xref: /libCEED/backends/ref/ceed-ref-operator.c (revision db2becc9f302fe8eb3a32ace50ce3f3a5d42e6c4)
1 // Copyright (c) 2017-2024, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 #include <ceed.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, 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   // Drop duplicate input restrictions
82   if (is_input) {
83     for (CeedInt i = 0; i < num_fields; i++) {
84       CeedVector          vec_i;
85       CeedElemRestriction rstr_i;
86 
87       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
88       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
89       for (CeedInt j = i + 1; j < num_fields; j++) {
90         CeedVector          vec_j;
91         CeedElemRestriction rstr_j;
92 
93         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
94         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
95         if (vec_i == vec_j && rstr_i == rstr_j) {
96           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
97           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i], &e_vecs_full[j]));
98           skip_rstr[j] = true;
99         }
100       }
101     }
102   }
103   return CEED_ERROR_SUCCESS;
104 }
105 
106 //------------------------------------------------------------------------------
107 // Setup Operator
108 //------------------------------------------------------------------------------/*
109 static int CeedOperatorSetup_Ref(CeedOperator op) {
110   bool                is_setup_done;
111   CeedInt             Q, num_input_fields, num_output_fields;
112   CeedQFunctionField *qf_input_fields, *qf_output_fields;
113   CeedQFunction       qf;
114   CeedOperatorField  *op_input_fields, *op_output_fields;
115   CeedOperator_Ref   *impl;
116 
117   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
118   if (is_setup_done) return CEED_ERROR_SUCCESS;
119 
120   CeedCallBackend(CeedOperatorGetData(op, &impl));
121   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
122   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
123   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
124   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
125   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
126 
127   // Allocate
128   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
129 
130   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
131   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
132   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
133   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
134   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
135   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
136 
137   impl->num_inputs  = num_input_fields;
138   impl->num_outputs = num_output_fields;
139 
140   // Set up infield and outfield e_vecs and q_vecs
141   // Infields
142   CeedCallBackend(
143       CeedOperatorSetupFields_Ref(qf, op, true, impl->skip_rstr_in, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
144   // Outfields
145   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, false, NULL, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
146                                               num_output_fields, Q));
147 
148   // Identity QFunctions
149   if (impl->is_identity_qf) {
150     CeedEvalMode        in_mode, out_mode;
151     CeedQFunctionField *in_fields, *out_fields;
152 
153     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
154     CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
155     CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));
156 
157     if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
158       impl->is_identity_rstr_op = true;
159     } else {
160       CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
161     }
162   }
163 
164   CeedCallBackend(CeedOperatorSetSetupDone(op));
165   return CEED_ERROR_SUCCESS;
166 }
167 
168 //------------------------------------------------------------------------------
169 // Setup Operator Inputs
170 //------------------------------------------------------------------------------
171 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
172                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
173                                               CeedOperator_Ref *impl, CeedRequest *request) {
174   for (CeedInt i = 0; i < num_input_fields; i++) {
175     uint64_t            state;
176     CeedEvalMode        eval_mode;
177     CeedVector          vec;
178     CeedElemRestriction elem_rstr;
179 
180     // Get input vector
181     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
182     if (vec == CEED_VECTOR_ACTIVE) {
183       if (skip_active) continue;
184       else vec = in_vec;
185     }
186 
187     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
188     // Restrict and Evec
189     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
190     } else {
191       // Restrict
192       CeedCallBackend(CeedVectorGetState(vec, &state));
193       // Skip restriction if input is unchanged
194       if ((state != impl->input_states[i] || vec == in_vec) && !impl->skip_rstr_in[i]) {
195         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
196         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
197       }
198       impl->input_states[i] = state;
199       // Get evec
200       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
201     }
202   }
203   return CEED_ERROR_SUCCESS;
204 }
205 
206 //------------------------------------------------------------------------------
207 // Input Basis Action
208 //------------------------------------------------------------------------------
209 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
210                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
211                                              CeedOperator_Ref *impl) {
212   for (CeedInt i = 0; i < num_input_fields; i++) {
213     CeedInt             elem_size, size, num_comp;
214     CeedEvalMode        eval_mode;
215     CeedElemRestriction elem_rstr;
216     CeedBasis           basis;
217 
218     // Skip active input
219     if (skip_active) {
220       CeedVector vec;
221 
222       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
223       if (vec == CEED_VECTOR_ACTIVE) continue;
224     }
225     // Get elem_size, eval_mode, size
226     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
227     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
228     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
229     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
230     // Basis action
231     switch (eval_mode) {
232       case CEED_EVAL_NONE:
233         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * Q * size]));
234         break;
235       case CEED_EVAL_INTERP:
236       case CEED_EVAL_GRAD:
237       case CEED_EVAL_DIV:
238       case CEED_EVAL_CURL:
239         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
240         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
241         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * elem_size * num_comp]));
242         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
243         break;
244       case CEED_EVAL_WEIGHT:
245         break;  // No action
246     }
247   }
248   return CEED_ERROR_SUCCESS;
249 }
250 
251 //------------------------------------------------------------------------------
252 // Output Basis Action
253 //------------------------------------------------------------------------------
254 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
255                                               CeedInt num_input_fields, CeedInt num_output_fields, CeedOperator op,
256                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
257   for (CeedInt i = 0; i < num_output_fields; i++) {
258     CeedInt             elem_size, num_comp;
259     CeedEvalMode        eval_mode;
260     CeedElemRestriction elem_rstr;
261     CeedBasis           basis;
262 
263     // Get elem_size, eval_mode
264     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
265     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
266     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
267     // Basis action
268     switch (eval_mode) {
269       case CEED_EVAL_NONE:
270         break;  // No action
271       case CEED_EVAL_INTERP:
272       case CEED_EVAL_GRAD:
273       case CEED_EVAL_DIV:
274       case CEED_EVAL_CURL:
275         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
276         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
277         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER,
278                                            &e_data_full[i + num_input_fields][(CeedSize)e * elem_size * num_comp]));
279         CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
280         break;
281       // LCOV_EXCL_START
282       case CEED_EVAL_WEIGHT: {
283         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
284         // LCOV_EXCL_STOP
285       }
286     }
287   }
288   return CEED_ERROR_SUCCESS;
289 }
290 
291 //------------------------------------------------------------------------------
292 // Restore Input Vectors
293 //------------------------------------------------------------------------------
294 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
295                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
296   for (CeedInt i = 0; i < num_input_fields; i++) {
297     CeedEvalMode eval_mode;
298 
299     // Skip active inputs
300     if (skip_active) {
301       CeedVector vec;
302 
303       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
304       if (vec == CEED_VECTOR_ACTIVE) continue;
305     }
306     // Restore input
307     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
308     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
309     } else {
310       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
311     }
312   }
313   return CEED_ERROR_SUCCESS;
314 }
315 
316 //------------------------------------------------------------------------------
317 // Operator Apply
318 //------------------------------------------------------------------------------
319 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
320   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
321   CeedEvalMode        eval_mode;
322   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
323   CeedQFunctionField *qf_input_fields, *qf_output_fields;
324   CeedQFunction       qf;
325   CeedOperatorField  *op_input_fields, *op_output_fields;
326   CeedOperator_Ref   *impl;
327 
328   CeedCallBackend(CeedOperatorGetData(op, &impl));
329   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
330   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
331   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
332   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
333   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
334 
335   // Setup
336   CeedCallBackend(CeedOperatorSetup_Ref(op));
337 
338   // Restriction only operator
339   if (impl->is_identity_rstr_op) {
340     CeedElemRestriction elem_rstr;
341 
342     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
343     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
344     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
345     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
346     return CEED_ERROR_SUCCESS;
347   }
348 
349   // Input Evecs and Restriction
350   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
351 
352   // Output Evecs
353   for (CeedInt i = 0; i < num_output_fields; i++) {
354     CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
355   }
356 
357   // Loop through elements
358   for (CeedInt e = 0; e < num_elem; e++) {
359     // Output pointers
360     for (CeedInt i = 0; i < num_output_fields; i++) {
361       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
362       if (eval_mode == CEED_EVAL_NONE) {
363         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
364         CeedCallBackend(
365             CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][(CeedSize)e * Q * size]));
366       }
367     }
368 
369     // Input basis apply
370     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
371 
372     // Q function
373     if (!impl->is_identity_qf) {
374       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
375     }
376 
377     // Output basis apply
378     CeedCallBackend(
379         CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields, op, e_data_full, impl));
380   }
381 
382   // Output restriction
383   for (CeedInt i = 0; i < num_output_fields; i++) {
384     CeedVector          vec;
385     CeedElemRestriction elem_rstr;
386 
387     // Restore Evec
388     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
389     // Get output vector
390     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
391     // Active
392     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
393     // Restrict
394     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
395     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
396   }
397 
398   // Restore input arrays
399   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
400   return CEED_ERROR_SUCCESS;
401 }
402 
403 //------------------------------------------------------------------------------
404 // Core code for assembling linear QFunction
405 //------------------------------------------------------------------------------
406 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
407                                                               CeedRequest *request) {
408   Ceed                ceed, ceed_parent;
409   CeedInt             qf_size_in, qf_size_out, Q, num_elem, num_input_fields, num_output_fields;
410   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
411   CeedQFunctionField *qf_input_fields, *qf_output_fields;
412   CeedQFunction       qf;
413   CeedOperatorField  *op_input_fields, *op_output_fields;
414   CeedOperator_Ref   *impl;
415 
416   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
417   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
418   CeedCallBackend(CeedOperatorGetData(op, &impl));
419   qf_size_in  = impl->qf_size_in;
420   qf_size_out = impl->qf_size_out;
421   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
422   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
423   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
424   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
425   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
426 
427   // Setup
428   CeedCallBackend(CeedOperatorSetup_Ref(op));
429 
430   // Check for restriction only operator
431   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
432 
433   // Input Evecs and Restriction
434   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
435 
436   // Count number of active input fields
437   if (qf_size_in == 0) {
438     for (CeedInt i = 0; i < num_input_fields; i++) {
439       CeedInt    field_size;
440       CeedVector vec;
441 
442       // Get input vector
443       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
444       // Check if active input
445       if (vec == CEED_VECTOR_ACTIVE) {
446         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
447         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
448         qf_size_in += field_size;
449       }
450     }
451     CeedCheck(qf_size_in > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
452     impl->qf_size_in = qf_size_in;
453   }
454 
455   // Count number of active output fields
456   if (qf_size_out == 0) {
457     for (CeedInt i = 0; i < num_output_fields; i++) {
458       CeedInt    field_size;
459       CeedVector vec;
460 
461       // Get output vector
462       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
463       // Check if active output
464       if (vec == CEED_VECTOR_ACTIVE) {
465         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
466         qf_size_out += field_size;
467       }
468     }
469     CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
470     impl->qf_size_out = qf_size_out;
471   }
472 
473   // Build objects if needed
474   if (build_objects) {
475     const CeedSize l_size     = (CeedSize)num_elem * Q * qf_size_in * qf_size_out;
476     CeedInt        strides[3] = {1, Q, qf_size_in * qf_size_out * Q}; /* *NOPAD* */
477 
478     // Create output restriction
479     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, qf_size_in * qf_size_out,
480                                                      (CeedSize)qf_size_in * (CeedSize)qf_size_out * (CeedSize)num_elem * (CeedSize)Q, strides, rstr));
481     // Create assembled vector
482     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
483   }
484   // Clear output vector
485   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
486   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
487 
488   // Loop through elements
489   for (CeedInt e = 0; e < num_elem; e++) {
490     // Input basis apply
491     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
492 
493     // Assemble QFunction
494 
495     for (CeedInt i = 0; i < num_input_fields; i++) {
496       CeedInt    field_size;
497       CeedVector vec;
498 
499       // Set Inputs
500       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
501       if (vec != CEED_VECTOR_ACTIVE) continue;
502       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
503       for (CeedInt field = 0; field < field_size; field++) {
504         // Set current portion of input to 1.0
505         {
506           CeedScalar *array;
507 
508           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
509           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 1.0;
510           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
511         }
512 
513         if (!impl->is_identity_qf) {
514           // Set Outputs
515           for (CeedInt out = 0; out < num_output_fields; out++) {
516             CeedVector vec;
517 
518             // Get output vector
519             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
520             // Check if active output
521             if (vec == CEED_VECTOR_ACTIVE) {
522               CeedInt field_size;
523 
524               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
525               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
526               assembled_array += field_size * Q;  // Advance the pointer by the size of the output
527             }
528           }
529           // Apply QFunction
530           CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
531         } else {
532           CeedInt           field_size;
533           const CeedScalar *array;
534 
535           // Copy Identity Outputs
536           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
537           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
538           for (CeedInt j = 0; j < field_size * Q; j++) assembled_array[j] = array[j];
539           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
540           assembled_array += field_size * Q;
541         }
542         // Reset input to 0.0
543         {
544           CeedScalar *array;
545 
546           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
547           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 0.0;
548           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
549         }
550       }
551     }
552   }
553 
554   // Un-set output Qvecs to prevent accidental overwrite of Assembled
555   if (!impl->is_identity_qf) {
556     for (CeedInt out = 0; out < num_output_fields; out++) {
557       CeedVector vec;
558 
559       // Get output vector
560       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
561       // Check if active output
562       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
563         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
564       }
565     }
566   }
567 
568   // Restore input arrays
569   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
570 
571   // Restore output
572   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
573   return CEED_ERROR_SUCCESS;
574 }
575 
576 //------------------------------------------------------------------------------
577 // Assemble Linear QFunction
578 //------------------------------------------------------------------------------
579 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
580   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
581 }
582 
583 //------------------------------------------------------------------------------
584 // Update Assembled Linear QFunction
585 //------------------------------------------------------------------------------
586 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
587   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
588 }
589 
590 //------------------------------------------------------------------------------
591 // Setup Input/Output Fields
592 //------------------------------------------------------------------------------
593 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, bool *skip_rstr, CeedVector *e_vecs_full,
594                                                CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
595   Ceed                ceed;
596   CeedSize            e_size, q_size;
597   CeedInt             max_num_points, num_comp, size, P;
598   CeedQFunctionField *qf_fields;
599   CeedOperatorField  *op_fields;
600 
601   {
602     Ceed ceed_parent;
603 
604     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
605     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
606     if (ceed_parent) ceed = ceed_parent;
607   }
608   if (is_input) {
609     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
610     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
611   } else {
612     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
613     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
614   }
615 
616   // Get max number of points
617   {
618     CeedInt             dim;
619     CeedElemRestriction rstr_points = NULL;
620     CeedOperator_Ref   *impl;
621 
622     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
623     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
624     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
625     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
626     CeedCallBackend(CeedOperatorGetData(op, &impl));
627     if (is_input) {
628       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
629       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
630     }
631   }
632 
633   // Loop over fields
634   for (CeedInt i = 0; i < num_fields; i++) {
635     CeedEvalMode eval_mode;
636     CeedBasis    basis;
637 
638     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
639     if (eval_mode != CEED_EVAL_WEIGHT) {
640       CeedElemRestriction elem_rstr;
641 
642       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
643       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
644       CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
645     }
646 
647     switch (eval_mode) {
648       case CEED_EVAL_NONE: {
649         CeedVector vec;
650 
651         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
652         e_size = (CeedSize)max_num_points * size;
653         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
654         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
655         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
656           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
657         } else {
658           q_size = (CeedSize)max_num_points * size;
659           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
660         }
661         break;
662       }
663       case CEED_EVAL_INTERP:
664       case CEED_EVAL_GRAD:
665       case CEED_EVAL_DIV:
666       case CEED_EVAL_CURL:
667         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
668         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
669         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
670         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
671         e_size = (CeedSize)P * num_comp;
672         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
673         q_size = (CeedSize)max_num_points * size;
674         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
675         break;
676       case CEED_EVAL_WEIGHT:  // Only on input fields
677         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
678         q_size = (CeedSize)max_num_points;
679         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
680         CeedCallBackend(
681             CeedBasisApplyAtPoints(basis, 1, &max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
682         break;
683     }
684     // Initialize full arrays for E-vectors and Q-vectors
685     if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
686     if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
687   }
688   // Drop duplicate input restrictions
689   if (is_input) {
690     for (CeedInt i = 0; i < num_fields; i++) {
691       CeedVector          vec_i;
692       CeedElemRestriction rstr_i;
693 
694       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
695       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
696       for (CeedInt j = i + 1; j < num_fields; j++) {
697         CeedVector          vec_j;
698         CeedElemRestriction rstr_j;
699 
700         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
701         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
702         if (vec_i == vec_j && rstr_i == rstr_j) {
703           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
704           skip_rstr[j] = true;
705         }
706       }
707     }
708   }
709   return CEED_ERROR_SUCCESS;
710 }
711 
712 //------------------------------------------------------------------------------
713 // Setup Operator
714 //------------------------------------------------------------------------------
715 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
716   bool                is_setup_done;
717   CeedInt             Q, num_input_fields, num_output_fields;
718   CeedQFunctionField *qf_input_fields, *qf_output_fields;
719   CeedQFunction       qf;
720   CeedOperatorField  *op_input_fields, *op_output_fields;
721   CeedOperator_Ref   *impl;
722 
723   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
724   if (is_setup_done) return CEED_ERROR_SUCCESS;
725 
726   CeedCallBackend(CeedOperatorGetData(op, &impl));
727   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
728   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
729   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
730   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
731   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
732 
733   // Allocate
734   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
735 
736   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
737   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
738   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
739   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
740   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
741   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
742 
743   impl->num_inputs  = num_input_fields;
744   impl->num_outputs = num_output_fields;
745 
746   // Set up infield and outfield pointer arrays
747   // Infields
748   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->skip_rstr_in, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
749                                                       num_input_fields, Q));
750   // Outfields
751   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, NULL, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
752                                                       num_output_fields, Q));
753 
754   // Identity QFunctions
755   if (impl->is_identity_qf) {
756     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
757     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
758   }
759 
760   CeedCallBackend(CeedOperatorSetSetupDone(op));
761   return CEED_ERROR_SUCCESS;
762 }
763 
764 //------------------------------------------------------------------------------
765 // Input Basis Action
766 //------------------------------------------------------------------------------
767 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
768                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
769                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
770                                                      CeedOperator_Ref *impl, CeedRequest *request) {
771   for (CeedInt i = 0; i < num_input_fields; i++) {
772     bool                is_active_input = false;
773     CeedInt             elem_size, size, num_comp;
774     CeedRestrictionType rstr_type;
775     CeedEvalMode        eval_mode;
776     CeedVector          vec;
777     CeedElemRestriction elem_rstr;
778     CeedBasis           basis;
779 
780     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
781     // Skip active input
782     is_active_input = vec == CEED_VECTOR_ACTIVE;
783     if (skip_active && is_active_input) continue;
784 
785     // Get elem_size, eval_mode, size
786     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
787     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
788     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
789     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
790     // Restrict block active input
791     if (is_active_input && !impl->skip_rstr_in[i]) {
792       if (rstr_type == CEED_RESTRICTION_POINTS) {
793         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
794       } else {
795         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
796       }
797     }
798     // Basis action
799     switch (eval_mode) {
800       case CEED_EVAL_NONE:
801         if (!is_active_input) {
802           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
803         }
804         break;
805       // Note - these basis eval modes require FEM fields
806       case CEED_EVAL_INTERP:
807       case CEED_EVAL_GRAD:
808       case CEED_EVAL_DIV:
809       case CEED_EVAL_CURL:
810         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
811         if (!is_active_input) {
812           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
813           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
814           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
815         }
816         CeedCallBackend(
817             CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
818         break;
819       case CEED_EVAL_WEIGHT:
820         break;  // No action
821     }
822   }
823   return CEED_ERROR_SUCCESS;
824 }
825 
826 //------------------------------------------------------------------------------
827 // Output Basis Action
828 //------------------------------------------------------------------------------
829 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
830                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
831                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
832                                                       CeedRequest *request) {
833   for (CeedInt i = 0; i < num_output_fields; i++) {
834     CeedRestrictionType rstr_type;
835     CeedEvalMode        eval_mode;
836     CeedVector          vec;
837     CeedElemRestriction elem_rstr;
838     CeedBasis           basis;
839 
840     // Get elem_size, eval_mode, size
841     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
842     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
843     // Basis action
844     switch (eval_mode) {
845       case CEED_EVAL_NONE:
846         break;  // No action
847       case CEED_EVAL_INTERP:
848       case CEED_EVAL_GRAD:
849       case CEED_EVAL_DIV:
850       case CEED_EVAL_CURL:
851         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
852         CeedCallBackend(
853             CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
854         break;
855       // LCOV_EXCL_START
856       case CEED_EVAL_WEIGHT: {
857         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
858         // LCOV_EXCL_STOP
859       }
860     }
861     // Restrict output block
862     // Get output vector
863     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
864     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
865     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
866     // Restrict
867     if (rstr_type == CEED_RESTRICTION_POINTS) {
868       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
869     } else {
870       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
871     }
872   }
873   return CEED_ERROR_SUCCESS;
874 }
875 
876 //------------------------------------------------------------------------------
877 // Operator Apply
878 //------------------------------------------------------------------------------
879 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
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(CeedOperatorGetData(op, &impl));
890   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
891   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
892   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
893   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
894 
895   // Setup
896   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
897 
898   // Point coordinates
899   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
900 
901   // Input Evecs and Restriction
902   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
903 
904   // Loop through elements
905   for (CeedInt e = 0; e < num_elem; e++) {
906     CeedInt num_points;
907 
908     // Setup points for element
909     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
910     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
911 
912     // Input basis apply
913     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
914                                                        impl->point_coords_elem, false, e_data, impl, request));
915 
916     // Q function
917     if (!impl->is_identity_qf) {
918       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
919     }
920 
921     // Output basis apply and restriction
922     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
923                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
924 
925     num_points_offset += num_points;
926   }
927 
928   // Restore input arrays
929   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
930 
931   // Cleanup point coordinates
932   CeedCallBackend(CeedVectorDestroy(&point_coords));
933   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
934   return CEED_ERROR_SUCCESS;
935 }
936 
937 //------------------------------------------------------------------------------
938 // Core code for assembling linear QFunction
939 //------------------------------------------------------------------------------
940 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
941                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
942   Ceed                ceed;
943   CeedInt             qf_size_in, qf_size_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
944   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
945   CeedVector          point_coords = NULL;
946   CeedQFunctionField *qf_input_fields, *qf_output_fields;
947   CeedQFunction       qf;
948   CeedOperatorField  *op_input_fields, *op_output_fields;
949   CeedOperator_Ref   *impl;
950   CeedElemRestriction rstr_points = NULL;
951 
952   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
953   CeedCallBackend(CeedOperatorGetData(op, &impl));
954   qf_size_in  = impl->qf_size_in;
955   qf_size_out = impl->qf_size_out;
956   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
957   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
958   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
959   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
960 
961   // Setup
962   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
963 
964   // Check for restriction only operator
965   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
966 
967   // Point coordinates
968   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
969   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
970 
971   // Input Evecs and Restriction
972   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
973 
974   // Count number of active input fields
975   if (qf_size_in == 0) {
976     for (CeedInt i = 0; i < num_input_fields; i++) {
977       CeedInt    field_size;
978       CeedVector vec;
979 
980       // Get input vector
981       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
982       // Check if active input
983       if (vec == CEED_VECTOR_ACTIVE) {
984         // Check that all active inputs are nodal fields
985         {
986           CeedElemRestriction elem_rstr;
987           bool                is_at_points = false;
988 
989           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
990           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
991           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
992         }
993         // Get size of active input
994         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
995         qf_size_in += field_size;
996       }
997     }
998     CeedCheck(qf_size_in, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
999     impl->qf_size_in = qf_size_in;
1000   }
1001 
1002   // Count number of active output fields
1003   if (qf_size_out == 0) {
1004     for (CeedInt i = 0; i < num_output_fields; i++) {
1005       CeedInt    field_size;
1006       CeedVector vec;
1007 
1008       // Get output vector
1009       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1010       // Check if active output
1011       if (vec == CEED_VECTOR_ACTIVE) {
1012         // Check that all active inputs are nodal fields
1013         {
1014           CeedElemRestriction elem_rstr;
1015           bool                is_at_points = false;
1016 
1017           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
1018           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1019           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1020         }
1021         // Get size of active output
1022         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
1023         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1024         qf_size_out += field_size;
1025       }
1026     }
1027     CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1028     impl->qf_size_out = qf_size_out;
1029   }
1030 
1031   // Build objects if needed
1032   if (build_objects) {
1033     CeedInt        num_points_total;
1034     const CeedInt *offsets;
1035 
1036     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1037 
1038     // Create output restriction (at points)
1039     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1040     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, qf_size_in * qf_size_out,
1041                                                       qf_size_in * qf_size_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets, rstr));
1042     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1043 
1044     // Create assembled vector
1045     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1046   }
1047   // Clear output vector
1048   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1049   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1050 
1051   // Loop through elements
1052   for (CeedInt e = 0; e < num_elem; e++) {
1053     CeedInt num_points;
1054 
1055     // Setup points for element
1056     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1057     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1058 
1059     // Input basis apply
1060     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1061                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1062 
1063     // Assemble QFunction
1064     for (CeedInt i = 0; i < num_input_fields; i++) {
1065       CeedInt    field_size;
1066       CeedVector vec;
1067 
1068       // Get input vector
1069       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1070       // Check if active input
1071       if (vec != CEED_VECTOR_ACTIVE) continue;
1072       // Get size of active input
1073       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1074       for (CeedInt field = 0; field < field_size; field++) {
1075         // Set current portion of input to 1.0
1076         {
1077           CeedScalar *array;
1078 
1079           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1080           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 1.0;
1081           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1082         }
1083 
1084         if (!impl->is_identity_qf) {
1085           // Set Outputs
1086           for (CeedInt out = 0; out < num_output_fields; out++) {
1087             CeedVector vec;
1088             CeedInt    field_size;
1089 
1090             // Get output vector
1091             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1092             // Check if active output
1093             if (vec == CEED_VECTOR_ACTIVE) {
1094               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1095               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1096               assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1097             }
1098           }
1099           // Apply QFunction
1100           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1101         } else {
1102           const CeedScalar *array;
1103           CeedInt           field_size;
1104 
1105           // Copy Identity Outputs
1106           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1107           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
1108           for (CeedInt j = 0; j < field_size * num_points; j++) assembled_array[j] = array[j];
1109           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
1110           assembled_array += field_size * num_points;
1111         }
1112         // Reset input to 0.0
1113         {
1114           CeedScalar *array;
1115 
1116           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1117           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 0.0;
1118           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1119         }
1120       }
1121     }
1122     num_points_offset += num_points;
1123   }
1124 
1125   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1126   if (!impl->is_identity_qf) {
1127     for (CeedInt out = 0; out < num_output_fields; out++) {
1128       CeedVector vec;
1129 
1130       // Get output vector
1131       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1132       // Check if active output
1133       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1134         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1135       }
1136     }
1137   }
1138 
1139   // Restore input arrays
1140   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1141 
1142   // Restore output
1143   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1144 
1145   // Cleanup
1146   CeedCallBackend(CeedVectorDestroy(&point_coords));
1147   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1148   return CEED_ERROR_SUCCESS;
1149 }
1150 
1151 //------------------------------------------------------------------------------
1152 // Assemble Linear QFunction
1153 //------------------------------------------------------------------------------
1154 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1155   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1156 }
1157 
1158 //------------------------------------------------------------------------------
1159 // Update Assembled Linear QFunction
1160 //------------------------------------------------------------------------------
1161 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1162                                                                  CeedRequest *request) {
1163   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1164 }
1165 
1166 //------------------------------------------------------------------------------
1167 // Assemble Operator Diagonal AtPoints
1168 //------------------------------------------------------------------------------
1169 static int CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1170   CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
1171   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1172   Ceed                ceed;
1173   CeedVector          point_coords = NULL, in_vec, out_vec;
1174   CeedElemRestriction rstr_points  = NULL;
1175   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1176   CeedQFunction       qf;
1177   CeedOperatorField  *op_input_fields, *op_output_fields;
1178   CeedOperator_Ref   *impl;
1179 
1180   CeedCallBackend(CeedOperatorGetData(op, &impl));
1181   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1182   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1183   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1184   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1185 
1186   // Setup
1187   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1188 
1189   // Ceed
1190   {
1191     Ceed ceed_parent;
1192 
1193     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1194     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
1195     if (ceed_parent) ceed = ceed_parent;
1196   }
1197 
1198   // Point coordinates
1199   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1200 
1201   // Input and output vectors
1202   {
1203     CeedSize input_size, output_size;
1204 
1205     CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1206     CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
1207     CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
1208     CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
1209   }
1210 
1211   // Clear input Qvecs
1212   for (CeedInt i = 0; i < num_input_fields; i++) {
1213     CeedVector vec;
1214 
1215     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1216     if (vec != CEED_VECTOR_ACTIVE) continue;
1217     CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1218   }
1219 
1220   // Input Evecs and Restriction
1221   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1222 
1223   // Loop through elements
1224   for (CeedInt e = 0; e < num_elem; e++) {
1225     CeedInt num_points, e_vec_size = 0;
1226 
1227     // Setup points for element
1228     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1229     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1230 
1231     // Input basis apply for non-active bases
1232     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1233                                                        impl->point_coords_elem, true, e_data, impl, request));
1234 
1235     // Loop over points on element
1236     for (CeedInt i = 0; i < num_input_fields; i++) {
1237       bool                is_active_at_points = true;
1238       CeedInt             elem_size_active    = 1;
1239       CeedRestrictionType rstr_type;
1240       CeedVector          vec;
1241       CeedElemRestriction elem_rstr;
1242 
1243       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1244       // -- Skip non-active input
1245       if (vec != CEED_VECTOR_ACTIVE) continue;
1246 
1247       // -- Get active restriction type
1248       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1249       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1250       is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
1251       if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
1252       else elem_size_active = num_points;
1253       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
1254 
1255       e_vec_size = elem_size_active * num_comp_active;
1256       for (CeedInt s = 0; s < e_vec_size; s++) {
1257         CeedEvalMode eval_mode;
1258         CeedBasis    basis;
1259 
1260         // -- Update unit vector
1261         {
1262           CeedScalar *array;
1263 
1264           if (s == 0) CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1265           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1266           array[s] = 1.0;
1267           if (s > 0) array[s - 1] = 0.0;
1268           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1269         }
1270         // -- Basis action
1271         CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
1272         switch (eval_mode) {
1273           case CEED_EVAL_NONE:
1274             break;
1275           // Note - these basis eval modes require FEM fields
1276           case CEED_EVAL_INTERP:
1277           case CEED_EVAL_GRAD:
1278           case CEED_EVAL_DIV:
1279           case CEED_EVAL_CURL:
1280             CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
1281             CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, impl->point_coords_elem, impl->e_vecs_in[i],
1282                                                    impl->q_vecs_in[i]));
1283             break;
1284           case CEED_EVAL_WEIGHT:
1285             break;  // No action
1286         }
1287 
1288         // -- Q function
1289         if (!impl->is_identity_qf) {
1290           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1291         }
1292 
1293         // -- Output basis apply and restriction
1294         CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1295                                                             num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
1296 
1297         // -- Grab diagonal value
1298         for (CeedInt j = 0; j < num_output_fields; j++) {
1299           bool                is_active_output = false;
1300           CeedInt             elem_size        = 0;
1301           CeedRestrictionType rstr_type;
1302           CeedEvalMode        eval_mode;
1303           CeedVector          vec;
1304           CeedElemRestriction elem_rstr;
1305           CeedBasis           basis;
1306 
1307           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
1308           // ---- Skip non-active output
1309           is_active_output = vec == CEED_VECTOR_ACTIVE;
1310           if (!is_active_output) continue;
1311 
1312           // ---- Check if elem size matches
1313           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
1314           CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1315           if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) continue;
1316           if (rstr_type == CEED_RESTRICTION_POINTS) {
1317             CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
1318           } else {
1319             CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
1320           }
1321           {
1322             CeedInt num_comp = 0;
1323 
1324             CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
1325             if (e_vec_size != num_comp * elem_size) continue;
1326           }
1327 
1328           // ---- Basis action
1329           CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[j], &eval_mode));
1330           switch (eval_mode) {
1331             case CEED_EVAL_NONE:
1332               break;  // No action
1333             case CEED_EVAL_INTERP:
1334             case CEED_EVAL_GRAD:
1335             case CEED_EVAL_DIV:
1336             case CEED_EVAL_CURL:
1337               CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[j], &basis));
1338               CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, impl->point_coords_elem, impl->q_vecs_out[j],
1339                                                      impl->e_vecs_out[j]));
1340               break;
1341             // LCOV_EXCL_START
1342             case CEED_EVAL_WEIGHT: {
1343               return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
1344               // LCOV_EXCL_STOP
1345             }
1346           }
1347           // ---- Update output vector
1348           {
1349             CeedScalar *array, current_value = 0.0;
1350 
1351             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1352             current_value = array[s];
1353             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1354             CeedCallBackend(CeedVectorSetValue(impl->e_vecs_out[j], 0.0));
1355             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1356             array[s] = current_value;
1357             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1358           }
1359           // ---- Restrict output block
1360           if (rstr_type == CEED_RESTRICTION_POINTS) {
1361             CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1362           } else {
1363             CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1364           }
1365         }
1366         // -- Reset unit vector
1367         if (s == e_vec_size - 1) CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1368       }
1369     }
1370     num_points_offset += num_points;
1371   }
1372 
1373   // Restore input arrays
1374   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1375 
1376   // Cleanup
1377   CeedCallBackend(CeedVectorDestroy(&in_vec));
1378   CeedCallBackend(CeedVectorDestroy(&out_vec));
1379   CeedCallBackend(CeedVectorDestroy(&point_coords));
1380   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1381   return CEED_ERROR_SUCCESS;
1382 }
1383 
1384 //------------------------------------------------------------------------------
1385 // Operator Destroy
1386 //------------------------------------------------------------------------------
1387 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1388   CeedOperator_Ref *impl;
1389 
1390   CeedCallBackend(CeedOperatorGetData(op, &impl));
1391   CeedCallBackend(CeedFree(&impl->skip_rstr_in));
1392   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1393     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1394   }
1395   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1396   CeedCallBackend(CeedFree(&impl->input_states));
1397 
1398   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1399     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1400     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1401   }
1402   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1403   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1404 
1405   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1406     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1407     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1408   }
1409   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1410   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1411   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1412 
1413   CeedCallBackend(CeedFree(&impl));
1414   return CEED_ERROR_SUCCESS;
1415 }
1416 
1417 //------------------------------------------------------------------------------
1418 // Operator Create
1419 //------------------------------------------------------------------------------
1420 int CeedOperatorCreate_Ref(CeedOperator op) {
1421   Ceed              ceed;
1422   CeedOperator_Ref *impl;
1423 
1424   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1425   CeedCallBackend(CeedCalloc(1, &impl));
1426   CeedCallBackend(CeedOperatorSetData(op, impl));
1427   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1428   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1429   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1430   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1431   return CEED_ERROR_SUCCESS;
1432 }
1433 
1434 //------------------------------------------------------------------------------
1435 // Operator Create At Points
1436 //------------------------------------------------------------------------------
1437 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1438   Ceed              ceed;
1439   CeedOperator_Ref *impl;
1440 
1441   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1442   CeedCallBackend(CeedCalloc(1, &impl));
1443   CeedCallBackend(CeedOperatorSetData(op, impl));
1444   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1445   CeedCallBackend(
1446       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1447   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal", CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref));
1448   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1449   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1450   return CEED_ERROR_SUCCESS;
1451 }
1452 
1453 //------------------------------------------------------------------------------
1454