in the same ordering.
1943 
1944    This will generally be slow unless your operator is low-order.
1945 
1946    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
1947 
1948    @param[in]  op          `CeedOperator` to assemble
1949    @param[out] num_entries Number of entries in coordinate nonzero pattern
1950    @param[out] rows        Row number for each entry
1951    @param[out] cols        Column number for each entry
1952 
1953    @ref User
1954 **/
1955 int CeedOperatorLinearAssemblePointBlockDiagonalSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
1956   Ceed          ceed;
1957   bool          is_composite;
1958   CeedInt       num_active_components, num_sub_operators;
1959   CeedOperator *sub_operators;
1960 
1961   CeedCall(CeedOperatorGetCeed(op, &ceed));
1962   CeedCall(CeedOperatorIsComposite(op, &is_composite));
1963 
1964   CeedSize input_size = 0, output_size = 0;
1965   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1966   CeedCheck(input_size == output_size, ceed, CEED_ERROR_DIMENSION, "Operator must be square");
1967 
1968   if (is_composite) {
1969     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_sub_operators));
1970     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
1971   } else {
1972     sub_operators     = &op;
1973     num_sub_operators = 1;
1974   }
1975 
1976   // Verify operator can be assembled correctly
1977   {
1978     CeedOperatorAssemblyData data;
1979     CeedInt                  num_active_elem_rstrs, comp_stride;
1980     CeedElemRestriction     *active_elem_rstrs;
1981 
1982     // Get initial values to check against
1983     CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[0], &data));
1984     CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
1985     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[0], &comp_stride));
1986     CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[0], &num_active_components));
1987 
1988     // Verify that all active element restrictions have same component stride and number of components
1989     for (CeedInt k = 0; k < num_sub_operators; k++) {
1990       CeedCall(CeedOperatorGetOperatorAssemblyData(sub_operators[k], &data));
1991       CeedCall(CeedOperatorAssemblyDataGetElemRestrictions(data, &num_active_elem_rstrs, &active_elem_rstrs, NULL, NULL));
1992       for (CeedInt i = 0; i < num_active_elem_rstrs; i++) {
1993         CeedInt comp_stride_sub, num_active_components_sub;
1994 
1995         CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstrs[i], &comp_stride_sub));
1996         CeedCheck(comp_stride == comp_stride_sub, ceed, CEED_ERROR_DIMENSION,
1997                   "Active element restrictions must have the same component stride: %d vs %d", comp_stride, comp_stride_sub);
1998         CeedCall(CeedElemRestrictionGetNumComponents(active_elem_rstrs[i], &num_active_components_sub));
1999         CeedCheck(num_active_components == num_active_components_sub, ceed, CEED_ERROR_INCOMPATIBLE,
2000                   "All suboperators must have the same number of output components");
2001       }
2002     }
2003   }
2004   *num_entries = input_size * num_active_components;
2005   CeedCall(CeedCalloc(*num_entries, rows));
2006   CeedCall(CeedCalloc(*num_entries, cols));
2007 
2008   for (CeedInt o = 0; o < num_sub_operators; o++) {
2009     CeedElemRestriction active_elem_rstr, point_block_active_elem_rstr;
2010     CeedInt             comp_stride, num_elem, elem_size;
2011     const CeedInt      *offsets, *point_block_offsets;
2012 
2013     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[o], &active_elem_rstr));
2014     CeedCall(CeedElemRestrictionGetCompStride(active_elem_rstr, &comp_stride));
2015     CeedCall(CeedElemRestrictionGetNumElements(active_elem_rstr, &num_elem));
2016     CeedCall(CeedElemRestrictionGetElementSize(active_elem_rstr, &elem_size));
2017     CeedCall(CeedElemRestrictionGetOffsets(active_elem_rstr, CEED_MEM_HOST, &offsets));
2018 
2019     CeedCall(CeedOperatorCreateActivePointBlockRestriction(active_elem_rstr, &point_block_active_elem_rstr));
2020     CeedCall(CeedElemRestrictionGetOffsets(point_block_active_elem_rstr, CEED_MEM_HOST, &point_block_offsets));
2021 
2022     for (CeedSize i = 0; i < num_elem * elem_size; i++) {
2023       for (CeedInt c_out = 0; c_out < num_active_components; c_out++) {
2024         for (CeedInt c_in = 0; c_in < num_active_components; c_in++) {
2025           (*rows)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_out * comp_stride;
2026           (*cols)[point_block_offsets[i] + c_out * num_active_components + c_in] = offsets[i] + c_in * comp_stride;
2027         }
2028       }
2029     }
2030 
2031     CeedCall(CeedElemRestrictionRestoreOffsets(active_elem_rstr, &offsets));
2032     CeedCall(CeedElemRestrictionRestoreOffsets(point_block_active_elem_rstr, &point_block_offsets));
2033     CeedCall(CeedElemRestrictionDestroy(&point_block_active_elem_rstr));
2034   }
2035   return CEED_ERROR_SUCCESS;
2036 }
2037 
2038 /**
2039   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2040 
2041   This overwrites a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2042 
2043   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2044 
2045   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2046 
2047   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2048   @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.
2049                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2050                           The array has shape `[nodes, component out, component in]`.
2051   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2052 
2053   @return An error code: 0 - success, otherwise - failure
2054 
2055   @ref User
2056 **/
2057 int CeedOperatorLinearAssemblePointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2058   bool     is_composite;
2059   CeedSize input_size = 0, output_size = 0;
2060 
2061   CeedCall(CeedOperatorCheckReady(op));
2062   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2063 
2064   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2065   CeedCheck(input_size == output_size, op->ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2066 
2067   // Early exit for empty operator
2068   if (!is_composite) {
2069     CeedInt num_elem = 0;
2070 
2071     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2072     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2073   }
2074 
2075   if (op->LinearAssemblePointBlockDiagonal) {
2076     // Backend version
2077     CeedCall(op->LinearAssemblePointBlockDiagonal(op, assembled, request));
2078     return CEED_ERROR_SUCCESS;
2079   } else if (op->LinearAssembleAddPointBlockDiagonal) {
2080     // Backend version with zeroing first
2081     CeedCall(CeedVectorSetValue(assembled, 0.0));
2082     CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2083     return CEED_ERROR_SUCCESS;
2084   } else {
2085     // Operator fallback
2086     CeedOperator op_fallback;
2087 
2088     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2089     if (op_fallback) {
2090       CeedCall(CeedOperatorLinearAssemblePointBlockDiagonal(op_fallback, assembled, request));
2091       return CEED_ERROR_SUCCESS;
2092     }
2093   }
2094   // Default interface implementation
2095   CeedCall(CeedVectorSetValue(assembled, 0.0));
2096   CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op, assembled, request));
2097   return CEED_ERROR_SUCCESS;
2098 }
2099 
2100 /**
2101   @brief Assemble the point block diagonal of a square linear `CeedOperator`.
2102 
2103   This sums into a `CeedVector` with the point block diagonal of a linear `CeedOperator`.
2104 
2105   Note: Currently only non-composite `CeedOperator` with a single field and composite `CeedOperator` with single field sub-operators are supported.
2106 
2107   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2108 
2109   @param[in]  op        `CeedOperator` to assemble `CeedQFunction`
2110   @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.
2111                           The dimensions of this vector are derived from the active vector for the `CeedOperator`.
2112                           The array has shape `[nodes, component out, component in]`.
2113   @param[in]  request   Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2114 
2115   @return An error code: 0 - success, otherwise - failure
2116 
2117   @ref User
2118 **/
2119 int CeedOperatorLinearAssembleAddPointBlockDiagonal(CeedOperator op, CeedVector assembled, CeedRequest *request) {
2120   bool     is_composite;
2121   CeedSize input_size = 0, output_size = 0;
2122 
2123   CeedCall(CeedOperatorCheckReady(op));
2124   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2125 
2126   CeedCall(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
2127   CeedCheck(input_size == output_size, op->ceed, CEED_ERROR_DIMENSION, "Operator must be square");
2128 
2129   // Early exit for empty operator
2130   if (!is_composite) {
2131     CeedInt num_elem = 0;
2132 
2133     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2134     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2135   }
2136 
2137   if (op->LinearAssembleAddPointBlockDiagonal) {
2138     // Backend version
2139     CeedCall(op->LinearAssembleAddPointBlockDiagonal(op, assembled, request));
2140     return CEED_ERROR_SUCCESS;
2141   } else {
2142     // Operator fallback
2143     CeedOperator op_fallback;
2144 
2145     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2146     if (op_fallback) {
2147       CeedCall(CeedOperatorLinearAssembleAddPointBlockDiagonal(op_fallback, assembled, request));
2148       return CEED_ERROR_SUCCESS;
2149     }
2150   }
2151   // Default interface implementation
2152   if (is_composite) {
2153     CeedCall(CeedCompositeOperatorLinearAssembleAddDiagonal(op, request, true, assembled));
2154   } else {
2155     CeedCall(CeedSingleOperatorAssembleAddDiagonal_Core(op, request, true, assembled));
2156   }
2157   return CEED_ERROR_SUCCESS;
2158 }
2159 
2160 /**
2161    @brief Fully assemble the nonzero pattern of a linear `CeedOperator`.
2162 
2163    Expected to be used in conjunction with @ref CeedOperatorLinearAssemble().
2164 
2165    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)`.
2166    Note that the `(i, j)` pairs are not unique and may repeat.
2167    This function returns the number of entries and their `(i, j)` locations, while @ref CeedOperatorLinearAssemble() provides the values in the same ordering.
2168 
2169    This will generally be slow unless your operator is low-order.
2170 
2171    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2172 
2173    @param[in]  op          `CeedOperator` to assemble
2174    @param[out] num_entries Number of entries in coordinate nonzero pattern
2175    @param[out] rows        Row number for each entry
2176    @param[out] cols        Column number for each entry
2177 
2178    @ref User
2179 **/
2180 int CeedOperatorLinearAssembleSymbolic(CeedOperator op, CeedSize *num_entries, CeedInt **rows, CeedInt **cols) {
2181   bool          is_composite;
2182   CeedInt       num_suboperators, offset = 0;
2183   CeedSize      single_entries;
2184   CeedOperator *sub_operators;
2185 
2186   CeedCall(CeedOperatorCheckReady(op));
2187   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2188 
2189   if (op->LinearAssembleSymbolic) {
2190     // Backend version
2191     CeedCall(op->LinearAssembleSymbolic(op, num_entries, rows, cols));
2192     return CEED_ERROR_SUCCESS;
2193   } else {
2194     // Operator fallback
2195     CeedOperator op_fallback;
2196 
2197     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2198     if (op_fallback) {
2199       CeedCall(CeedOperatorLinearAssembleSymbolic(op_fallback, num_entries, rows, cols));
2200       return CEED_ERROR_SUCCESS;
2201     }
2202   }
2203 
2204   // Default interface implementation
2205 
2206   // Count entries and allocate rows, cols arrays
2207   *num_entries = 0;
2208   if (is_composite) {
2209     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2210     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2211     for (CeedInt k = 0; k < num_suboperators; ++k) {
2212       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2213       *num_entries += single_entries;
2214     }
2215   } else {
2216     CeedCall(CeedSingleOperatorAssemblyCountEntries(op, &single_entries));
2217     *num_entries += single_entries;
2218   }
2219   CeedCall(CeedCalloc(*num_entries, rows));
2220   CeedCall(CeedCalloc(*num_entries, cols));
2221 
2222   // Assemble nonzero locations
2223   if (is_composite) {
2224     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2225     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2226     for (CeedInt k = 0; k < num_suboperators; ++k) {
2227       CeedCall(CeedSingleOperatorAssembleSymbolic(sub_operators[k], offset, *rows, *cols));
2228       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2229       offset += single_entries;
2230     }
2231   } else {
2232     CeedCall(CeedSingleOperatorAssembleSymbolic(op, offset, *rows, *cols));
2233   }
2234   return CEED_ERROR_SUCCESS;
2235 }
2236 
2237 /**
2238    @brief Fully assemble the nonzero entries of a linear operator.
2239 
2240    Expected to be used in conjunction with @ref CeedOperatorLinearAssembleSymbolic().
2241 
2242    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)`.
2243    Note that the `(i, j)` pairs are not unique and may repeat.
2244    This function returns the values of the nonzero entries to be added, their `(i, j)` locations are provided by @ref CeedOperatorLinearAssembleSymbolic().
2245 
2246    This will generally be slow unless your operator is low-order.
2247 
2248    Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2249 
2250    @param[in]  op     `CeedOperator` to assemble
2251    @param[out] values Values to assemble into matrix
2252 
2253    @ref User
2254 **/
2255 int CeedOperatorLinearAssemble(CeedOperator op, CeedVector values) {
2256   bool          is_composite;
2257   CeedInt       num_suboperators, offset = 0;
2258   CeedSize      single_entries = 0;
2259   CeedOperator *sub_operators;
2260 
2261   CeedCall(CeedOperatorCheckReady(op));
2262   CeedCall(CeedOperatorIsComposite(op, &is_composite));
2263 
2264   // Early exit for empty operator
2265   if (!is_composite) {
2266     CeedInt num_elem = 0;
2267 
2268     CeedCall(CeedOperatorGetNumElements(op, &num_elem));
2269     if (num_elem == 0) return CEED_ERROR_SUCCESS;
2270   }
2271 
2272   if (op->LinearAssemble) {
2273     // Backend version
2274     CeedCall(op->LinearAssemble(op, values));
2275     return CEED_ERROR_SUCCESS;
2276   } else {
2277     // Operator fallback
2278     CeedOperator op_fallback;
2279 
2280     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2281     if (op_fallback) {
2282       CeedCall(CeedOperatorLinearAssemble(op_fallback, values));
2283       return CEED_ERROR_SUCCESS;
2284     }
2285   }
2286 
2287   // Default interface implementation
2288   CeedCall(CeedVectorSetValue(values, 0.0));
2289   if (is_composite) {
2290     CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2291     CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2292     for (CeedInt k = 0; k < num_suboperators; k++) {
2293       CeedCall(CeedSingleOperatorAssemble(sub_operators[k], offset, values));
2294       CeedCall(CeedSingleOperatorAssemblyCountEntries(sub_operators[k], &single_entries));
2295       offset += single_entries;
2296     }
2297   } else {
2298     CeedCall(CeedSingleOperatorAssemble(op, offset, values));
2299   }
2300   return CEED_ERROR_SUCCESS;
2301 }
2302 
2303 /**
2304   @brief Get the multiplicity of nodes across sub-operators in a composite `CeedOperator`.
2305 
2306   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2307 
2308   @param[in]  op               Composite `CeedOperator`
2309   @param[in]  num_skip_indices Number of sub-operators to skip
2310   @param[in]  skip_indices     Array of indices of sub-operators to skip
2311   @param[out] mult             Vector to store multiplicity (of size `l_size` )
2312 
2313   @return An error code: 0 - success, otherwise - failure
2314 
2315   @ref User
2316 **/
2317 int CeedCompositeOperatorGetMultiplicity(CeedOperator op, CeedInt num_skip_indices, CeedInt *skip_indices, CeedVector mult) {
2318   Ceed                ceed;
2319   CeedInt             num_suboperators;
2320   CeedSize            l_vec_len;
2321   CeedScalar         *mult_array;
2322   CeedVector          ones_l_vec;
2323   CeedElemRestriction elem_rstr, mult_elem_rstr;
2324   CeedOperator       *sub_operators;
2325 
2326   CeedCall(CeedOperatorCheckReady(op));
2327 
2328   CeedCall(CeedOperatorGetCeed(op, &ceed));
2329 
2330   // Zero mult vector
2331   CeedCall(CeedVectorSetValue(mult, 0.0));
2332 
2333   // Get suboperators
2334   CeedCall(CeedCompositeOperatorGetNumSub(op, &num_suboperators));
2335   CeedCall(CeedCompositeOperatorGetSubList(op, &sub_operators));
2336   if (num_suboperators == 0) return CEED_ERROR_SUCCESS;
2337 
2338   // Work vector
2339   CeedCall(CeedVectorGetLength(mult, &l_vec_len));
2340   CeedCall(CeedVectorCreate(ceed, l_vec_len, &ones_l_vec));
2341   CeedCall(CeedVectorSetValue(ones_l_vec, 1.0));
2342   CeedCall(CeedVectorGetArray(mult, CEED_MEM_HOST, &mult_array));
2343 
2344   // Compute multiplicity across suboperators
2345   for (CeedInt i = 0; i < num_suboperators; i++) {
2346     const CeedScalar *sub_mult_array;
2347     CeedVector        sub_mult_l_vec, ones_e_vec;
2348 
2349     // -- Check for suboperator to skip
2350     for (CeedInt j = 0; j < num_skip_indices; j++) {
2351       if (skip_indices[j] == i) continue;
2352     }
2353 
2354     // -- Sub operator multiplicity
2355     CeedCall(CeedOperatorGetActiveElemRestriction(sub_operators[i], &elem_rstr));
2356     CeedCall(CeedElemRestrictionCreateUnorientedCopy(elem_rstr, &mult_elem_rstr));
2357     CeedCall(CeedElemRestrictionCreateVector(mult_elem_rstr, &sub_mult_l_vec, &ones_e_vec));
2358     CeedCall(CeedVectorSetValue(sub_mult_l_vec, 0.0));
2359     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_NOTRANSPOSE, ones_l_vec, ones_e_vec, CEED_REQUEST_IMMEDIATE));
2360     CeedCall(CeedElemRestrictionApply(mult_elem_rstr, CEED_TRANSPOSE, ones_e_vec, sub_mult_l_vec, CEED_REQUEST_IMMEDIATE));
2361     CeedCall(CeedVectorGetArrayRead(sub_mult_l_vec, CEED_MEM_HOST, &sub_mult_array));
2362     // ---- Flag every node present in the current suboperator
2363     for (CeedInt j = 0; j < l_vec_len; j++) {
2364       if (sub_mult_array[j] > 0.0) mult_array[j] += 1.0;
2365     }
2366     CeedCall(CeedVectorRestoreArrayRead(sub_mult_l_vec, &sub_mult_array));
2367     CeedCall(CeedVectorDestroy(&sub_mult_l_vec));
2368     CeedCall(CeedVectorDestroy(&ones_e_vec));
2369     CeedCall(CeedElemRestrictionDestroy(&mult_elem_rstr));
2370   }
2371   CeedCall(CeedVectorRestoreArray(mult, &mult_array));
2372   CeedCall(CeedVectorDestroy(&ones_l_vec));
2373   return CEED_ERROR_SUCCESS;
2374 }
2375 
2376 /**
2377   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator`, creating the prolongation basis from the fine and coarse grid interpolation.
2378 
2379   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2380 
2381   @param[in]  op_fine      Fine grid `CeedOperator`
2382   @param[in]  p_mult_fine  L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2383   @param[in]  rstr_coarse  Coarse grid `CeedElemRestriction`
2384   @param[in]  basis_coarse Coarse grid active vector `CeedBasis`
2385   @param[out] op_coarse    Coarse grid `CeedOperator`
2386   @param[out] op_prolong   Coarse to fine `CeedOperator`, or `NULL`
2387   @param[out] op_restrict  Fine to coarse `CeedOperator`, or `NULL`
2388 
2389   @return An error code: 0 - success, otherwise - failure
2390 
2391   @ref User
2392 **/
2393 int CeedOperatorMultigridLevelCreate(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2394                                      CeedOperator *op_coarse, CeedOperator *op_prolong, CeedOperator *op_restrict) {
2395   CeedBasis basis_c_to_f = NULL;
2396 
2397   CeedCall(CeedOperatorCheckReady(op_fine));
2398 
2399   // Build prolongation matrix, if required
2400   if (op_prolong || op_restrict) {
2401     CeedBasis basis_fine;
2402 
2403     CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2404     CeedCall(CeedBasisCreateProjection(basis_coarse, basis_fine, &basis_c_to_f));
2405   }
2406 
2407   // Core code
2408   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2409   return CEED_ERROR_SUCCESS;
2410 }
2411 
2412 /**
2413   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a tensor basis for the active basis.
2414 
2415   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2416 
2417   @param[in]  op_fine       Fine grid `CeedOperator`
2418   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2419   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2420   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2421   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2422   @param[out] op_coarse     Coarse grid `CeedOperator`
2423   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2424   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2425 
2426   @return An error code: 0 - success, otherwise - failure
2427 
2428   @ref User
2429 **/
2430 int CeedOperatorMultigridLevelCreateTensorH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2431                                              const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2432                                              CeedOperator *op_restrict) {
2433   Ceed      ceed;
2434   CeedInt   Q_f, Q_c;
2435   CeedBasis basis_fine, basis_c_to_f = NULL;
2436 
2437   CeedCall(CeedOperatorCheckReady(op_fine));
2438   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2439 
2440   // Check for compatible quadrature spaces
2441   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2442   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2443   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2444   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2445 
2446   // Create coarse to fine basis, if required
2447   if (op_prolong || op_restrict) {
2448     CeedInt     dim, num_comp, num_nodes_c, P_1d_f, P_1d_c;
2449     CeedScalar *q_ref, *q_weight, *grad;
2450 
2451     // Check if interpolation matrix is provided
2452     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2453               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2454     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2455     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2456     CeedCall(CeedBasisGetNumNodes1D(basis_fine, &P_1d_f));
2457     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2458     P_1d_c = dim == 1 ? num_nodes_c : dim == 2 ? sqrt(num_nodes_c) : cbrt(num_nodes_c);
2459     CeedCall(CeedCalloc(P_1d_f, &q_ref));
2460     CeedCall(CeedCalloc(P_1d_f, &q_weight));
2461     CeedCall(CeedCalloc(P_1d_f * P_1d_c * dim, &grad));
2462     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));
2463     CeedCall(CeedFree(&q_ref));
2464     CeedCall(CeedFree(&q_weight));
2465     CeedCall(CeedFree(&grad));
2466   }
2467 
2468   // Core code
2469   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2470   return CEED_ERROR_SUCCESS;
2471 }
2472 
2473 /**
2474   @brief Create a multigrid coarse `CeedOperator` and level transfer `CeedOperator` for a `CeedOperator` with a non-tensor basis for the active vector
2475 
2476   Note: Calling this function asserts that setup is complete and sets all four `CeedOperator` as immutable.
2477 
2478   @param[in]  op_fine       Fine grid `CeedOperator`
2479   @param[in]  p_mult_fine   L-vector multiplicity in parallel gather/scatter, or `NULL` if not creating prolongation/restriction `CeedOperator`
2480   @param[in]  rstr_coarse   Coarse grid `CeedElemRestriction`
2481   @param[in]  basis_coarse  Coarse grid active vector `CeedBasis`
2482   @param[in]  interp_c_to_f Matrix for coarse to fine interpolation, or `NULL` if not creating prolongation/restriction `CeedOperator`
2483   @param[out] op_coarse     Coarse grid `CeedOperator`
2484   @param[out] op_prolong    Coarse to fine `CeedOperator`, or `NULL`
2485   @param[out] op_restrict   Fine to coarse `CeedOperator`, or `NULL`
2486 
2487   @return An error code: 0 - success, otherwise - failure
2488 
2489   @ref User
2490 **/
2491 int CeedOperatorMultigridLevelCreateH1(CeedOperator op_fine, CeedVector p_mult_fine, CeedElemRestriction rstr_coarse, CeedBasis basis_coarse,
2492                                        const CeedScalar *interp_c_to_f, CeedOperator *op_coarse, CeedOperator *op_prolong,
2493                                        CeedOperator *op_restrict) {
2494   Ceed      ceed;
2495   CeedInt   Q_f, Q_c;
2496   CeedBasis basis_fine, basis_c_to_f = NULL;
2497 
2498   CeedCall(CeedOperatorCheckReady(op_fine));
2499   CeedCall(CeedOperatorGetCeed(op_fine, &ceed));
2500 
2501   // Check for compatible quadrature spaces
2502   CeedCall(CeedOperatorGetActiveBasis(op_fine, &basis_fine));
2503   CeedCall(CeedBasisGetNumQuadraturePoints(basis_fine, &Q_f));
2504   CeedCall(CeedBasisGetNumQuadraturePoints(basis_coarse, &Q_c));
2505   CeedCheck(Q_f == Q_c, ceed, CEED_ERROR_DIMENSION, "Bases must have compatible quadrature spaces");
2506 
2507   // Coarse to fine basis
2508   if (op_prolong || op_restrict) {
2509     CeedInt          dim, num_comp, num_nodes_c, num_nodes_f;
2510     CeedScalar      *q_ref, *q_weight, *grad;
2511     CeedElemTopology topo;
2512 
2513     // Check if interpolation matrix is provided
2514     CeedCheck(interp_c_to_f, ceed, CEED_ERROR_INCOMPATIBLE,
2515               "Prolongation or restriction operator creation requires coarse-to-fine interpolation matrix");
2516     CeedCall(CeedBasisGetTopology(basis_fine, &topo));
2517     CeedCall(CeedBasisGetDimension(basis_fine, &dim));
2518     CeedCall(CeedBasisGetNumComponents(basis_fine, &num_comp));
2519     CeedCall(CeedBasisGetNumNodes(basis_fine, &num_nodes_f));
2520     CeedCall(CeedElemRestrictionGetElementSize(rstr_coarse, &num_nodes_c));
2521     CeedCall(CeedCalloc(num_nodes_f * dim, &q_ref));
2522     CeedCall(CeedCalloc(num_nodes_f, &q_weight));
2523     CeedCall(CeedCalloc(num_nodes_f * num_nodes_c * dim, &grad));
2524     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));
2525     CeedCall(CeedFree(&q_ref));
2526     CeedCall(CeedFree(&q_weight));
2527     CeedCall(CeedFree(&grad));
2528   }
2529 
2530   // Core code
2531   CeedCall(CeedSingleOperatorMultigridLevel(op_fine, p_mult_fine, rstr_coarse, basis_coarse, basis_c_to_f, op_coarse, op_prolong, op_restrict));
2532   return CEED_ERROR_SUCCESS;
2533 }
2534 
2535 /**
2536   @brief Build a FDM based approximate inverse for each element for a `CeedOperator`.
2537 
2538   This returns a `CeedOperator` and `CeedVector` to apply a Fast Diagonalization Method based approximate inverse.
2539   This function obtains the simultaneous diagonalization for the 1D mass and Laplacian operators, \f$M = V^T V, K = V^T S V\f$.
2540   The assembled `CeedQFunction` is used to modify the eigenvalues from simultaneous diagonalization and obtain an approximate inverse of the form \f$V^T \hat S V\f$.
2541   The `CeedOperator` must be linear and non-composite.
2542   The associated `CeedQFunction` must therefore also be linear.
2543 
2544   Note: Calling this function asserts that setup is complete and sets the `CeedOperator` as immutable.
2545 
2546   @param[in]  op      `CeedOperator` to create element inverses
2547   @param[out] fdm_inv `CeedOperator` to apply the action of a FDM based inverse for each element
2548   @param[in]  request Address of @ref CeedRequest for non-blocking completion, else @ref CEED_REQUEST_IMMEDIATE
2549 
2550   @return An error code: 0 - success, otherwise - failure
2551 
2552   @ref User
2553 **/
2554 int CeedOperatorCreateFDMElementInverse(CeedOperator op, CeedOperator *fdm_inv, CeedRequest *request) {
2555   Ceed                 ceed, ceed_parent;
2556   bool                 interp = false, grad = false, is_tensor_basis = true;
2557   CeedInt              num_input_fields, P_1d, Q_1d, num_nodes, num_qpts, dim, num_comp = 1, num_elem = 1;
2558   CeedSize             l_size = 1;
2559   CeedScalar          *mass, *laplace, *x, *fdm_interp, *lambda, *elem_avg;
2560   const CeedScalar    *interp_1d, *grad_1d, *q_weight_1d;
2561   CeedVector           q_data;
2562   CeedElemRestriction  rstr  = NULL, rstr_qd_i;
2563   CeedBasis            basis = NULL, fdm_basis;
2564   CeedQFunctionContext ctx_fdm;
2565   CeedQFunctionField  *qf_fields;
2566   CeedQFunction        qf, qf_fdm;
2567   CeedOperatorField   *op_fields;
2568 
2569   CeedCall(CeedOperatorCheckReady(op));
2570 
2571   if (op->CreateFDMElementInverse) {
2572     // Backend version
2573     CeedCall(op->CreateFDMElementInverse(op, fdm_inv, request));
2574     return CEED_ERROR_SUCCESS;
2575   } else {
2576     // Operator fallback
2577     CeedOperator op_fallback;
2578 
2579     CeedCall(CeedOperatorGetFallback(op, &op_fallback));
2580     if (op_fallback) {
2581       CeedCall(CeedOperatorCreateFDMElementInverse(op_fallback, fdm_inv, request));
2582       return CEED_ERROR_SUCCESS;
2583     }
2584   }
2585 
2586   // Default interface implementation
2587   CeedCall(CeedOperatorGetCeed(op, &ceed));
2588   CeedCall(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
2589   CeedCall(CeedOperatorGetQFunction(op, &qf));
2590 
2591   // Determine active input basis
2592   CeedCall(CeedOperatorGetFields(op, &num_input_fields, &op_fields, NULL, NULL));
2593   CeedCall(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
2594   for (CeedInt i = 0; i < num_input_fields; i++) {
2595     CeedVector vec;
2596 
2597     CeedCall(CeedOperatorFieldGetVector(op_fields[i], &vec));
2598     if (vec == CEED_VECTOR_ACTIVE) {
2599       CeedEvalMode eval_mode;
2600 
2601       CeedCall(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
2602       interp = interp || eval_mode == CEED_EVAL_INTERP;
2603       grad   = grad || eval_mode == CEED_EVAL_GRAD;
2604       CeedCall(CeedOperatorFieldGetBasis(op_fields[i], &basis));
2605       CeedCall(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr));
2606     }
2607   }
2608   CeedCheck(basis, ceed, CEED_ERROR_BACKEND, "No active field set");
2609   CeedCall(CeedBasisGetNumNodes1D(basis, &P_1d));
2610   CeedCall(CeedBasisGetNumNodes(basis, &num_nodes));
2611   CeedCall(CeedBasisGetNumQuadraturePoints1D(basis, &Q_1d));
2612   CeedCall(CeedBasisGetNumQuadraturePoints(basis, &num_qpts));
2613   CeedCall(CeedBasisGetDimension(basis, &dim));
2614   CeedCall(CeedBasisGetNumComponents(basis, &num_comp));
2615   CeedCall(CeedElemRestrictionGetNumElements(rstr, &num_elem));
2616   CeedCall(CeedElemRestrictionGetLVectorSize(rstr, &l_size));
2617 
2618   // Build and diagonalize 1D Mass and Laplacian
2619   CeedCall(CeedBasisIsTensor(basis, &is_tensor_basis));
2620   CeedCheck(is_tensor_basis, ceed, CEED_ERROR_BACKEND, "FDMElementInverse only supported for tensor bases");
2621   CeedCall(CeedCalloc(P_1d * P_1d, &mass));
2622   CeedCall(CeedCalloc(P_1d * P_1d, &laplace));
2623   CeedCall(CeedCalloc(P_1d * P_1d, &x));
2624   CeedCall(CeedCalloc(P_1d * P_1d, &fdm_interp));
2625   CeedCall(CeedCalloc(P_1d, &lambda));
2626   // -- Build matrices
2627   CeedCall(CeedBasisGetInterp1D(basis, &interp_1d));
2628   CeedCall(CeedBasisGetGrad1D(basis, &grad_1d));
2629   CeedCall(CeedBasisGetQWeights(basis, &q_weight_1d));
2630   CeedCall(CeedBuildMassLaplace(interp_1d, grad_1d, q_weight_1d, P_1d, Q_1d, dim, mass, laplace));
2631 
2632   // -- Diagonalize
2633   CeedCall(CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P_1d));
2634   CeedCall(CeedFree(&mass));
2635   CeedCall(CeedFree(&laplace));
2636   for (CeedInt i = 0; i < P_1d; i++) {
2637     for (CeedInt j = 0; j < P_1d; j++) fdm_interp[i + j * P_1d] = x[j + i * P_1d];
2638   }
2639   CeedCall(CeedFree(&x));
2640 
2641   {
2642     CeedInt             layout[3], num_modes = (interp ? 1 : 0) + (grad ? dim : 0);
2643     CeedScalar          max_norm = 0;
2644     const CeedScalar   *assembled_array, *q_weight_array;
2645     CeedVector          assembled = NULL, q_weight;
2646     CeedElemRestriction rstr_qf   = NULL;
2647 
2648     // Assemble QFunction
2649     CeedCall(CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembled, &rstr_qf, request));
2650     CeedCall(CeedElemRestrictionGetELayout(rstr_qf, layout));
2651     CeedCall(CeedElemRestrictionDestroy(&rstr_qf));
2652     CeedCall(CeedVectorNorm(assembled, CEED_NORM_MAX, &max_norm));
2653 
2654     // Calculate element averages
2655     CeedCall(CeedVectorCreate(ceed_parent, num_qpts, &q_weight));
2656     CeedCall(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_weight));
2657     CeedCall(CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembled_array));
2658     CeedCall(CeedVectorGetArrayRead(q_weight, CEED_MEM_HOST, &q_weight_array));
2659     CeedCall(CeedCalloc(num_elem, &elem_avg));
2660     const CeedScalar qf_value_bound = max_norm * 100 * CEED_EPSILON;
2661 
2662     for (CeedInt e = 0; e < num_elem; e++) {
2663       CeedInt count = 0;
2664 
2665       for (CeedInt q = 0; q < num_qpts; q++) {
2666         for (CeedInt i = 0; i < num_comp * num_comp * num_modes * num_modes; i++) {
2667           if (fabs(assembled_array[q * layout[0] + i * layout[1] + e * layout[2]]) > qf_value_bound) {
2668             elem_avg[e] += assembled_array[q * layout[0] + i * layout[1] + e * layout[2]] / q_weight_array[q];
2669             count++;
2670           }
2671         }
2672       }
2673       if (count) {
2674         elem_avg[e] /= count;
2675       } else {
2676         elem_avg[e] = 1.0;
2677       }
2678     }
2679     CeedCall(CeedVectorRestoreArrayRead(assembled, &assembled_array));
2680     CeedCall(CeedVectorDestroy(&assembled));
2681     CeedCall(CeedVectorRestoreArrayRead(q_weight, &q_weight_array));
2682     CeedCall(CeedVectorDestroy(&q_weight));
2683   }
2684 
2685   // Build FDM diagonal
2686   {
2687     CeedScalar *q_data_array, *fdm_diagonal;
2688 
2689     CeedCall(CeedCalloc(num_comp * num_nodes, &fdm_diagonal));
2690     const CeedScalar fdm_diagonal_bound = num_nodes * CEED_EPSILON;
2691     for (CeedInt c = 0; c < num_comp; c++) {
2692       for (CeedInt n = 0; n < num_nodes; n++) {
2693         if (interp) fdm_diagonal[c * num_nodes + n] = 1.0;
2694         if (grad) {
2695           for (CeedInt d = 0; d < dim; d++) {
2696             CeedInt i = (n / CeedIntPow(P_1d, d)) % P_1d;
2697             fdm_diagonal[c * num_nodes + n] += lambda[i];
2698           }
2699         }
2700         if (fabs(fdm_diagonal[c * num_nodes + n]) < fdm_diagonal_bound) fdm_diagonal[c * num_nodes + n] = fdm_diagonal_bound;
2701       }
2702     }
2703     CeedCall(CeedVectorCreate(ceed_parent, num_elem * num_comp * num_nodes, &q_data));
2704     CeedCall(CeedVectorSetValue(q_data, 0.0));
2705     CeedCall(CeedVectorGetArrayWrite(q_data, CEED_MEM_HOST, &q_data_array));
2706     for (CeedInt e = 0; e < num_elem; e++) {
2707       for (CeedInt c = 0; c < num_comp; c++) {
2708         for (CeedInt n = 0; n < num_nodes; n++)
2709           q_data_array[(e * num_comp + c) * num_nodes + n] = 1. / (elem_avg[e] * fdm_diagonal[c * num_nodes + n]);
2710       }
2711     }
2712     CeedCall(CeedFree(&elem_avg));
2713     CeedCall(CeedFree(&fdm_diagonal));
2714     CeedCall(CeedVectorRestoreArray(q_data, &q_data_array));
2715   }
2716 
2717   // Setup FDM operator
2718   // -- Basis
2719   {
2720     CeedScalar *grad_dummy, *q_ref_dummy, *q_weight_dummy;
2721 
2722     CeedCall(CeedCalloc(P_1d * P_1d, &grad_dummy));
2723     CeedCall(CeedCalloc(P_1d, &q_ref_dummy));
2724     CeedCall(CeedCalloc(P_1d, &q_weight_dummy));
2725     CeedCall(CeedBasisCreateTensorH1(ceed_parent, dim, num_comp, P_1d, P_1d, fdm_interp, grad_dummy, q_ref_dummy, q_weight_dummy, &fdm_basis));
2726     CeedCall(CeedFree(&fdm_interp));
2727     CeedCall(CeedFree(&grad_dummy));
2728     CeedCall(CeedFree(&q_ref_dummy));
2729     CeedCall(CeedFree(&q_weight_dummy));
2730     CeedCall(CeedFree(&lambda));
2731   }
2732 
2733   // -- Restriction
2734   {
2735     CeedInt strides[3] = {1, num_nodes, num_nodes * num_comp};
2736     CeedCall(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, num_nodes, num_comp, num_elem * num_comp * num_nodes, strides, &rstr_qd_i));
2737   }
2738 
2739   // -- QFunction
2740   CeedCall(CeedQFunctionCreateInteriorByName(ceed_parent, "Scale", &qf_fdm));
2741   CeedCall(CeedQFunctionAddInput(qf_fdm, "input", num_comp, CEED_EVAL_INTERP));
2742   CeedCall(CeedQFunctionAddInput(qf_fdm, "scale", num_comp, CEED_EVAL_NONE));
2743   CeedCall(CeedQFunctionAddOutput(qf_fdm, "output", num_comp, CEED_EVAL_INTERP));
2744   CeedCall(CeedQFunctionSetUserFlopsEstimate(qf_fdm, num_comp));
2745 
2746   // -- QFunction context
2747   {
2748     CeedInt *num_comp_data;
2749 
2750     CeedCall(CeedCalloc(1, &num_comp_data));
2751     num_comp_data[0] = num_comp;
2752     CeedCall(CeedQFunctionContextCreate(ceed, &ctx_fdm));
2753     CeedCall(CeedQFunctionContextSetData(ctx_fdm, CEED_MEM_HOST, CEED_OWN_POINTER, sizeof(*num_comp_data), num_comp_data));
2754   }
2755   CeedCall(CeedQFunctionSetContext(qf_fdm, ctx_fdm));
2756   CeedCall(CeedQFunctionContextDestroy(&ctx_fdm));
2757 
2758   // -- Operator
2759   CeedCall(CeedOperatorCreate(ceed_parent, qf_fdm, NULL, NULL, fdm_inv));
2760   CeedCall(CeedOperatorSetField(*fdm_inv, "input", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2761   CeedCall(CeedOperatorSetField(*fdm_inv, "scale", rstr_qd_i, CEED_BASIS_NONE, q_data));
2762   CeedCall(CeedOperatorSetField(*fdm_inv, "output", rstr, fdm_basis, CEED_VECTOR_ACTIVE));
2763 
2764   // Cleanup
2765   CeedCall(CeedVectorDestroy(&q_data));
2766   CeedCall(CeedBasisDestroy(&fdm_basis));
2767   CeedCall(CeedElemRestrictionDestroy(&rstr_qd_i));
2768   CeedCall(CeedQFunctionDestroy(&qf_fdm));
2769   return CEED_ERROR_SUCCESS;
2770 }
2771 
2772 /// @}
2773