xref: /libCEED/backends/ref/ceed-ref-operator.c (revision e3ae47f6083a97dd785ae32cf6cad3c05e295e6c)
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, 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, CeedScalar *e_data[2 * CEED_FIELD_MAX],
890                                                      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 
906     // Get elem_size, eval_mode, size
907     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
908     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
909     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
910     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
911     // Restrict block active input
912     if (is_active && !impl->skip_rstr_in[i]) {
913       if (rstr_type == CEED_RESTRICTION_POINTS) {
914         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
915       } else {
916         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
917       }
918     }
919     // Basis action
920     switch (eval_mode) {
921       case CEED_EVAL_NONE:
922         if (!is_active) {
923           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
924         }
925         break;
926       // Note - these basis eval modes require FEM fields
927       case CEED_EVAL_INTERP:
928       case CEED_EVAL_GRAD:
929       case CEED_EVAL_DIV:
930       case CEED_EVAL_CURL:
931         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
932         if (!is_active) {
933           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
934           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
935           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
936         }
937         CeedCallBackend(
938             CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
939         CeedCallBackend(CeedBasisDestroy(&basis));
940         break;
941       case CEED_EVAL_WEIGHT:
942         break;  // No action
943     }
944     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
945   }
946   return CEED_ERROR_SUCCESS;
947 }
948 
949 //------------------------------------------------------------------------------
950 // Output Basis Action
951 //------------------------------------------------------------------------------
952 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
953                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
954                                                       bool *apply_add_basis, bool *skip_rstr, CeedOperator op, CeedVector out_vec,
955                                                       CeedVector point_coords_elem, CeedOperator_Ref *impl, CeedRequest *request) {
956   for (CeedInt i = 0; i < num_output_fields; i++) {
957     bool                is_active;
958     CeedRestrictionType rstr_type;
959     CeedEvalMode        eval_mode;
960     CeedVector          vec;
961     CeedElemRestriction elem_rstr;
962     CeedBasis           basis;
963 
964     // Get elem_size, eval_mode, size
965     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
966     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
967     // Basis action
968     switch (eval_mode) {
969       case CEED_EVAL_NONE:
970         break;  // No action
971       case CEED_EVAL_INTERP:
972       case CEED_EVAL_GRAD:
973       case CEED_EVAL_DIV:
974       case CEED_EVAL_CURL:
975         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
976         if (apply_add_basis[i]) {
977           CeedCallBackend(CeedBasisApplyAddAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i],
978                                                     impl->e_vecs_out[i]));
979         } else {
980           CeedCallBackend(
981               CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
982         }
983         CeedCallBackend(CeedBasisDestroy(&basis));
984         break;
985       // LCOV_EXCL_START
986       case CEED_EVAL_WEIGHT: {
987         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
988         // LCOV_EXCL_STOP
989       }
990     }
991     // Restrict output block
992     if (skip_rstr[i]) {
993       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
994       continue;
995     }
996 
997     // Get output vector
998     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
999     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1000     is_active = vec == CEED_VECTOR_ACTIVE;
1001     if (is_active) vec = out_vec;
1002     // Restrict
1003     if (rstr_type == CEED_RESTRICTION_POINTS) {
1004       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1005     } else {
1006       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1007     }
1008     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
1009     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1010   }
1011   return CEED_ERROR_SUCCESS;
1012 }
1013 
1014 //------------------------------------------------------------------------------
1015 // Operator Apply
1016 //------------------------------------------------------------------------------
1017 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
1018   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
1019   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1020   CeedVector          point_coords               = NULL;
1021   CeedElemRestriction rstr_points                = NULL;
1022   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1023   CeedQFunction       qf;
1024   CeedOperatorField  *op_input_fields, *op_output_fields;
1025   CeedOperator_Ref   *impl;
1026 
1027   CeedCallBackend(CeedOperatorGetData(op, &impl));
1028   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1029   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1030   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1031   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1032 
1033   // Setup
1034   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1035 
1036   // Point coordinates
1037   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1038 
1039   // Input Evecs and Restriction
1040   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1041 
1042   // Loop through elements
1043   for (CeedInt e = 0; e < num_elem; e++) {
1044     CeedInt num_points;
1045 
1046     // Setup points for element
1047     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1048     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1049 
1050     // Input basis apply
1051     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1052                                                        impl->point_coords_elem, false, e_data, impl, request));
1053 
1054     // Q function
1055     if (!impl->is_identity_qf) {
1056       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1057     }
1058 
1059     // Output basis apply and restriction
1060     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1061                                                         num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1062                                                         impl->point_coords_elem, impl, request));
1063 
1064     num_points_offset += num_points;
1065   }
1066 
1067   // Restore input arrays
1068   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1069 
1070   // Cleanup point coordinates
1071   CeedCallBackend(CeedVectorDestroy(&point_coords));
1072   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1073   CeedCallBackend(CeedQFunctionDestroy(&qf));
1074   return CEED_ERROR_SUCCESS;
1075 }
1076 
1077 //------------------------------------------------------------------------------
1078 // Core code for assembling linear QFunction
1079 //------------------------------------------------------------------------------
1080 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
1081                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
1082   Ceed                ceed;
1083   CeedInt             qf_size_in, qf_size_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
1084   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
1085   CeedVector          point_coords = NULL;
1086   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1087   CeedQFunction       qf;
1088   CeedOperatorField  *op_input_fields, *op_output_fields;
1089   CeedOperator_Ref   *impl;
1090   CeedElemRestriction rstr_points = NULL;
1091 
1092   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1093   CeedCallBackend(CeedOperatorGetData(op, &impl));
1094   qf_size_in  = impl->qf_size_in;
1095   qf_size_out = impl->qf_size_out;
1096   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1097   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1098   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1099   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1100 
1101   // Setup
1102   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1103 
1104   // Check for restriction only operator
1105   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
1106 
1107   // Point coordinates
1108   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1109   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
1110 
1111   // Input Evecs and Restriction
1112   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
1113 
1114   // Count number of active input fields
1115   if (qf_size_in == 0) {
1116     for (CeedInt i = 0; i < num_input_fields; i++) {
1117       CeedInt    field_size;
1118       CeedVector vec;
1119 
1120       // Get input vector
1121       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1122       // Check if active input
1123       if (vec == CEED_VECTOR_ACTIVE) {
1124         // Check that all active inputs are nodal fields
1125         {
1126           CeedElemRestriction elem_rstr;
1127           bool                is_at_points = false;
1128 
1129           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1130           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1131           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1132           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1133         }
1134         // Get size of active input
1135         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1136         qf_size_in += field_size;
1137       }
1138       CeedCallBackend(CeedVectorDestroy(&vec));
1139     }
1140     CeedCheck(qf_size_in, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1141     impl->qf_size_in = qf_size_in;
1142   }
1143 
1144   // Count number of active output fields
1145   if (qf_size_out == 0) {
1146     for (CeedInt i = 0; i < num_output_fields; i++) {
1147       CeedInt    field_size;
1148       CeedVector vec;
1149 
1150       // Get output vector
1151       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1152       // Check if active output
1153       if (vec == CEED_VECTOR_ACTIVE) {
1154         // Check that all active inputs are nodal fields
1155         {
1156           CeedElemRestriction elem_rstr;
1157           bool                is_at_points = false;
1158 
1159           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
1160           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1161           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1162           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1163         }
1164         // Get size of active output
1165         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
1166         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1167         qf_size_out += field_size;
1168       }
1169       CeedCallBackend(CeedVectorDestroy(&vec));
1170     }
1171     CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1172     impl->qf_size_out = qf_size_out;
1173   }
1174 
1175   // Build objects if needed
1176   if (build_objects) {
1177     CeedInt        num_points_total;
1178     const CeedInt *offsets;
1179 
1180     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1181 
1182     // Create output restriction (at points)
1183     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1184     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, qf_size_in * qf_size_out,
1185                                                       qf_size_in * qf_size_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets, rstr));
1186     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1187 
1188     // Create assembled vector
1189     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1190   }
1191   // Clear output vector
1192   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1193   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1194 
1195   // Loop through elements
1196   for (CeedInt e = 0; e < num_elem; e++) {
1197     CeedInt num_points;
1198 
1199     // Setup points for element
1200     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1201     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1202 
1203     // Input basis apply
1204     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1205                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1206 
1207     // Assemble QFunction
1208     for (CeedInt i = 0; i < num_input_fields; i++) {
1209       bool       is_active;
1210       CeedInt    field_size;
1211       CeedVector vec;
1212 
1213       // Get input vector
1214       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1215       is_active = vec == CEED_VECTOR_ACTIVE;
1216       CeedCallBackend(CeedVectorDestroy(&vec));
1217       // Check if active input
1218       if (!is_active) continue;
1219       // Get size of active input
1220       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1221       for (CeedInt field = 0; field < field_size; field++) {
1222         // Set current portion of input to 1.0
1223         {
1224           CeedScalar *array;
1225 
1226           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1227           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 1.0;
1228           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1229         }
1230 
1231         if (!impl->is_identity_qf) {
1232           // Set Outputs
1233           for (CeedInt out = 0; out < num_output_fields; out++) {
1234             CeedVector vec;
1235             CeedInt    field_size;
1236 
1237             // Get output vector
1238             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1239             // Check if active output
1240             if (vec == CEED_VECTOR_ACTIVE) {
1241               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1242               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1243               assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1244             }
1245             CeedCallBackend(CeedVectorDestroy(&vec));
1246           }
1247           // Apply QFunction
1248           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1249         } else {
1250           const CeedScalar *array;
1251           CeedInt           field_size;
1252 
1253           // Copy Identity Outputs
1254           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1255           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
1256           for (CeedInt j = 0; j < field_size * num_points; j++) assembled_array[j] = array[j];
1257           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
1258           assembled_array += field_size * num_points;
1259         }
1260         // Reset input to 0.0
1261         {
1262           CeedScalar *array;
1263 
1264           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1265           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 0.0;
1266           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1267         }
1268       }
1269     }
1270     num_points_offset += num_points;
1271   }
1272 
1273   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1274   if (!impl->is_identity_qf) {
1275     for (CeedInt out = 0; out < num_output_fields; out++) {
1276       CeedVector vec;
1277 
1278       // Get output vector
1279       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1280       // Check if active output
1281       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1282         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1283       }
1284       CeedCallBackend(CeedVectorDestroy(&vec));
1285     }
1286   }
1287 
1288   // Restore input arrays
1289   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1290 
1291   // Restore output
1292   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1293 
1294   // Cleanup
1295   CeedCallBackend(CeedDestroy(&ceed));
1296   CeedCallBackend(CeedVectorDestroy(&point_coords));
1297   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1298   CeedCallBackend(CeedQFunctionDestroy(&qf));
1299   return CEED_ERROR_SUCCESS;
1300 }
1301 
1302 //------------------------------------------------------------------------------
1303 // Assemble Linear QFunction
1304 //------------------------------------------------------------------------------
1305 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1306   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1307 }
1308 
1309 //------------------------------------------------------------------------------
1310 // Update Assembled Linear QFunction
1311 //------------------------------------------------------------------------------
1312 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1313                                                                  CeedRequest *request) {
1314   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1315 }
1316 
1317 //------------------------------------------------------------------------------
1318 // Assemble Operator Diagonal AtPoints
1319 //------------------------------------------------------------------------------
1320 static int CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1321   CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
1322   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1323   Ceed                ceed;
1324   CeedVector          point_coords = NULL, in_vec, out_vec;
1325   CeedElemRestriction rstr_points  = NULL;
1326   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1327   CeedQFunction       qf;
1328   CeedOperatorField  *op_input_fields, *op_output_fields;
1329   CeedOperator_Ref   *impl;
1330 
1331   CeedCallBackend(CeedOperatorGetData(op, &impl));
1332   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1333   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1334   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1335   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1336 
1337   // Setup
1338   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1339 
1340   // Ceed
1341   {
1342     Ceed ceed_parent;
1343 
1344     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1345     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
1346     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
1347     CeedCallBackend(CeedDestroy(&ceed_parent));
1348   }
1349 
1350   // Point coordinates
1351   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1352 
1353   // Input and output vectors
1354   {
1355     CeedSize input_size, output_size;
1356 
1357     CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1358     CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
1359     CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
1360     CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
1361   }
1362 
1363   // Clear input Qvecs
1364   for (CeedInt i = 0; i < num_input_fields; i++) {
1365     bool       is_active;
1366     CeedVector vec;
1367 
1368     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1369     is_active = vec == CEED_VECTOR_ACTIVE;
1370     CeedCallBackend(CeedVectorDestroy(&vec));
1371     if (!is_active) continue;
1372     CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1373   }
1374 
1375   // Input Evecs and Restriction
1376   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1377 
1378   // Loop through elements
1379   for (CeedInt e = 0; e < num_elem; e++) {
1380     CeedInt num_points, e_vec_size = 0;
1381 
1382     // Setup points for element
1383     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1384     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1385 
1386     // Input basis apply for non-active bases
1387     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1388                                                        impl->point_coords_elem, true, e_data, impl, request));
1389 
1390     // Loop over points on element
1391     for (CeedInt i = 0; i < num_input_fields; i++) {
1392       bool                is_active_at_points = true, is_active;
1393       CeedInt             elem_size_active    = 1;
1394       CeedRestrictionType rstr_type;
1395       CeedVector          vec;
1396       CeedElemRestriction elem_rstr;
1397 
1398       // -- Skip non-active input
1399       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1400       is_active = vec == CEED_VECTOR_ACTIVE;
1401       CeedCallBackend(CeedVectorDestroy(&vec));
1402       if (!is_active) continue;
1403 
1404       // -- Get active restriction type
1405       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1406       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1407       is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
1408       if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
1409       else elem_size_active = num_points;
1410       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
1411       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1412 
1413       e_vec_size = elem_size_active * num_comp_active;
1414       for (CeedInt s = 0; s < e_vec_size; s++) {
1415         CeedEvalMode eval_mode;
1416         CeedBasis    basis;
1417 
1418         // -- Update unit vector
1419         {
1420           CeedScalar *array;
1421 
1422           if (s == 0) CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1423           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1424           array[s] = 1.0;
1425           if (s > 0) array[s - 1] = 0.0;
1426           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1427         }
1428         // -- Basis action
1429         CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
1430         switch (eval_mode) {
1431           case CEED_EVAL_NONE:
1432             break;
1433           // Note - these basis eval modes require FEM fields
1434           case CEED_EVAL_INTERP:
1435           case CEED_EVAL_GRAD:
1436           case CEED_EVAL_DIV:
1437           case CEED_EVAL_CURL:
1438             CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
1439             CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, impl->point_coords_elem, impl->e_vecs_in[i],
1440                                                    impl->q_vecs_in[i]));
1441             CeedCallBackend(CeedBasisDestroy(&basis));
1442             break;
1443           case CEED_EVAL_WEIGHT:
1444             break;  // No action
1445         }
1446 
1447         // -- Q function
1448         if (!impl->is_identity_qf) {
1449           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1450         }
1451 
1452         // -- Output basis apply and restriction
1453         CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1454                                                             num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1455                                                             impl->point_coords_elem, impl, request));
1456 
1457         // -- Grab diagonal value
1458         for (CeedInt j = 0; j < num_output_fields; j++) {
1459           bool                is_active;
1460           CeedInt             elem_size = 0;
1461           CeedRestrictionType rstr_type;
1462           CeedEvalMode        eval_mode;
1463           CeedVector          vec;
1464           CeedElemRestriction elem_rstr;
1465           CeedBasis           basis;
1466 
1467           // ---- Skip non-active output
1468           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
1469           is_active = vec == CEED_VECTOR_ACTIVE;
1470           CeedCallBackend(CeedVectorDestroy(&vec));
1471           if (!is_active) continue;
1472 
1473           // ---- Check if elem size matches
1474           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
1475           CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1476           if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
1477             CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1478             continue;
1479           }
1480           if (rstr_type == CEED_RESTRICTION_POINTS) {
1481             CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
1482           } else {
1483             CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
1484           }
1485           {
1486             CeedInt num_comp = 0;
1487 
1488             CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
1489             if (e_vec_size != num_comp * elem_size) {
1490               CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1491               continue;
1492             }
1493           }
1494 
1495           // ---- Basis action
1496           CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[j], &eval_mode));
1497           switch (eval_mode) {
1498             case CEED_EVAL_NONE:
1499               break;  // No action
1500             case CEED_EVAL_INTERP:
1501             case CEED_EVAL_GRAD:
1502             case CEED_EVAL_DIV:
1503             case CEED_EVAL_CURL:
1504               CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[j], &basis));
1505               CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, impl->point_coords_elem, impl->q_vecs_out[j],
1506                                                      impl->e_vecs_out[j]));
1507               CeedCallBackend(CeedBasisDestroy(&basis));
1508               break;
1509             // LCOV_EXCL_START
1510             case CEED_EVAL_WEIGHT: {
1511               return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
1512               // LCOV_EXCL_STOP
1513             }
1514           }
1515           // ---- Update output vector
1516           {
1517             CeedScalar *array, current_value = 0.0;
1518 
1519             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1520             current_value = array[s];
1521             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1522             CeedCallBackend(CeedVectorSetValue(impl->e_vecs_out[j], 0.0));
1523             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1524             array[s] = current_value;
1525             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1526           }
1527           // ---- Restrict output block
1528           if (rstr_type == CEED_RESTRICTION_POINTS) {
1529             CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1530           } else {
1531             CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1532           }
1533           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1534         }
1535         // -- Reset unit vector
1536         if (s == e_vec_size - 1) CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1537       }
1538     }
1539     num_points_offset += num_points;
1540   }
1541 
1542   // Restore input arrays
1543   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1544 
1545   // Cleanup
1546   CeedCallBackend(CeedDestroy(&ceed));
1547   CeedCallBackend(CeedVectorDestroy(&in_vec));
1548   CeedCallBackend(CeedVectorDestroy(&out_vec));
1549   CeedCallBackend(CeedVectorDestroy(&point_coords));
1550   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1551   CeedCallBackend(CeedQFunctionDestroy(&qf));
1552   return CEED_ERROR_SUCCESS;
1553 }
1554 
1555 //------------------------------------------------------------------------------
1556 // Operator Destroy
1557 //------------------------------------------------------------------------------
1558 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1559   CeedOperator_Ref *impl;
1560 
1561   CeedCallBackend(CeedOperatorGetData(op, &impl));
1562   CeedCallBackend(CeedFree(&impl->skip_rstr_in));
1563   CeedCallBackend(CeedFree(&impl->skip_rstr_out));
1564   CeedCallBackend(CeedFree(&impl->e_data_out_indices));
1565   CeedCallBackend(CeedFree(&impl->apply_add_basis_out));
1566   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1567     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1568   }
1569   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1570   CeedCallBackend(CeedFree(&impl->input_states));
1571 
1572   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1573     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1574     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1575   }
1576   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1577   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1578 
1579   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1580     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1581     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1582   }
1583   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1584   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1585   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1586 
1587   CeedCallBackend(CeedFree(&impl));
1588   return CEED_ERROR_SUCCESS;
1589 }
1590 
1591 //------------------------------------------------------------------------------
1592 // Operator Create
1593 //------------------------------------------------------------------------------
1594 int CeedOperatorCreate_Ref(CeedOperator op) {
1595   Ceed              ceed;
1596   CeedOperator_Ref *impl;
1597 
1598   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1599   CeedCallBackend(CeedCalloc(1, &impl));
1600   CeedCallBackend(CeedOperatorSetData(op, impl));
1601   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1602   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1603   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1604   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1605   CeedCallBackend(CeedDestroy(&ceed));
1606   return CEED_ERROR_SUCCESS;
1607 }
1608 
1609 //------------------------------------------------------------------------------
1610 // Operator Create At Points
1611 //------------------------------------------------------------------------------
1612 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1613   Ceed              ceed;
1614   CeedOperator_Ref *impl;
1615 
1616   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1617   CeedCallBackend(CeedCalloc(1, &impl));
1618   CeedCallBackend(CeedOperatorSetData(op, impl));
1619   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1620   CeedCallBackend(
1621       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1622   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal", CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref));
1623   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1624   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1625   CeedCallBackend(CeedDestroy(&ceed));
1626   return CEED_ERROR_SUCCESS;
1627 }
1628 
1629 //------------------------------------------------------------------------------
1630