xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 2247a93f19c75a71369fb56e8f7b7446bda8ddb1)
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.h>
9 #include <ceed/backend.h>
10 #include <stdbool.h>
11 #include <stddef.h>
12 #include <stdint.h>
13 
14 #include "ceed-ref.h"
15 
16 //------------------------------------------------------------------------------
17 // Setup Input/Output Fields
18 //------------------------------------------------------------------------------
19 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
20                                        CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
21   Ceed                ceed;
22   CeedSize            e_size, q_size;
23   CeedInt             num_comp, size, P;
24   CeedQFunctionField *qf_fields;
25   CeedOperatorField  *op_fields;
26 
27   {
28     Ceed ceed_parent;
29 
30     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
31     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
32     if (ceed_parent) ceed = ceed_parent;
33   }
34   if (is_input) {
35     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
36     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
37   } else {
38     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
39     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
40   }
41 
42   // Loop over fields
43   for (CeedInt i = 0; i < num_fields; i++) {
44     CeedEvalMode        eval_mode;
45     CeedElemRestriction elem_rstr;
46     CeedBasis           basis;
47 
48     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
49     if (eval_mode != CEED_EVAL_WEIGHT) {
50       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
51       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
52     }
53 
54     switch (eval_mode) {
55       case CEED_EVAL_NONE:
56         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
57         q_size = (CeedSize)Q * size;
58         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
59         break;
60       case CEED_EVAL_INTERP:
61       case CEED_EVAL_GRAD:
62       case CEED_EVAL_DIV:
63       case CEED_EVAL_CURL:
64         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
65         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
66         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
67         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
68         e_size = (CeedSize)P * num_comp;
69         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
70         q_size = (CeedSize)Q * size;
71         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
72         break;
73       case CEED_EVAL_WEIGHT:  // Only on input fields
74         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
75         q_size = (CeedSize)Q;
76         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
77         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_vecs[i]));
78         break;
79     }
80   }
81   return CEED_ERROR_SUCCESS;
82 }
83 
84 //------------------------------------------------------------------------------
85 // Setup Operator
86 //------------------------------------------------------------------------------/*
87 static int CeedOperatorSetup_Ref(CeedOperator op) {
88   bool                is_setup_done;
89   Ceed                ceed;
90   CeedInt             Q, num_input_fields, num_output_fields;
91   CeedQFunctionField *qf_input_fields, *qf_output_fields;
92   CeedQFunction       qf;
93   CeedOperatorField  *op_input_fields, *op_output_fields;
94   CeedOperator_Ref   *impl;
95 
96   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
97   if (is_setup_done) return CEED_ERROR_SUCCESS;
98 
99   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
100   CeedCallBackend(CeedOperatorGetData(op, &impl));
101   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
102   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
103   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
104   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
105   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
106 
107   // Allocate
108   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
109 
110   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
111   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
112   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
113   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
114   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
115 
116   impl->num_inputs  = num_input_fields;
117   impl->num_outputs = num_output_fields;
118 
119   // Set up infield and outfield e_vecs and q_vecs
120   // Infields
121   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
122   // Outfields
123   CeedCallBackend(
124       CeedOperatorSetupFields_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
125 
126   // Identity QFunctions
127   if (impl->is_identity_qf) {
128     CeedEvalMode        in_mode, out_mode;
129     CeedQFunctionField *in_fields, *out_fields;
130 
131     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
132     CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
133     CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));
134 
135     if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
136       impl->is_identity_rstr_op = true;
137     } else {
138       CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
139     }
140   }
141 
142   CeedCallBackend(CeedOperatorSetSetupDone(op));
143   return CEED_ERROR_SUCCESS;
144 }
145 
146 //------------------------------------------------------------------------------
147 // Setup Operator Inputs
148 //------------------------------------------------------------------------------
149 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
150                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
151                                               CeedOperator_Ref *impl, CeedRequest *request) {
152   for (CeedInt i = 0; i < num_input_fields; i++) {
153     uint64_t            state;
154     CeedEvalMode        eval_mode;
155     CeedVector          vec;
156     CeedElemRestriction elem_rstr;
157 
158     // Get input vector
159     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
160     if (vec == CEED_VECTOR_ACTIVE) {
161       if (skip_active) continue;
162       else vec = in_vec;
163     }
164 
165     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
166     // Restrict and Evec
167     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
168     } else {
169       // Restrict
170       CeedCallBackend(CeedVectorGetState(vec, &state));
171       // Skip restriction if input is unchanged
172       if (state != impl->input_states[i] || vec == in_vec) {
173         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
174         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
175         impl->input_states[i] = state;
176       }
177       // Get evec
178       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
179     }
180   }
181   return CEED_ERROR_SUCCESS;
182 }
183 
184 //------------------------------------------------------------------------------
185 // Input Basis Action
186 //------------------------------------------------------------------------------
187 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
188                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
189                                              CeedOperator_Ref *impl) {
190   for (CeedInt i = 0; i < num_input_fields; i++) {
191     CeedInt             elem_size, size, num_comp;
192     CeedEvalMode        eval_mode;
193     CeedElemRestriction elem_rstr;
194     CeedBasis           basis;
195 
196     // Skip active input
197     if (skip_active) {
198       CeedVector vec;
199 
200       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
201       if (vec == CEED_VECTOR_ACTIVE) continue;
202     }
203     // Get elem_size, eval_mode, size
204     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
205     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
206     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
207     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
208     // Basis action
209     switch (eval_mode) {
210       case CEED_EVAL_NONE:
211         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][e * Q * size]));
212         break;
213       case CEED_EVAL_INTERP:
214       case CEED_EVAL_GRAD:
215       case CEED_EVAL_DIV:
216       case CEED_EVAL_CURL:
217         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
218         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
219         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][e * elem_size * num_comp]));
220         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
221         break;
222       case CEED_EVAL_WEIGHT:
223         break;  // No action
224     }
225   }
226   return CEED_ERROR_SUCCESS;
227 }
228 
229 //------------------------------------------------------------------------------
230 // Output Basis Action
231 //------------------------------------------------------------------------------
232 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
233                                               CeedInt num_input_fields, CeedInt num_output_fields, CeedOperator op,
234                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
235   for (CeedInt i = 0; i < num_output_fields; i++) {
236     CeedInt             elem_size, num_comp;
237     CeedEvalMode        eval_mode;
238     CeedElemRestriction elem_rstr;
239     CeedBasis           basis;
240 
241     // Get elem_size, eval_mode
242     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
243     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
244     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
245     // Basis action
246     switch (eval_mode) {
247       case CEED_EVAL_NONE:
248         break;  // No action
249       case CEED_EVAL_INTERP:
250       case CEED_EVAL_GRAD:
251       case CEED_EVAL_DIV:
252       case CEED_EVAL_CURL:
253         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
254         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
255         CeedCallBackend(
256             CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][e * elem_size * num_comp]));
257         CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
258         break;
259       // LCOV_EXCL_START
260       case CEED_EVAL_WEIGHT: {
261         Ceed ceed;
262 
263         CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
264         return CeedError(ceed, CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
265         // LCOV_EXCL_STOP
266       }
267     }
268   }
269   return CEED_ERROR_SUCCESS;
270 }
271 
272 //------------------------------------------------------------------------------
273 // Restore Input Vectors
274 //------------------------------------------------------------------------------
275 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
276                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
277   for (CeedInt i = 0; i < num_input_fields; i++) {
278     CeedEvalMode eval_mode;
279 
280     // Skip active inputs
281     if (skip_active) {
282       CeedVector vec;
283 
284       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
285       if (vec == CEED_VECTOR_ACTIVE) continue;
286     }
287     // Restore input
288     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
289     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
290     } else {
291       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
292     }
293   }
294   return CEED_ERROR_SUCCESS;
295 }
296 
297 //------------------------------------------------------------------------------
298 // Operator Apply
299 //------------------------------------------------------------------------------
300 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
301   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
302   CeedEvalMode        eval_mode;
303   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
304   CeedQFunctionField *qf_input_fields, *qf_output_fields;
305   CeedQFunction       qf;
306   CeedOperatorField  *op_input_fields, *op_output_fields;
307   CeedOperator_Ref   *impl;
308 
309   CeedCallBackend(CeedOperatorGetData(op, &impl));
310   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
311   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
312   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
313   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
314   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
315 
316   // Setup
317   CeedCallBackend(CeedOperatorSetup_Ref(op));
318 
319   // Restriction only operator
320   if (impl->is_identity_rstr_op) {
321     CeedElemRestriction elem_rstr;
322 
323     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
324     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
325     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
326     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
327     return CEED_ERROR_SUCCESS;
328   }
329 
330   // Input Evecs and Restriction
331   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
332 
333   // Output Evecs
334   for (CeedInt i = 0; i < num_output_fields; i++) {
335     CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
336   }
337 
338   // Loop through elements
339   for (CeedInt e = 0; e < num_elem; e++) {
340     // Output pointers
341     for (CeedInt i = 0; i < num_output_fields; i++) {
342       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
343       if (eval_mode == CEED_EVAL_NONE) {
344         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
345         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][e * Q * size]));
346       }
347     }
348 
349     // Input basis apply
350     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
351 
352     // Q function
353     if (!impl->is_identity_qf) {
354       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
355     }
356 
357     // Output basis apply
358     CeedCallBackend(
359         CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields, op, e_data_full, impl));
360   }
361 
362   // Output restriction
363   for (CeedInt i = 0; i < num_output_fields; i++) {
364     CeedVector          vec;
365     CeedElemRestriction elem_rstr;
366 
367     // Restore Evec
368     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
369     // Get output vector
370     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
371     // Active
372     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
373     // Restrict
374     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
375     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
376   }
377 
378   // Restore input arrays
379   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
380   return CEED_ERROR_SUCCESS;
381 }
382 
383 //------------------------------------------------------------------------------
384 // Core code for assembling linear QFunction
385 //------------------------------------------------------------------------------
386 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
387                                                               CeedRequest *request) {
388   Ceed                ceed, ceed_parent;
389   CeedSize            q_size;
390   CeedInt             num_active_in, num_active_out, Q, num_elem, num_input_fields, num_output_fields, size;
391   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
392   CeedVector         *active_in;
393   CeedQFunctionField *qf_input_fields, *qf_output_fields;
394   CeedQFunction       qf;
395   CeedOperatorField  *op_input_fields, *op_output_fields;
396   CeedOperator_Ref   *impl;
397 
398   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
399   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
400   CeedCallBackend(CeedOperatorGetData(op, &impl));
401   active_in     = impl->qf_active_in;
402   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
403   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
404   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
405   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
406   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
407   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
408 
409   // Setup
410   CeedCallBackend(CeedOperatorSetup_Ref(op));
411 
412   // Check for restriction only operator
413   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
414 
415   // Input Evecs and Restriction
416   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
417 
418   // Count number of active input fields
419   if (!num_active_in) {
420     for (CeedInt i = 0; i < num_input_fields; i++) {
421       CeedScalar *q_vec_array;
422       CeedVector  vec;
423 
424       // Get input vector
425       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
426       // Check if active input
427       if (vec == CEED_VECTOR_ACTIVE) {
428         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
429         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
430         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
431         CeedCallBackend(CeedRealloc(num_active_in + size, &active_in));
432         for (CeedInt field = 0; field < size; field++) {
433           q_size = (CeedSize)Q;
434           CeedCallBackend(CeedVectorCreate(ceed_parent, q_size, &active_in[num_active_in + field]));
435           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * Q]));
436         }
437         num_active_in += size;
438         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
439       }
440     }
441     impl->num_active_in = num_active_in;
442     impl->qf_active_in  = active_in;
443   }
444 
445   // Count number of active output fields
446   if (!num_active_out) {
447     for (CeedInt i = 0; i < num_output_fields; i++) {
448       CeedVector vec;
449 
450       // Get output vector
451       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
452       // Check if active output
453       if (vec == CEED_VECTOR_ACTIVE) {
454         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
455         num_active_out += size;
456       }
457     }
458     impl->num_active_out = num_active_out;
459   }
460 
461   // Check sizes
462   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
463 
464   // Build objects if needed
465   if (build_objects) {
466     const CeedSize l_size     = (CeedSize)num_elem * Q * num_active_in * num_active_out;
467     CeedInt        strides[3] = {1, Q, num_active_in * num_active_out * Q}; /* *NOPAD* */
468 
469     // Create output restriction
470     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, num_active_in * num_active_out,
471                                                      num_active_in * num_active_out * num_elem * Q, strides, rstr));
472     // Create assembled vector
473     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
474   }
475   // Clear output vector
476   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
477   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
478 
479   // Loop through elements
480   for (CeedInt e = 0; e < num_elem; e++) {
481     // Input basis apply
482     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
483 
484     // Assemble QFunction
485     for (CeedInt in = 0; in < num_active_in; in++) {
486       // Set Inputs
487       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
488       if (num_active_in > 1) {
489         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
490       }
491       if (!impl->is_identity_qf) {
492         // Set Outputs
493         for (CeedInt out = 0; out < num_output_fields; out++) {
494           CeedVector vec;
495 
496           // Get output vector
497           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
498           // Check if active output
499           if (vec == CEED_VECTOR_ACTIVE) {
500             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
501             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &size));
502             assembled_array += size * Q;  // Advance the pointer by the size of the output
503           }
504         }
505         // Apply QFunction
506         CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
507       } else {
508         const CeedScalar *q_vec_array;
509 
510         // Copy Identity Outputs
511         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &size));
512         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
513         for (CeedInt i = 0; i < size * Q; i++) assembled_array[i] = q_vec_array[i];
514         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
515         assembled_array += size * Q;
516       }
517     }
518   }
519 
520   // Un-set output Qvecs to prevent accidental overwrite of Assembled
521   if (!impl->is_identity_qf) {
522     for (CeedInt out = 0; out < num_output_fields; out++) {
523       CeedVector vec;
524 
525       // Get output vector
526       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
527       // Check if active output
528       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
529         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
530       }
531     }
532   }
533 
534   // Restore input arrays
535   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
536 
537   // Restore output
538   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
539   return CEED_ERROR_SUCCESS;
540 }
541 
542 //------------------------------------------------------------------------------
543 // Assemble Linear QFunction
544 //------------------------------------------------------------------------------
545 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
546   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
547 }
548 
549 //------------------------------------------------------------------------------
550 // Update Assembled Linear QFunction
551 //------------------------------------------------------------------------------
552 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
553   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
554 }
555 
556 //------------------------------------------------------------------------------
557 // Setup Input/Output Fields
558 //------------------------------------------------------------------------------
559 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
560                                                CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
561   Ceed                ceed;
562   CeedSize            e_size, q_size;
563   CeedInt             max_num_points, num_comp, size, P;
564   CeedQFunctionField *qf_fields;
565   CeedOperatorField  *op_fields;
566 
567   {
568     Ceed ceed_parent;
569 
570     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
571     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
572     if (ceed_parent) ceed = ceed_parent;
573   }
574   if (is_input) {
575     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
576     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
577   } else {
578     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
579     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
580   }
581 
582   // Get max number of points
583   {
584     CeedInt             dim;
585     CeedElemRestriction rstr_points = NULL;
586     CeedOperator_Ref   *impl;
587 
588     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
589     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
590     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
591     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
592     CeedCallBackend(CeedOperatorGetData(op, &impl));
593     if (is_input) CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
594   }
595 
596   // Loop over fields
597   for (CeedInt i = 0; i < num_fields; i++) {
598     CeedEvalMode eval_mode;
599     CeedBasis    basis;
600 
601     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
602     if (eval_mode != CEED_EVAL_WEIGHT) {
603       CeedRestrictionType rstr_type;
604       CeedElemRestriction elem_rstr;
605 
606       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
607       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
608       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
609       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
610     }
611 
612     switch (eval_mode) {
613       case CEED_EVAL_NONE: {
614         CeedVector vec;
615 
616         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
617         e_size = (CeedSize)max_num_points * size;
618         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
619         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
620         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
621           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
622         } else {
623           q_size = (CeedSize)max_num_points * size;
624           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
625         }
626         break;
627       }
628       case CEED_EVAL_INTERP:
629       case CEED_EVAL_GRAD:
630       case CEED_EVAL_DIV:
631       case CEED_EVAL_CURL:
632         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
633         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
634         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
635         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
636         e_size = (CeedSize)P * num_comp;
637         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
638         q_size = (CeedSize)max_num_points * size;
639         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
640         break;
641       case CEED_EVAL_WEIGHT:  // Only on input fields
642         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
643         q_size = (CeedSize)max_num_points;
644         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
645         CeedCallBackend(
646             CeedBasisApplyAtPoints(basis, max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
647         break;
648     }
649     if (is_input && e_vecs[i]) {
650       CeedCallBackend(CeedVectorSetArray(e_vecs[i], CEED_MEM_HOST, CEED_COPY_VALUES, NULL));
651     }
652   }
653   return CEED_ERROR_SUCCESS;
654 }
655 
656 //------------------------------------------------------------------------------
657 // Setup Operator
658 //------------------------------------------------------------------------------
659 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
660   bool                is_setup_done;
661   Ceed                ceed;
662   CeedInt             Q, num_input_fields, num_output_fields;
663   CeedQFunctionField *qf_input_fields, *qf_output_fields;
664   CeedQFunction       qf;
665   CeedOperatorField  *op_input_fields, *op_output_fields;
666   CeedOperator_Ref   *impl;
667 
668   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
669   if (is_setup_done) return CEED_ERROR_SUCCESS;
670 
671   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
672   CeedCallBackend(CeedOperatorGetData(op, &impl));
673   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
674   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
675   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
676   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
677   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
678 
679   // Allocate
680   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
681 
682   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
683   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
684   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
685   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
686   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
687 
688   impl->num_inputs  = num_input_fields;
689   impl->num_outputs = num_output_fields;
690 
691   // Set up infield and outfield pointer arrays
692   // Infields
693   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
694   // Outfields
695   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
696                                                       num_output_fields, Q));
697 
698   // Identity QFunctions
699   if (impl->is_identity_qf) {
700     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
701     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
702   }
703 
704   CeedCallBackend(CeedOperatorSetSetupDone(op));
705   return CEED_ERROR_SUCCESS;
706 }
707 
708 //------------------------------------------------------------------------------
709 // Setup Input Fields
710 //------------------------------------------------------------------------------
711 static inline int CeedOperatorSetupInputsAtPoints_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields,
712                                                       CeedOperatorField *op_input_fields, CeedVector in_vec, CeedScalar *e_data[2 * CEED_FIELD_MAX],
713                                                       CeedOperator_Ref *impl, CeedRequest *request) {
714   for (CeedInt i = 0; i < num_input_fields; i++) {
715     uint64_t            state;
716     CeedEvalMode        eval_mode;
717     CeedVector          vec;
718     CeedElemRestriction elem_rstr;
719 
720     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
721     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
722     } else {
723       // Get input vector
724       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
725       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
726       if (vec != CEED_VECTOR_ACTIVE) {
727         // Restrict
728         CeedCallBackend(CeedVectorGetState(vec, &state));
729         if (state != impl->input_states[i]) {
730           CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
731           impl->input_states[i] = state;
732         }
733         // Get evec
734         CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data[i]));
735       }
736     }
737   }
738   return CEED_ERROR_SUCCESS;
739 }
740 
741 //------------------------------------------------------------------------------
742 // Input Basis Action
743 //------------------------------------------------------------------------------
744 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
745                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
746                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
747                                                      CeedOperator_Ref *impl, CeedRequest *request) {
748   for (CeedInt i = 0; i < num_input_fields; i++) {
749     bool                is_active_input = false;
750     CeedInt             elem_size, size, num_comp;
751     CeedRestrictionType rstr_type;
752     CeedEvalMode        eval_mode;
753     CeedVector          vec;
754     CeedElemRestriction elem_rstr;
755     CeedBasis           basis;
756 
757     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
758     // Skip active input
759     is_active_input = vec == CEED_VECTOR_ACTIVE;
760     if (skip_active && is_active_input) continue;
761 
762     // Get elem_size, eval_mode, size
763     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
764     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
765     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
766     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
767     // Restrict block active input
768     if (is_active_input) {
769       if (rstr_type == CEED_RESTRICTION_POINTS) {
770         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
771       } else {
772         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
773       }
774     }
775     // Basis action
776     switch (eval_mode) {
777       case CEED_EVAL_NONE:
778         if (!is_active_input) {
779           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
780         }
781         break;
782       // Note - these basis eval modes require FEM fields
783       case CEED_EVAL_INTERP:
784       case CEED_EVAL_GRAD:
785       case CEED_EVAL_DIV:
786       case CEED_EVAL_CURL:
787         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
788         if (!is_active_input) {
789           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
790           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
791           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][e * elem_size * num_comp]));
792         }
793         CeedCallBackend(
794             CeedBasisApplyAtPoints(basis, num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
795         break;
796       case CEED_EVAL_WEIGHT:
797         break;  // No action
798     }
799   }
800   return CEED_ERROR_SUCCESS;
801 }
802 
803 //------------------------------------------------------------------------------
804 // Output Basis Action
805 //------------------------------------------------------------------------------
806 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
807                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
808                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
809                                                       CeedRequest *request) {
810   for (CeedInt i = 0; i < num_output_fields; i++) {
811     CeedRestrictionType rstr_type;
812     CeedEvalMode        eval_mode;
813     CeedVector          vec;
814     CeedElemRestriction elem_rstr;
815     CeedBasis           basis;
816 
817     // Get elem_size, eval_mode, size
818     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
819     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
820     // Basis action
821     switch (eval_mode) {
822       case CEED_EVAL_NONE:
823         break;  // No action
824       case CEED_EVAL_INTERP:
825       case CEED_EVAL_GRAD:
826       case CEED_EVAL_DIV:
827       case CEED_EVAL_CURL:
828         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
829         CeedCallBackend(
830             CeedBasisApplyAtPoints(basis, num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
831         break;
832       // LCOV_EXCL_START
833       case CEED_EVAL_WEIGHT: {
834         Ceed ceed;
835 
836         CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
837         return CeedError(ceed, CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
838         // LCOV_EXCL_STOP
839       }
840     }
841     // Restrict output block
842     // Get output vector
843     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
844     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
845     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
846     // Restrict
847     if (rstr_type == CEED_RESTRICTION_POINTS) {
848       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
849     } else {
850       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
851     }
852   }
853   return CEED_ERROR_SUCCESS;
854 }
855 
856 //------------------------------------------------------------------------------
857 // Restore Input Vectors
858 //------------------------------------------------------------------------------
859 static inline int CeedOperatorRestoreInputsAtPoints_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields,
860                                                         CeedOperatorField *op_input_fields, CeedScalar *e_data[2 * CEED_FIELD_MAX],
861                                                         CeedOperator_Ref *impl) {
862   for (CeedInt i = 0; i < num_input_fields; i++) {
863     CeedEvalMode eval_mode;
864     CeedVector   vec;
865 
866     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
867     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
868     if (eval_mode != CEED_EVAL_WEIGHT && vec != CEED_VECTOR_ACTIVE) {
869       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data[i]));
870     }
871   }
872   return CEED_ERROR_SUCCESS;
873 }
874 
875 //------------------------------------------------------------------------------
876 // Operator Apply
877 //------------------------------------------------------------------------------
878 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
879   Ceed                ceed;
880   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
881   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
882   CeedVector          point_coords               = NULL;
883   CeedElemRestriction rstr_points                = NULL;
884   CeedQFunctionField *qf_input_fields, *qf_output_fields;
885   CeedQFunction       qf;
886   CeedOperatorField  *op_input_fields, *op_output_fields;
887   CeedOperator_Ref   *impl;
888 
889   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
890   CeedCallBackend(CeedOperatorGetData(op, &impl));
891   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
892   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
893   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
894   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
895 
896   // Setup
897   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
898 
899   // Point coordinates
900   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
901 
902   // Input Evecs and Restriction
903   CeedCallBackend(CeedOperatorSetupInputsAtPoints_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, e_data, impl, request));
904 
905   // Loop through elements
906   for (CeedInt e = 0; e < num_elem; e++) {
907     CeedInt num_points;
908 
909     // Setup points for element
910     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
911     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
912 
913     // Input basis apply
914     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
915                                                        impl->point_coords_elem, false, e_data, impl, request));
916 
917     // Q function
918     if (!impl->is_identity_qf) {
919       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
920     }
921 
922     // Output basis apply and restriction
923     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
924                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
925 
926     num_points_offset += num_points;
927   }
928 
929   // Restore input arrays
930   CeedCallBackend(CeedOperatorRestoreInputsAtPoints_Ref(num_input_fields, qf_input_fields, op_input_fields, e_data, impl));
931 
932   // Cleanup point coordinates
933   CeedCallBackend(CeedVectorDestroy(&point_coords));
934   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
935   return CEED_ERROR_SUCCESS;
936 }
937 
938 //------------------------------------------------------------------------------
939 // Operator Destroy
940 //------------------------------------------------------------------------------
941 static int CeedOperatorDestroy_Ref(CeedOperator op) {
942   CeedOperator_Ref *impl;
943 
944   CeedCallBackend(CeedOperatorGetData(op, &impl));
945   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
946     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
947   }
948   CeedCallBackend(CeedFree(&impl->e_vecs_full));
949   CeedCallBackend(CeedFree(&impl->input_states));
950 
951   for (CeedInt i = 0; i < impl->num_inputs; i++) {
952     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
953     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
954   }
955   CeedCallBackend(CeedFree(&impl->e_vecs_in));
956   CeedCallBackend(CeedFree(&impl->q_vecs_in));
957 
958   for (CeedInt i = 0; i < impl->num_outputs; i++) {
959     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
960     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
961   }
962   CeedCallBackend(CeedFree(&impl->e_vecs_out));
963   CeedCallBackend(CeedFree(&impl->q_vecs_out));
964   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
965 
966   // QFunction assembly
967   for (CeedInt i = 0; i < impl->num_active_in; i++) {
968     CeedCallBackend(CeedVectorDestroy(&impl->qf_active_in[i]));
969   }
970   CeedCallBackend(CeedFree(&impl->qf_active_in));
971 
972   CeedCallBackend(CeedFree(&impl));
973   return CEED_ERROR_SUCCESS;
974 }
975 
976 //------------------------------------------------------------------------------
977 // Operator Create
978 //------------------------------------------------------------------------------
979 int CeedOperatorCreate_Ref(CeedOperator op) {
980   Ceed              ceed;
981   CeedOperator_Ref *impl;
982 
983   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
984   CeedCallBackend(CeedCalloc(1, &impl));
985   CeedCallBackend(CeedOperatorSetData(op, impl));
986   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
987   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
988   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
989   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
990   return CEED_ERROR_SUCCESS;
991 }
992 
993 //------------------------------------------------------------------------------
994 // Operator Create At Points
995 //------------------------------------------------------------------------------
996 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
997   Ceed              ceed;
998   CeedOperator_Ref *impl;
999 
1000   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1001   CeedCallBackend(CeedCalloc(1, &impl));
1002   CeedCallBackend(CeedOperatorSetData(op, impl));
1003   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1004   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1005   return CEED_ERROR_SUCCESS;
1006 }
1007 
1008 //------------------------------------------------------------------------------
1009