xref: /libCEED/backends/ref/ceed-ref-operator.c (revision debdbcfd6d1bf75f737a96117abce91cc9b450a2)
1 // Copyright (c) 2017-2025, 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, bool *skip_rstr, CeedInt *e_data_out_indices,
20                                        bool *apply_add_basis, CeedVector *e_vecs_full, CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e,
21                                        CeedInt num_fields, CeedInt Q) {
22   Ceed                ceed;
23   CeedSize            e_size, q_size;
24   CeedInt             num_comp, size, P;
25   CeedQFunctionField *qf_fields;
26   CeedOperatorField  *op_fields;
27 
28   {
29     Ceed ceed_parent;
30 
31     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
32     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
33     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
34     CeedCallBackend(CeedDestroy(&ceed_parent));
35   }
36   if (is_input) {
37     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
38     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
39   } else {
40     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
41     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
42   }
43 
44   // Loop over fields
45   for (CeedInt i = 0; i < num_fields; i++) {
46     CeedEvalMode        eval_mode;
47     CeedElemRestriction elem_rstr;
48     CeedBasis           basis;
49 
50     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
51     if (eval_mode != CEED_EVAL_WEIGHT) {
52       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
53       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
54       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
55     }
56 
57     switch (eval_mode) {
58       case CEED_EVAL_NONE:
59         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
60         q_size = (CeedSize)Q * size;
61         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
62         break;
63       case CEED_EVAL_INTERP:
64       case CEED_EVAL_GRAD:
65       case CEED_EVAL_DIV:
66       case CEED_EVAL_CURL:
67         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
68         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
69         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
70         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
71         e_size = (CeedSize)P * num_comp;
72         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
73         q_size = (CeedSize)Q * size;
74         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
75         CeedCallBackend(CeedBasisDestroy(&basis));
76         break;
77       case CEED_EVAL_WEIGHT:  // Only on input fields
78         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
79         q_size = (CeedSize)Q;
80         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
81         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_vecs[i]));
82         CeedCallBackend(CeedBasisDestroy(&basis));
83         break;
84     }
85   }
86   // Drop duplicate restrictions
87   if (is_input) {
88     for (CeedInt i = 0; i < num_fields; i++) {
89       CeedVector          vec_i;
90       CeedElemRestriction rstr_i;
91 
92       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
93       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
94       for (CeedInt j = i + 1; j < num_fields; j++) {
95         CeedVector          vec_j;
96         CeedElemRestriction rstr_j;
97 
98         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
99         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
100         if (vec_i == vec_j && rstr_i == rstr_j) {
101           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
102           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
103           skip_rstr[j] = true;
104         }
105         CeedCallBackend(CeedVectorDestroy(&vec_j));
106         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
107       }
108       CeedCallBackend(CeedVectorDestroy(&vec_i));
109       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
110     }
111   } else {
112     for (CeedInt i = num_fields - 1; i >= 0; i--) {
113       CeedVector          vec_i;
114       CeedElemRestriction rstr_i;
115 
116       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
117       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
118       for (CeedInt j = i - 1; j >= 0; j--) {
119         CeedVector          vec_j;
120         CeedElemRestriction rstr_j;
121 
122         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
123         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
124         if (vec_i == vec_j && rstr_i == rstr_j) {
125           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
126           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
127           skip_rstr[j]          = true;
128           apply_add_basis[i]    = true;
129           e_data_out_indices[j] = i;
130         }
131         CeedCallBackend(CeedVectorDestroy(&vec_j));
132         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
133       }
134       CeedCallBackend(CeedVectorDestroy(&vec_i));
135       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
136     }
137   }
138   CeedCallBackend(CeedDestroy(&ceed));
139   return CEED_ERROR_SUCCESS;
140 }
141 
142 //------------------------------------------------------------------------------
143 // Setup Operator
144 //------------------------------------------------------------------------------/*
145 static int CeedOperatorSetup_Ref(CeedOperator op) {
146   bool                is_setup_done;
147   CeedInt             Q, num_input_fields, num_output_fields;
148   CeedQFunctionField *qf_input_fields, *qf_output_fields;
149   CeedQFunction       qf;
150   CeedOperatorField  *op_input_fields, *op_output_fields;
151   CeedOperator_Ref   *impl;
152 
153   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
154   if (is_setup_done) return CEED_ERROR_SUCCESS;
155 
156   CeedCallBackend(CeedOperatorGetData(op, &impl));
157   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
158   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
159   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
160   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
161   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
162 
163   // Allocate
164   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
165 
166   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
167   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_out));
168   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_data_out_indices));
169   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->apply_add_basis_out));
170   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
171   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
172   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
173   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
174   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
175 
176   impl->num_inputs  = num_input_fields;
177   impl->num_outputs = num_output_fields;
178 
179   // Set up infield and outfield e_vecs and q_vecs
180   // Infields
181   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, true, impl->skip_rstr_in, NULL, NULL, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
182                                               num_input_fields, Q));
183   // Outfields
184   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, false, impl->skip_rstr_out, impl->e_data_out_indices, impl->apply_add_basis_out,
185                                               impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
186 
187   // Identity QFunctions
188   if (impl->is_identity_qf) {
189     CeedEvalMode        in_mode, out_mode;
190     CeedQFunctionField *in_fields, *out_fields;
191 
192     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
193     CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
194     CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));
195 
196     if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
197       impl->is_identity_rstr_op = true;
198     } else {
199       CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
200     }
201   }
202 
203   CeedCallBackend(CeedOperatorSetSetupDone(op));
204   CeedCallBackend(CeedQFunctionDestroy(&qf));
205   return CEED_ERROR_SUCCESS;
206 }
207 
208 //------------------------------------------------------------------------------
209 // Setup Operator Inputs
210 //------------------------------------------------------------------------------
211 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
212                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
213                                               CeedOperator_Ref *impl, CeedRequest *request) {
214   for (CeedInt i = 0; i < num_input_fields; i++) {
215     bool         is_active;
216     uint64_t     state;
217     CeedEvalMode eval_mode;
218     CeedVector   vec;
219 
220     // Get input vector
221     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
222     is_active = vec == CEED_VECTOR_ACTIVE;
223     if (is_active) {
224       if (skip_active) continue;
225       else vec = in_vec;
226     }
227 
228     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
229     // Restrict and Evec
230     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
231     } else {
232       // Restrict
233       CeedCallBackend(CeedVectorGetState(vec, &state));
234       // Skip restriction if input is unchanged
235       if ((state != impl->input_states[i] || vec == in_vec) && !impl->skip_rstr_in[i]) {
236         CeedElemRestriction elem_rstr;
237 
238         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
239         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
240         CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
241       }
242       impl->input_states[i] = state;
243       // Get evec
244       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
245     }
246     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
247   }
248   return CEED_ERROR_SUCCESS;
249 }
250 
251 //------------------------------------------------------------------------------
252 // Input Basis Action
253 //------------------------------------------------------------------------------
254 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
255                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
256                                              CeedOperator_Ref *impl) {
257   for (CeedInt i = 0; i < num_input_fields; i++) {
258     CeedInt             elem_size, size, num_comp;
259     CeedEvalMode        eval_mode;
260     CeedElemRestriction elem_rstr;
261     CeedBasis           basis;
262 
263     // Skip active input
264     if (skip_active) {
265       bool       is_active;
266       CeedVector vec;
267 
268       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
269       is_active = vec == CEED_VECTOR_ACTIVE;
270       CeedCallBackend(CeedVectorDestroy(&vec));
271       if (is_active) continue;
272     }
273     // Get elem_size, eval_mode, size
274     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
275     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
276     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
277     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
278     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
279     // Basis action
280     switch (eval_mode) {
281       case CEED_EVAL_NONE:
282         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * Q * size]));
283         break;
284       case CEED_EVAL_INTERP:
285       case CEED_EVAL_GRAD:
286       case CEED_EVAL_DIV:
287       case CEED_EVAL_CURL:
288         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
289         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
290         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * elem_size * num_comp]));
291         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
292         CeedCallBackend(CeedBasisDestroy(&basis));
293         break;
294       case CEED_EVAL_WEIGHT:
295         break;  // No action
296     }
297   }
298   return CEED_ERROR_SUCCESS;
299 }
300 
301 //------------------------------------------------------------------------------
302 // Output Basis Action
303 //------------------------------------------------------------------------------
304 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
305                                               CeedInt num_input_fields, CeedInt num_output_fields, bool *apply_add_basis, CeedOperator op,
306                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
307   for (CeedInt i = 0; i < num_output_fields; i++) {
308     CeedInt             elem_size, num_comp;
309     CeedEvalMode        eval_mode;
310     CeedElemRestriction elem_rstr;
311     CeedBasis           basis;
312 
313     // Get elem_size, eval_mode
314     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
315     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
316     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
317     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
318     // Basis action
319     switch (eval_mode) {
320       case CEED_EVAL_NONE:
321         break;  // No action
322       case CEED_EVAL_INTERP:
323       case CEED_EVAL_GRAD:
324       case CEED_EVAL_DIV:
325       case CEED_EVAL_CURL:
326         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
327         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
328         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER,
329                                            &e_data_full[i + num_input_fields][(CeedSize)e * elem_size * num_comp]));
330         if (apply_add_basis[i]) {
331           CeedCallBackend(CeedBasisApplyAdd(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
332         } else {
333           CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
334         }
335         CeedCallBackend(CeedBasisDestroy(&basis));
336         break;
337       // LCOV_EXCL_START
338       case CEED_EVAL_WEIGHT: {
339         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
340         // LCOV_EXCL_STOP
341       }
342     }
343   }
344   return CEED_ERROR_SUCCESS;
345 }
346 
347 //------------------------------------------------------------------------------
348 // Restore Input Vectors
349 //------------------------------------------------------------------------------
350 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
351                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
352   for (CeedInt i = 0; i < num_input_fields; i++) {
353     CeedEvalMode eval_mode;
354 
355     // Skip active inputs
356     if (skip_active) {
357       bool       is_active;
358       CeedVector vec;
359 
360       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
361       is_active = vec == CEED_VECTOR_ACTIVE;
362       CeedCallBackend(CeedVectorDestroy(&vec));
363       if (is_active) continue;
364     }
365     // Restore input
366     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
367     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
368     } else {
369       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
370     }
371   }
372   return CEED_ERROR_SUCCESS;
373 }
374 
375 //------------------------------------------------------------------------------
376 // Operator Apply
377 //------------------------------------------------------------------------------
378 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
379   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
380   CeedEvalMode        eval_mode;
381   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
382   CeedQFunctionField *qf_input_fields, *qf_output_fields;
383   CeedQFunction       qf;
384   CeedOperatorField  *op_input_fields, *op_output_fields;
385   CeedOperator_Ref   *impl;
386 
387   // Setup
388   CeedCallBackend(CeedOperatorSetup_Ref(op));
389 
390   CeedCallBackend(CeedOperatorGetData(op, &impl));
391   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
392 
393   // Restriction only operator
394   if (impl->is_identity_rstr_op) {
395     CeedElemRestriction elem_rstr;
396 
397     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
398     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
399     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
400     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
401     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
402     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
403     return CEED_ERROR_SUCCESS;
404   }
405 
406   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
407   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
408   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
409   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
410 
411   // Input Evecs and Restriction
412   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
413 
414   // Output Evecs
415   for (CeedInt i = num_output_fields - 1; i >= 0; i--) {
416     if (impl->skip_rstr_out[i]) {
417       e_data_full[i + num_input_fields] = e_data_full[impl->e_data_out_indices[i] + num_input_fields];
418     } else {
419       CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
420     }
421   }
422 
423   // Loop through elements
424   for (CeedInt e = 0; e < num_elem; e++) {
425     // Output pointers
426     for (CeedInt i = 0; i < num_output_fields; i++) {
427       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
428       if (eval_mode == CEED_EVAL_NONE) {
429         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
430         CeedCallBackend(
431             CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][(CeedSize)e * Q * size]));
432       }
433     }
434 
435     // Input basis apply
436     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
437 
438     // Q function
439     if (!impl->is_identity_qf) {
440       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
441     }
442 
443     // Output basis apply
444     CeedCallBackend(CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields,
445                                                 impl->apply_add_basis_out, op, e_data_full, impl));
446   }
447 
448   // Output restriction
449   for (CeedInt i = 0; i < num_output_fields; i++) {
450     bool                is_active;
451     CeedVector          vec;
452     CeedElemRestriction elem_rstr;
453 
454     if (impl->skip_rstr_out[i]) continue;
455     // Restore Evec
456     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
457     // Get output vector
458     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
459     // Active
460     is_active = vec == CEED_VECTOR_ACTIVE;
461     if (is_active) vec = out_vec;
462     // Restrict
463     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
464     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
465     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
466     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
467   }
468 
469   // Restore input arrays
470   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
471   CeedCallBackend(CeedQFunctionDestroy(&qf));
472   return CEED_ERROR_SUCCESS;
473 }
474 
475 //------------------------------------------------------------------------------
476 // Core code for assembling linear QFunction
477 //------------------------------------------------------------------------------
478 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
479                                                               CeedRequest *request) {
480   Ceed                ceed_parent;
481   CeedInt             qf_size_in, qf_size_out, Q, num_elem, num_input_fields, num_output_fields;
482   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
483   CeedQFunctionField *qf_input_fields, *qf_output_fields;
484   CeedQFunction       qf;
485   CeedOperatorField  *op_input_fields, *op_output_fields;
486   CeedOperator_Ref   *impl;
487 
488   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
489   CeedCallBackend(CeedOperatorGetData(op, &impl));
490   qf_size_in  = impl->qf_size_in;
491   qf_size_out = impl->qf_size_out;
492   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
493   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
494   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
495   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
496   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
497 
498   // Setup
499   CeedCallBackend(CeedOperatorSetup_Ref(op));
500 
501   // Check for restriction only operator
502   CeedCheck(!impl->is_identity_rstr_op, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
503 
504   // Input Evecs and Restriction
505   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
506 
507   // Count number of active input fields
508   if (qf_size_in == 0) {
509     for (CeedInt i = 0; i < num_input_fields; i++) {
510       CeedInt    field_size;
511       CeedVector vec;
512 
513       // Get input vector
514       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
515       // Check if active input
516       if (vec == CEED_VECTOR_ACTIVE) {
517         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
518         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
519         qf_size_in += field_size;
520       }
521       CeedCallBackend(CeedVectorDestroy(&vec));
522     }
523     CeedCheck(qf_size_in > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
524     impl->qf_size_in = qf_size_in;
525   }
526 
527   // Count number of active output fields
528   if (qf_size_out == 0) {
529     for (CeedInt i = 0; i < num_output_fields; i++) {
530       CeedInt    field_size;
531       CeedVector vec;
532 
533       // Get output vector
534       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
535       // Check if active output
536       if (vec == CEED_VECTOR_ACTIVE) {
537         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
538         qf_size_out += field_size;
539       }
540       CeedCallBackend(CeedVectorDestroy(&vec));
541     }
542     CeedCheck(qf_size_out > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
543     impl->qf_size_out = qf_size_out;
544   }
545 
546   // Build objects if needed
547   if (build_objects) {
548     const CeedSize l_size     = (CeedSize)num_elem * Q * qf_size_in * qf_size_out;
549     CeedInt        strides[3] = {1, Q, qf_size_in * qf_size_out * Q}; /* *NOPAD* */
550 
551     // Create output restriction
552     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, qf_size_in * qf_size_out,
553                                                      (CeedSize)qf_size_in * (CeedSize)qf_size_out * (CeedSize)num_elem * (CeedSize)Q, strides, rstr));
554     // Create assembled vector
555     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
556   }
557   // Clear output vector
558   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
559   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
560 
561   // Loop through elements
562   for (CeedInt e = 0; e < num_elem; e++) {
563     // Input basis apply
564     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
565 
566     // Assemble QFunction
567 
568     for (CeedInt i = 0; i < num_input_fields; i++) {
569       bool       is_active;
570       CeedInt    field_size;
571       CeedVector vec;
572 
573       // Set Inputs
574       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
575       is_active = vec == CEED_VECTOR_ACTIVE;
576       CeedCallBackend(CeedVectorDestroy(&vec));
577       if (!is_active) continue;
578       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
579       for (CeedInt field = 0; field < field_size; field++) {
580         // Set current portion of input to 1.0
581         {
582           CeedScalar *array;
583 
584           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
585           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 1.0;
586           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
587         }
588 
589         if (!impl->is_identity_qf) {
590           // Set Outputs
591           for (CeedInt out = 0; out < num_output_fields; out++) {
592             CeedVector vec;
593 
594             // Get output vector
595             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
596             // Check if active output
597             if (vec == CEED_VECTOR_ACTIVE) {
598               CeedInt field_size;
599 
600               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
601               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
602               assembled_array += field_size * Q;  // Advance the pointer by the size of the output
603             }
604             CeedCallBackend(CeedVectorDestroy(&vec));
605           }
606           // Apply QFunction
607           CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
608         } else {
609           CeedInt           field_size;
610           const CeedScalar *array;
611 
612           // Copy Identity Outputs
613           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
614           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
615           for (CeedInt j = 0; j < field_size * Q; j++) assembled_array[j] = array[j];
616           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
617           assembled_array += field_size * Q;
618         }
619         // Reset input to 0.0
620         {
621           CeedScalar *array;
622 
623           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
624           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 0.0;
625           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
626         }
627       }
628     }
629   }
630 
631   // Un-set output Qvecs to prevent accidental overwrite of Assembled
632   if (!impl->is_identity_qf) {
633     for (CeedInt out = 0; out < num_output_fields; out++) {
634       CeedVector vec;
635 
636       // Get output vector
637       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
638       // Check if active output
639       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
640         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
641       }
642       CeedCallBackend(CeedVectorDestroy(&vec));
643     }
644   }
645 
646   // Restore input arrays
647   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
648 
649   // Restore output
650   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
651   CeedCallBackend(CeedDestroy(&ceed_parent));
652   CeedCallBackend(CeedQFunctionDestroy(&qf));
653   return CEED_ERROR_SUCCESS;
654 }
655 
656 //------------------------------------------------------------------------------
657 // Assemble Linear QFunction
658 //------------------------------------------------------------------------------
659 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
660   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
661 }
662 
663 //------------------------------------------------------------------------------
664 // Update Assembled Linear QFunction
665 //------------------------------------------------------------------------------
666 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
667   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
668 }
669 
670 //------------------------------------------------------------------------------
671 // Setup Input/Output Fields
672 //------------------------------------------------------------------------------
673 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, bool *skip_rstr, bool *apply_add_basis,
674                                                CeedVector *e_vecs_full, CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields,
675                                                CeedInt Q) {
676   Ceed                ceed;
677   CeedSize            e_size, q_size;
678   CeedInt             max_num_points, num_comp, size, P;
679   CeedQFunctionField *qf_fields;
680   CeedOperatorField  *op_fields;
681 
682   {
683     Ceed ceed_parent;
684 
685     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
686     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
687     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
688     CeedCallBackend(CeedDestroy(&ceed_parent));
689   }
690   if (is_input) {
691     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
692     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
693   } else {
694     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
695     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
696   }
697 
698   // Get max number of points
699   {
700     CeedInt             dim;
701     CeedElemRestriction rstr_points = NULL;
702     CeedOperator_Ref   *impl;
703 
704     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
705     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
706     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
707     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
708     CeedCallBackend(CeedOperatorGetData(op, &impl));
709     if (is_input) {
710       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
711       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
712     }
713   }
714 
715   // Loop over fields
716   for (CeedInt i = 0; i < num_fields; i++) {
717     CeedEvalMode eval_mode;
718     CeedBasis    basis;
719 
720     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
721     if (eval_mode != CEED_EVAL_WEIGHT) {
722       CeedElemRestriction elem_rstr;
723 
724       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
725       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
726       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
727       CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
728     }
729 
730     switch (eval_mode) {
731       case CEED_EVAL_NONE: {
732         CeedVector vec;
733 
734         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
735         e_size = (CeedSize)max_num_points * size;
736         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
737         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
738         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
739           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
740         } else {
741           q_size = (CeedSize)max_num_points * size;
742           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
743         }
744         CeedCallBackend(CeedVectorDestroy(&vec));
745         break;
746       }
747       case CEED_EVAL_INTERP:
748       case CEED_EVAL_GRAD:
749       case CEED_EVAL_DIV:
750       case CEED_EVAL_CURL:
751         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
752         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
753         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
754         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
755         e_size = (CeedSize)P * num_comp;
756         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
757         q_size = (CeedSize)max_num_points * size;
758         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
759         CeedCallBackend(CeedBasisDestroy(&basis));
760         break;
761       case CEED_EVAL_WEIGHT:  // Only on input fields
762         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
763         q_size = (CeedSize)max_num_points;
764         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
765         CeedCallBackend(
766             CeedBasisApplyAtPoints(basis, 1, &max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
767         CeedCallBackend(CeedBasisDestroy(&basis));
768         break;
769     }
770     // Initialize full arrays for E-vectors and Q-vectors
771     if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
772     if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
773   }
774   // Drop duplicate restrictions
775   if (is_input) {
776     for (CeedInt i = 0; i < num_fields; i++) {
777       CeedVector          vec_i;
778       CeedElemRestriction rstr_i;
779 
780       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
781       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
782       for (CeedInt j = i + 1; j < num_fields; j++) {
783         CeedVector          vec_j;
784         CeedElemRestriction rstr_j;
785 
786         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
787         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
788         if (vec_i == vec_j && rstr_i == rstr_j) {
789           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
790           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
791           skip_rstr[j] = true;
792         }
793         CeedCallBackend(CeedVectorDestroy(&vec_j));
794         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
795       }
796       CeedCallBackend(CeedVectorDestroy(&vec_i));
797       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
798     }
799   } else {
800     for (CeedInt i = num_fields - 1; i >= 0; i--) {
801       CeedVector          vec_i;
802       CeedElemRestriction rstr_i;
803 
804       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
805       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
806       for (CeedInt j = i - 1; j >= 0; j--) {
807         CeedVector          vec_j;
808         CeedElemRestriction rstr_j;
809 
810         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
811         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
812         if (vec_i == vec_j && rstr_i == rstr_j) {
813           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
814           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
815           skip_rstr[j]       = true;
816           apply_add_basis[i] = true;
817         }
818         CeedCallBackend(CeedVectorDestroy(&vec_j));
819         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
820       }
821       CeedCallBackend(CeedVectorDestroy(&vec_i));
822       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
823     }
824   }
825   CeedCallBackend(CeedDestroy(&ceed));
826   return CEED_ERROR_SUCCESS;
827 }
828 
829 //------------------------------------------------------------------------------
830 // Setup Operator
831 //------------------------------------------------------------------------------
832 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
833   bool                is_setup_done;
834   CeedInt             Q, num_input_fields, num_output_fields;
835   CeedQFunctionField *qf_input_fields, *qf_output_fields;
836   CeedQFunction       qf;
837   CeedOperatorField  *op_input_fields, *op_output_fields;
838   CeedOperator_Ref   *impl;
839 
840   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
841   if (is_setup_done) return CEED_ERROR_SUCCESS;
842 
843   CeedCallBackend(CeedOperatorGetData(op, &impl));
844   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
845   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
846   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
847   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
848   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
849 
850   // Allocate
851   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
852 
853   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
854   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_out));
855   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->apply_add_basis_out));
856   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
857   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
858   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
859   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
860   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
861 
862   impl->num_inputs  = num_input_fields;
863   impl->num_outputs = num_output_fields;
864 
865   // Set up infield and outfield pointer arrays
866   // Infields
867   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->skip_rstr_in, NULL, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
868                                                       num_input_fields, Q));
869   // Outfields
870   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->skip_rstr_out, impl->apply_add_basis_out, impl->e_vecs_full,
871                                                       impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
872 
873   // Identity QFunctions
874   if (impl->is_identity_qf) {
875     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
876     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
877   }
878 
879   CeedCallBackend(CeedOperatorSetSetupDone(op));
880   CeedCallBackend(CeedQFunctionDestroy(&qf));
881   return CEED_ERROR_SUCCESS;
882 }
883 
884 //------------------------------------------------------------------------------
885 // Input Basis Action
886 //------------------------------------------------------------------------------
887 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
888                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
889                                                      CeedVector point_coords_elem, bool skip_active, bool skip_passive,
890                                                      CeedScalar *e_data[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl, CeedRequest *request) {
891   for (CeedInt i = 0; i < num_input_fields; i++) {
892     bool                is_active;
893     CeedInt             elem_size, size, num_comp;
894     CeedRestrictionType rstr_type;
895     CeedEvalMode        eval_mode;
896     CeedVector          vec;
897     CeedElemRestriction elem_rstr;
898     CeedBasis           basis;
899 
900     // Skip active input
901     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
902     is_active = vec == CEED_VECTOR_ACTIVE;
903     CeedCallBackend(CeedVectorDestroy(&vec));
904     if (skip_active && is_active) continue;
905     if (skip_passive && !is_active) continue;
906 
907     // Get elem_size, eval_mode, size
908     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
909     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
910     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
911     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
912     // Restrict block active input
913     // When skipping passive inputs, we're doing assembly and should not restrict
914     if (is_active && !impl->skip_rstr_in[i] && !skip_passive) {
915       if (rstr_type == CEED_RESTRICTION_POINTS) {
916         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
917       } else {
918         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
919       }
920     }
921     // Basis action
922     switch (eval_mode) {
923       case CEED_EVAL_NONE:
924         if (!is_active) {
925           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
926         }
927         break;
928       // Note - these basis eval modes require FEM fields
929       case CEED_EVAL_INTERP:
930       case CEED_EVAL_GRAD:
931       case CEED_EVAL_DIV:
932       case CEED_EVAL_CURL:
933         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
934         if (!is_active) {
935           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
936           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
937           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
938         }
939         CeedCallBackend(
940             CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
941         CeedCallBackend(CeedBasisDestroy(&basis));
942         break;
943       case CEED_EVAL_WEIGHT:
944         break;  // No action
945     }
946     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
947   }
948   return CEED_ERROR_SUCCESS;
949 }
950 
951 //------------------------------------------------------------------------------
952 // Output Basis Action
953 //------------------------------------------------------------------------------
954 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
955                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
956                                                       bool *apply_add_basis, bool *skip_rstr, CeedOperator op, CeedVector out_vec,
957                                                       CeedVector point_coords_elem, bool skip_passive, CeedOperator_Ref *impl, CeedRequest *request) {
958   for (CeedInt i = 0; i < num_output_fields; i++) {
959     bool                is_active;
960     CeedRestrictionType rstr_type;
961     CeedEvalMode        eval_mode;
962     CeedVector          vec;
963     CeedElemRestriction elem_rstr;
964     CeedBasis           basis;
965 
966     // Skip active input
967     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
968     is_active = vec == CEED_VECTOR_ACTIVE;
969     CeedCallBackend(CeedVectorDestroy(&vec));
970     if (skip_passive && !is_active) continue;
971 
972     // Get elem_size, eval_mode, size
973     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
974     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
975     // Basis action
976     switch (eval_mode) {
977       case CEED_EVAL_NONE:
978         break;  // No action
979       case CEED_EVAL_INTERP:
980       case CEED_EVAL_GRAD:
981       case CEED_EVAL_DIV:
982       case CEED_EVAL_CURL:
983         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
984         if (apply_add_basis[i]) {
985           CeedCallBackend(CeedBasisApplyAddAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i],
986                                                     impl->e_vecs_out[i]));
987         } else {
988           CeedCallBackend(
989               CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
990         }
991         CeedCallBackend(CeedBasisDestroy(&basis));
992         break;
993       // LCOV_EXCL_START
994       case CEED_EVAL_WEIGHT: {
995         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
996         // LCOV_EXCL_STOP
997       }
998     }
999     // Restrict output block
1000     // When skipping passive outputs, we're doing assembly and should not restrict
1001     if (skip_rstr[i] || skip_passive) {
1002       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1003       continue;
1004     }
1005 
1006     // Get output vector
1007     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1008     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1009     if (is_active) vec = out_vec;
1010     // Restrict
1011     if (rstr_type == CEED_RESTRICTION_POINTS) {
1012       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1013     } else {
1014       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1015     }
1016     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
1017     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1018   }
1019   return CEED_ERROR_SUCCESS;
1020 }
1021 
1022 //------------------------------------------------------------------------------
1023 // Operator Apply
1024 //------------------------------------------------------------------------------
1025 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
1026   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
1027   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1028   CeedVector          point_coords               = NULL;
1029   CeedElemRestriction rstr_points                = NULL;
1030   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1031   CeedQFunction       qf;
1032   CeedOperatorField  *op_input_fields, *op_output_fields;
1033   CeedOperator_Ref   *impl;
1034 
1035   CeedCallBackend(CeedOperatorGetData(op, &impl));
1036   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1037   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1038   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1039   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1040 
1041   // Setup
1042   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1043 
1044   // Point coordinates
1045   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1046 
1047   // Input Evecs and Restriction
1048   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1049 
1050   // Loop through elements
1051   for (CeedInt e = 0; e < num_elem; e++) {
1052     CeedInt num_points;
1053 
1054     // Setup points for element
1055     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1056     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1057 
1058     // Input basis apply
1059     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1060                                                        impl->point_coords_elem, false, false, e_data, impl, request));
1061 
1062     // Q function
1063     if (!impl->is_identity_qf) {
1064       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1065     }
1066 
1067     // Output basis apply and restriction
1068     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1069                                                         num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1070                                                         impl->point_coords_elem, false, impl, request));
1071 
1072     num_points_offset += num_points;
1073   }
1074 
1075   // Restore input arrays
1076   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1077 
1078   // Cleanup point coordinates
1079   CeedCallBackend(CeedVectorDestroy(&point_coords));
1080   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1081   CeedCallBackend(CeedQFunctionDestroy(&qf));
1082   return CEED_ERROR_SUCCESS;
1083 }
1084 
1085 //------------------------------------------------------------------------------
1086 // Core code for assembling linear QFunction
1087 //------------------------------------------------------------------------------
1088 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
1089                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
1090   Ceed                ceed;
1091   CeedInt             qf_size_in, qf_size_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
1092   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
1093   CeedVector          point_coords = NULL;
1094   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1095   CeedQFunction       qf;
1096   CeedOperatorField  *op_input_fields, *op_output_fields;
1097   CeedOperator_Ref   *impl;
1098   CeedElemRestriction rstr_points = NULL;
1099 
1100   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1101   CeedCallBackend(CeedOperatorGetData(op, &impl));
1102   qf_size_in  = impl->qf_size_in;
1103   qf_size_out = impl->qf_size_out;
1104   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1105   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1106   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1107   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1108 
1109   // Setup
1110   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1111 
1112   // Check for restriction only operator
1113   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
1114 
1115   // Point coordinates
1116   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1117   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
1118 
1119   // Input Evecs and Restriction
1120   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
1121 
1122   // Count number of active input fields
1123   if (qf_size_in == 0) {
1124     for (CeedInt i = 0; i < num_input_fields; i++) {
1125       CeedInt    field_size;
1126       CeedVector vec;
1127 
1128       // Get input vector
1129       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1130       // Check if active input
1131       if (vec == CEED_VECTOR_ACTIVE) {
1132         // Check that all active inputs are nodal fields
1133         {
1134           CeedElemRestriction elem_rstr;
1135           bool                is_at_points = false;
1136 
1137           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1138           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1139           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1140           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1141         }
1142         // Get size of active input
1143         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1144         qf_size_in += field_size;
1145       }
1146       CeedCallBackend(CeedVectorDestroy(&vec));
1147     }
1148     CeedCheck(qf_size_in, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1149     impl->qf_size_in = qf_size_in;
1150   }
1151 
1152   // Count number of active output fields
1153   if (qf_size_out == 0) {
1154     for (CeedInt i = 0; i < num_output_fields; i++) {
1155       CeedInt    field_size;
1156       CeedVector vec;
1157 
1158       // Get output vector
1159       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1160       // Check if active output
1161       if (vec == CEED_VECTOR_ACTIVE) {
1162         // Check that all active inputs are nodal fields
1163         {
1164           CeedElemRestriction elem_rstr;
1165           bool                is_at_points = false;
1166 
1167           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
1168           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1169           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1170           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1171         }
1172         // Get size of active output
1173         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
1174         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1175         qf_size_out += field_size;
1176       }
1177       CeedCallBackend(CeedVectorDestroy(&vec));
1178     }
1179     CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1180     impl->qf_size_out = qf_size_out;
1181   }
1182 
1183   // Build objects if needed
1184   if (build_objects) {
1185     CeedInt        num_points_total;
1186     const CeedInt *offsets;
1187 
1188     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1189 
1190     // Create output restriction (at points)
1191     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1192     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, qf_size_in * qf_size_out,
1193                                                       qf_size_in * qf_size_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets, rstr));
1194     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1195 
1196     // Create assembled vector
1197     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1198   }
1199   // Clear output vector
1200   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1201   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1202 
1203   // Loop through elements
1204   for (CeedInt e = 0; e < num_elem; e++) {
1205     CeedInt num_points;
1206 
1207     // Setup points for element
1208     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1209     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1210 
1211     // Input basis apply
1212     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1213                                                        impl->point_coords_elem, true, false, e_data_full, impl, request));
1214 
1215     // Assemble QFunction
1216     for (CeedInt i = 0; i < num_input_fields; i++) {
1217       bool       is_active;
1218       CeedInt    field_size;
1219       CeedVector vec;
1220 
1221       // Get input vector
1222       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1223       is_active = vec == CEED_VECTOR_ACTIVE;
1224       CeedCallBackend(CeedVectorDestroy(&vec));
1225       // Check if active input
1226       if (!is_active) continue;
1227       // Get size of active input
1228       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1229       for (CeedInt field = 0; field < field_size; field++) {
1230         // Set current portion of input to 1.0
1231         {
1232           CeedScalar *array;
1233 
1234           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1235           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 1.0;
1236           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1237         }
1238 
1239         if (!impl->is_identity_qf) {
1240           // Set Outputs
1241           for (CeedInt out = 0; out < num_output_fields; out++) {
1242             CeedVector vec;
1243             CeedInt    field_size;
1244 
1245             // Get output vector
1246             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1247             // Check if active output
1248             if (vec == CEED_VECTOR_ACTIVE) {
1249               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1250               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1251               assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1252             }
1253             CeedCallBackend(CeedVectorDestroy(&vec));
1254           }
1255           // Apply QFunction
1256           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1257         } else {
1258           const CeedScalar *array;
1259           CeedInt           field_size;
1260 
1261           // Copy Identity Outputs
1262           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1263           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
1264           for (CeedInt j = 0; j < field_size * num_points; j++) assembled_array[j] = array[j];
1265           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
1266           assembled_array += field_size * num_points;
1267         }
1268         // Reset input to 0.0
1269         {
1270           CeedScalar *array;
1271 
1272           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1273           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 0.0;
1274           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1275         }
1276       }
1277     }
1278     num_points_offset += num_points;
1279   }
1280 
1281   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1282   if (!impl->is_identity_qf) {
1283     for (CeedInt out = 0; out < num_output_fields; out++) {
1284       CeedVector vec;
1285 
1286       // Get output vector
1287       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1288       // Check if active output
1289       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1290         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1291       }
1292       CeedCallBackend(CeedVectorDestroy(&vec));
1293     }
1294   }
1295 
1296   // Restore input arrays
1297   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1298 
1299   // Restore output
1300   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1301 
1302   // Cleanup
1303   CeedCallBackend(CeedDestroy(&ceed));
1304   CeedCallBackend(CeedVectorDestroy(&point_coords));
1305   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1306   CeedCallBackend(CeedQFunctionDestroy(&qf));
1307   return CEED_ERROR_SUCCESS;
1308 }
1309 
1310 //------------------------------------------------------------------------------
1311 // Assemble Linear QFunction
1312 //------------------------------------------------------------------------------
1313 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1314   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1315 }
1316 
1317 //------------------------------------------------------------------------------
1318 // Update Assembled Linear QFunction
1319 //------------------------------------------------------------------------------
1320 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1321                                                                  CeedRequest *request) {
1322   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1323 }
1324 
1325 //------------------------------------------------------------------------------
1326 // Assemble Operator Diagonal AtPoints
1327 //------------------------------------------------------------------------------
1328 static int CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1329   CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
1330   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1331   Ceed                ceed;
1332   CeedVector          point_coords = NULL, in_vec, out_vec;
1333   CeedElemRestriction rstr_points  = NULL;
1334   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1335   CeedQFunction       qf;
1336   CeedOperatorField  *op_input_fields, *op_output_fields;
1337   CeedOperator_Ref   *impl;
1338 
1339   CeedCallBackend(CeedOperatorGetData(op, &impl));
1340   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1341   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1342   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1343   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1344 
1345   // Setup
1346   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1347 
1348   // Ceed
1349   {
1350     Ceed ceed_parent;
1351 
1352     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1353     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
1354     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
1355     CeedCallBackend(CeedDestroy(&ceed_parent));
1356   }
1357 
1358   // Point coordinates
1359   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1360 
1361   // Input and output vectors
1362   {
1363     CeedSize input_size, output_size;
1364 
1365     CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1366     CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
1367     CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
1368     CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
1369   }
1370 
1371   // Clear input Evecs
1372   for (CeedInt i = 0; i < num_input_fields; i++) {
1373     bool       is_active;
1374     CeedVector vec;
1375 
1376     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1377     is_active = vec == CEED_VECTOR_ACTIVE;
1378     CeedCallBackend(CeedVectorDestroy(&vec));
1379     if (!is_active || impl->skip_rstr_in[i]) continue;
1380     CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1381   }
1382 
1383   // Input Evecs and Restriction
1384   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1385 
1386   // Loop through elements
1387   for (CeedInt e = 0; e < num_elem; e++) {
1388     CeedInt num_points, e_vec_size = 0;
1389 
1390     // Setup points for element
1391     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1392     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1393 
1394     // Input basis apply for non-active bases
1395     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1396                                                        impl->point_coords_elem, true, false, e_data, impl, request));
1397 
1398     // Loop over points on element
1399     for (CeedInt i = 0; i < num_input_fields; i++) {
1400       bool                is_active_at_points = true, is_active;
1401       CeedInt             elem_size_active    = 1;
1402       CeedRestrictionType rstr_type;
1403       CeedVector          vec;
1404       CeedElemRestriction elem_rstr;
1405 
1406       // -- Skip non-active input
1407       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1408       is_active = vec == CEED_VECTOR_ACTIVE;
1409       CeedCallBackend(CeedVectorDestroy(&vec));
1410       if (!is_active || impl->skip_rstr_in[i]) continue;
1411 
1412       // -- Get active restriction type
1413       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1414       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1415       is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
1416       if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
1417       else elem_size_active = num_points;
1418       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
1419       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1420 
1421       e_vec_size = elem_size_active * num_comp_active;
1422       for (CeedInt s = 0; s < e_vec_size; s++) {
1423         // -- Update unit vector
1424         {
1425           CeedScalar *array;
1426 
1427           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1428           array[s] = 1.0;
1429           if (s > 0) array[s - 1] = 0.0;
1430           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1431         }
1432         // Input basis apply for active bases
1433         CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields,
1434                                                            in_vec, impl->point_coords_elem, false, true, e_data, impl, request));
1435 
1436         // -- Q function
1437         if (!impl->is_identity_qf) {
1438           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1439         }
1440 
1441         // -- Output basis apply and restriction
1442         CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1443                                                             num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1444                                                             impl->point_coords_elem, true, impl, request));
1445 
1446         // -- Grab diagonal value
1447         for (CeedInt j = 0; j < num_output_fields; j++) {
1448           bool                is_active;
1449           CeedInt             elem_size = 0;
1450           CeedRestrictionType rstr_type;
1451           CeedVector          vec;
1452           CeedElemRestriction elem_rstr;
1453 
1454           // ---- Skip non-active output
1455           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
1456           is_active = vec == CEED_VECTOR_ACTIVE;
1457           CeedCallBackend(CeedVectorDestroy(&vec));
1458           if (!is_active || impl->skip_rstr_out[j]) continue;
1459 
1460           // ---- Check if elem size matches
1461           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
1462           CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1463           if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
1464             CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1465             continue;
1466           }
1467           if (rstr_type == CEED_RESTRICTION_POINTS) {
1468             CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
1469           } else {
1470             CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
1471           }
1472           {
1473             CeedInt num_comp = 0;
1474 
1475             CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
1476             if (e_vec_size != num_comp * elem_size) {
1477               CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1478               continue;
1479             }
1480           }
1481           // ---- Update output vector
1482           {
1483             CeedScalar *array, current_value = 0.0;
1484 
1485             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1486             current_value = array[s];
1487             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1488             CeedCallBackend(CeedVectorSetValue(impl->e_vecs_out[j], 0.0));
1489             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1490             array[s] = current_value;
1491             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1492           }
1493           // ---- Restrict output block
1494           if (rstr_type == CEED_RESTRICTION_POINTS) {
1495             CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1496           } else {
1497             CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1498           }
1499           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1500         }
1501         // -- Reset unit vector
1502         if (s == e_vec_size - 1) {
1503           CeedScalar *array;
1504 
1505           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1506           array[s] = 0.0;
1507           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1508         }
1509       }
1510     }
1511     num_points_offset += num_points;
1512   }
1513 
1514   // Restore input arrays
1515   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1516 
1517   // Cleanup
1518   CeedCallBackend(CeedDestroy(&ceed));
1519   CeedCallBackend(CeedVectorDestroy(&in_vec));
1520   CeedCallBackend(CeedVectorDestroy(&out_vec));
1521   CeedCallBackend(CeedVectorDestroy(&point_coords));
1522   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1523   CeedCallBackend(CeedQFunctionDestroy(&qf));
1524   return CEED_ERROR_SUCCESS;
1525 }
1526 
1527 //------------------------------------------------------------------------------
1528 // Assemble Operator AtPoints
1529 //------------------------------------------------------------------------------
1530 static int CeedSingleOperatorAssembleAtPoints_Ref(CeedOperator op, CeedInt offset, CeedVector values) {
1531   CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
1532   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0}, *assembled;
1533   Ceed                ceed;
1534   CeedVector          point_coords = NULL, in_vec, out_vec;
1535   CeedElemRestriction rstr_points  = NULL;
1536   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1537   CeedQFunction       qf;
1538   CeedOperatorField  *op_input_fields, *op_output_fields;
1539   CeedOperator_Ref   *impl;
1540 
1541   CeedCallBackend(CeedOperatorGetData(op, &impl));
1542   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1543   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1544   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1545   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1546 
1547   // Setup
1548   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1549 
1550   // Ceed
1551   {
1552     Ceed ceed_parent;
1553 
1554     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1555     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
1556     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
1557     CeedCallBackend(CeedDestroy(&ceed_parent));
1558   }
1559 
1560   // Point coordinates
1561   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1562 
1563   // Input and output vectors
1564   {
1565     CeedSize input_size, output_size;
1566 
1567     CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1568     CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
1569     CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
1570     CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
1571   }
1572 
1573   // Assembled array
1574   CeedCallBackend(CeedVectorGetArray(values, CEED_MEM_HOST, &assembled));
1575 
1576   // Clear input Evecs
1577   for (CeedInt i = 0; i < num_input_fields; i++) {
1578     bool       is_active;
1579     CeedVector vec;
1580 
1581     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1582     is_active = vec == CEED_VECTOR_ACTIVE;
1583     CeedCallBackend(CeedVectorDestroy(&vec));
1584     if (!is_active || impl->skip_rstr_in[i]) continue;
1585     CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1586   }
1587 
1588   // Input Evecs and Restriction
1589   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, CEED_REQUEST_IMMEDIATE));
1590 
1591   // Loop through elements
1592   for (CeedInt e = 0; e < num_elem; e++) {
1593     CeedInt num_points, e_vec_size = 0;
1594 
1595     // Setup points for element
1596     CeedCallBackend(
1597         CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, CEED_REQUEST_IMMEDIATE));
1598     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1599 
1600     // Input basis apply for non-active bases
1601     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1602                                                        impl->point_coords_elem, true, false, e_data, impl, CEED_REQUEST_IMMEDIATE));
1603 
1604     // Loop over points on element
1605     for (CeedInt i = 0; i < num_input_fields; i++) {
1606       bool                is_active_at_points = true, is_active;
1607       CeedInt             elem_size_active    = 1;
1608       CeedRestrictionType rstr_type;
1609       CeedVector          vec;
1610       CeedElemRestriction elem_rstr;
1611 
1612       // -- Skip non-active input
1613       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1614       is_active = vec == CEED_VECTOR_ACTIVE;
1615       CeedCallBackend(CeedVectorDestroy(&vec));
1616       if (!is_active || impl->skip_rstr_in[i]) continue;
1617 
1618       // -- Get active restriction type
1619       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1620       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1621       is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
1622       if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
1623       else elem_size_active = num_points;
1624       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
1625       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1626 
1627       e_vec_size = elem_size_active * num_comp_active;
1628       for (CeedInt s = 0; s < e_vec_size; s++) {
1629         const CeedInt comp_in = s / elem_size_active;
1630         const CeedInt node_in = s % elem_size_active;
1631 
1632         // -- Update unit vector
1633         {
1634           CeedScalar *array;
1635 
1636           if (s == 0) CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1637           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1638           array[s] = 1.0;
1639           if (s > 0) array[s - 1] = 0.0;
1640           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1641         }
1642         // Input basis apply for active bases
1643         CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields,
1644                                                            in_vec, impl->point_coords_elem, false, true, e_data, impl, CEED_REQUEST_IMMEDIATE));
1645 
1646         // -- Q function
1647         if (!impl->is_identity_qf) {
1648           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1649         }
1650 
1651         // -- Output basis apply and restriction
1652         CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1653                                                             num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1654                                                             impl->point_coords_elem, true, impl, CEED_REQUEST_IMMEDIATE));
1655 
1656         // -- Build element matrix
1657         for (CeedInt j = 0; j < num_output_fields; j++) {
1658           bool                is_active;
1659           CeedInt             elem_size = 0;
1660           CeedRestrictionType rstr_type;
1661           CeedVector          vec;
1662           CeedElemRestriction elem_rstr;
1663 
1664           // ---- Skip non-active output
1665           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
1666           is_active = vec == CEED_VECTOR_ACTIVE;
1667           CeedCallBackend(CeedVectorDestroy(&vec));
1668           if (!is_active || impl->skip_rstr_out[j]) continue;
1669 
1670           // ---- Check if elem size matches
1671           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
1672           CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1673           if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
1674             CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1675             continue;
1676           }
1677           if (rstr_type == CEED_RESTRICTION_POINTS) {
1678             CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
1679           } else {
1680             CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
1681           }
1682           {
1683             CeedInt num_comp = 0;
1684 
1685             CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
1686             CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1687             if (e_vec_size != num_comp * elem_size) continue;
1688           }
1689           // ---- Copy output
1690           {
1691             const CeedScalar *output;
1692 
1693             CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_out[j], CEED_MEM_HOST, &output));
1694             for (CeedInt k = 0; k < e_vec_size; k++) {
1695               const CeedInt comp_out = k / elem_size_active;
1696               const CeedInt node_out = k % elem_size_active;
1697 
1698               assembled[offset + e * e_vec_size * e_vec_size + (comp_in * num_comp_active + comp_out) * elem_size_active * elem_size_active +
1699                         node_out * elem_size_active + node_in] = output[k];
1700             }
1701             CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_out[j], &output));
1702           }
1703         }
1704         // -- Reset unit vector
1705         if (s == e_vec_size - 1) {
1706           CeedScalar *array;
1707 
1708           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1709           array[s] = 0.0;
1710           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1711         }
1712       }
1713     }
1714     num_points_offset += num_points;
1715   }
1716 
1717   // Restore input arrays
1718   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1719 
1720   // Restore assembled values
1721   CeedCallBackend(CeedVectorRestoreArray(values, &assembled));
1722 
1723   // Cleanup
1724   CeedCallBackend(CeedDestroy(&ceed));
1725   CeedCallBackend(CeedVectorDestroy(&in_vec));
1726   CeedCallBackend(CeedVectorDestroy(&out_vec));
1727   CeedCallBackend(CeedVectorDestroy(&point_coords));
1728   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1729   CeedCallBackend(CeedQFunctionDestroy(&qf));
1730   return CEED_ERROR_SUCCESS;
1731 }
1732 
1733 //------------------------------------------------------------------------------
1734 // Operator Destroy
1735 //------------------------------------------------------------------------------
1736 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1737   CeedOperator_Ref *impl;
1738 
1739   CeedCallBackend(CeedOperatorGetData(op, &impl));
1740   CeedCallBackend(CeedFree(&impl->skip_rstr_in));
1741   CeedCallBackend(CeedFree(&impl->skip_rstr_out));
1742   CeedCallBackend(CeedFree(&impl->e_data_out_indices));
1743   CeedCallBackend(CeedFree(&impl->apply_add_basis_out));
1744   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1745     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1746   }
1747   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1748   CeedCallBackend(CeedFree(&impl->input_states));
1749 
1750   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1751     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1752     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1753   }
1754   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1755   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1756 
1757   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1758     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1759     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1760   }
1761   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1762   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1763   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1764 
1765   CeedCallBackend(CeedFree(&impl));
1766   return CEED_ERROR_SUCCESS;
1767 }
1768 
1769 //------------------------------------------------------------------------------
1770 // Operator Create
1771 //------------------------------------------------------------------------------
1772 int CeedOperatorCreate_Ref(CeedOperator op) {
1773   Ceed              ceed;
1774   CeedOperator_Ref *impl;
1775 
1776   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1777   CeedCallBackend(CeedCalloc(1, &impl));
1778   CeedCallBackend(CeedOperatorSetData(op, impl));
1779   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1780   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1781   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1782   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1783   CeedCallBackend(CeedDestroy(&ceed));
1784   return CEED_ERROR_SUCCESS;
1785 }
1786 
1787 //------------------------------------------------------------------------------
1788 // Operator Create At Points
1789 //------------------------------------------------------------------------------
1790 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1791   Ceed              ceed;
1792   CeedOperator_Ref *impl;
1793 
1794   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1795   CeedCallBackend(CeedCalloc(1, &impl));
1796   CeedCallBackend(CeedOperatorSetData(op, impl));
1797   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1798   CeedCallBackend(
1799       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1800   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal", CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref));
1801   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleSingle", CeedSingleOperatorAssembleAtPoints_Ref));
1802   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1803   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1804   CeedCallBackend(CeedDestroy(&ceed));
1805   return CEED_ERROR_SUCCESS;
1806 }
1807 
1808 //------------------------------------------------------------------------------
1809