xref: /libCEED/rust/libceed-sys/c-src/backends/ref/ceed-ref-operator.c (revision 9bc663991d6482bcb1d60b1f116148f11db83fa1)
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   return CEED_ERROR_SUCCESS;
205 }
206 
207 //------------------------------------------------------------------------------
208 // Setup Operator Inputs
209 //------------------------------------------------------------------------------
210 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
211                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
212                                               CeedOperator_Ref *impl, CeedRequest *request) {
213   for (CeedInt i = 0; i < num_input_fields; i++) {
214     bool         is_active;
215     uint64_t     state;
216     CeedEvalMode eval_mode;
217     CeedVector   vec;
218 
219     // Get input vector
220     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
221     is_active = vec == CEED_VECTOR_ACTIVE;
222     if (is_active) {
223       if (skip_active) continue;
224       else vec = in_vec;
225     }
226 
227     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
228     // Restrict and Evec
229     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
230     } else {
231       // Restrict
232       CeedCallBackend(CeedVectorGetState(vec, &state));
233       // Skip restriction if input is unchanged
234       if ((state != impl->input_states[i] || vec == in_vec) && !impl->skip_rstr_in[i]) {
235         CeedElemRestriction elem_rstr;
236 
237         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
238         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
239         CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
240       }
241       impl->input_states[i] = state;
242       // Get evec
243       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
244     }
245     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
246   }
247   return CEED_ERROR_SUCCESS;
248 }
249 
250 //------------------------------------------------------------------------------
251 // Input Basis Action
252 //------------------------------------------------------------------------------
253 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
254                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
255                                              CeedOperator_Ref *impl) {
256   for (CeedInt i = 0; i < num_input_fields; i++) {
257     CeedInt             elem_size, size, num_comp;
258     CeedEvalMode        eval_mode;
259     CeedElemRestriction elem_rstr;
260     CeedBasis           basis;
261 
262     // Skip active input
263     if (skip_active) {
264       bool       is_active;
265       CeedVector vec;
266 
267       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
268       is_active = vec == CEED_VECTOR_ACTIVE;
269       CeedCallBackend(CeedVectorDestroy(&vec));
270       if (is_active) continue;
271     }
272     // Get elem_size, eval_mode, size
273     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
274     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
275     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
276     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
277     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
278     // Basis action
279     switch (eval_mode) {
280       case CEED_EVAL_NONE:
281         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * Q * size]));
282         break;
283       case CEED_EVAL_INTERP:
284       case CEED_EVAL_GRAD:
285       case CEED_EVAL_DIV:
286       case CEED_EVAL_CURL:
287         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
288         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
289         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * elem_size * num_comp]));
290         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
291         CeedCallBackend(CeedBasisDestroy(&basis));
292         break;
293       case CEED_EVAL_WEIGHT:
294         break;  // No action
295     }
296   }
297   return CEED_ERROR_SUCCESS;
298 }
299 
300 //------------------------------------------------------------------------------
301 // Output Basis Action
302 //------------------------------------------------------------------------------
303 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
304                                               CeedInt num_input_fields, CeedInt num_output_fields, bool *apply_add_basis, CeedOperator op,
305                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
306   for (CeedInt i = 0; i < num_output_fields; i++) {
307     CeedInt             elem_size, num_comp;
308     CeedEvalMode        eval_mode;
309     CeedElemRestriction elem_rstr;
310     CeedBasis           basis;
311 
312     // Get elem_size, eval_mode
313     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
314     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
315     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
316     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
317     // Basis action
318     switch (eval_mode) {
319       case CEED_EVAL_NONE:
320         break;  // No action
321       case CEED_EVAL_INTERP:
322       case CEED_EVAL_GRAD:
323       case CEED_EVAL_DIV:
324       case CEED_EVAL_CURL:
325         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
326         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
327         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER,
328                                            &e_data_full[i + num_input_fields][(CeedSize)e * elem_size * num_comp]));
329         if (apply_add_basis[i]) {
330           CeedCallBackend(CeedBasisApplyAdd(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
331         } else {
332           CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
333         }
334         CeedCallBackend(CeedBasisDestroy(&basis));
335         break;
336       // LCOV_EXCL_START
337       case CEED_EVAL_WEIGHT: {
338         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
339         // LCOV_EXCL_STOP
340       }
341     }
342   }
343   return CEED_ERROR_SUCCESS;
344 }
345 
346 //------------------------------------------------------------------------------
347 // Restore Input Vectors
348 //------------------------------------------------------------------------------
349 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
350                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
351   for (CeedInt i = 0; i < num_input_fields; i++) {
352     CeedEvalMode eval_mode;
353 
354     // Skip active inputs
355     if (skip_active) {
356       bool       is_active;
357       CeedVector vec;
358 
359       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
360       is_active = vec == CEED_VECTOR_ACTIVE;
361       CeedCallBackend(CeedVectorDestroy(&vec));
362       if (is_active) continue;
363     }
364     // Restore input
365     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
366     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
367     } else {
368       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
369     }
370   }
371   return CEED_ERROR_SUCCESS;
372 }
373 
374 //------------------------------------------------------------------------------
375 // Operator Apply
376 //------------------------------------------------------------------------------
377 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
378   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
379   CeedEvalMode        eval_mode;
380   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
381   CeedQFunctionField *qf_input_fields, *qf_output_fields;
382   CeedQFunction       qf;
383   CeedOperatorField  *op_input_fields, *op_output_fields;
384   CeedOperator_Ref   *impl;
385 
386   CeedCallBackend(CeedOperatorGetData(op, &impl));
387   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
388   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
389   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
390   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
391   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
392 
393   // Setup
394   CeedCallBackend(CeedOperatorSetup_Ref(op));
395 
396   // Restriction only operator
397   if (impl->is_identity_rstr_op) {
398     CeedElemRestriction elem_rstr;
399 
400     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
401     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
402     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
403     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
404     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
405     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
406     return CEED_ERROR_SUCCESS;
407   }
408 
409   // Input Evecs and Restriction
410   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
411 
412   // Output Evecs
413   for (CeedInt i = num_output_fields - 1; i >= 0; i--) {
414     if (impl->skip_rstr_out[i]) {
415       e_data_full[i + num_input_fields] = e_data_full[impl->e_data_out_indices[i] + num_input_fields];
416     } else {
417       CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
418     }
419   }
420 
421   // Loop through elements
422   for (CeedInt e = 0; e < num_elem; e++) {
423     // Output pointers
424     for (CeedInt i = 0; i < num_output_fields; i++) {
425       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
426       if (eval_mode == CEED_EVAL_NONE) {
427         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
428         CeedCallBackend(
429             CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][(CeedSize)e * Q * size]));
430       }
431     }
432 
433     // Input basis apply
434     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
435 
436     // Q function
437     if (!impl->is_identity_qf) {
438       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
439     }
440 
441     // Output basis apply
442     CeedCallBackend(CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields,
443                                                 impl->apply_add_basis_out, op, e_data_full, impl));
444   }
445 
446   // Output restriction
447   for (CeedInt i = 0; i < num_output_fields; i++) {
448     bool                is_active;
449     CeedVector          vec;
450     CeedElemRestriction elem_rstr;
451 
452     if (impl->skip_rstr_out[i]) continue;
453     // Restore Evec
454     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
455     // Get output vector
456     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
457     // Active
458     is_active = vec == CEED_VECTOR_ACTIVE;
459     if (is_active) vec = out_vec;
460     // Restrict
461     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
462     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
463     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
464     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
465   }
466 
467   // Restore input arrays
468   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
469   return CEED_ERROR_SUCCESS;
470 }
471 
472 //------------------------------------------------------------------------------
473 // Core code for assembling linear QFunction
474 //------------------------------------------------------------------------------
475 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
476                                                               CeedRequest *request) {
477   Ceed                ceed_parent;
478   CeedInt             qf_size_in, qf_size_out, Q, num_elem, num_input_fields, num_output_fields;
479   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
480   CeedQFunctionField *qf_input_fields, *qf_output_fields;
481   CeedQFunction       qf;
482   CeedOperatorField  *op_input_fields, *op_output_fields;
483   CeedOperator_Ref   *impl;
484 
485   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
486   CeedCallBackend(CeedOperatorGetData(op, &impl));
487   qf_size_in  = impl->qf_size_in;
488   qf_size_out = impl->qf_size_out;
489   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
490   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
491   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
492   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
493   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
494 
495   // Setup
496   CeedCallBackend(CeedOperatorSetup_Ref(op));
497 
498   // Check for restriction only operator
499   CeedCheck(!impl->is_identity_rstr_op, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
500 
501   // Input Evecs and Restriction
502   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
503 
504   // Count number of active input fields
505   if (qf_size_in == 0) {
506     for (CeedInt i = 0; i < num_input_fields; i++) {
507       CeedInt    field_size;
508       CeedVector vec;
509 
510       // Get input vector
511       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
512       // Check if active input
513       if (vec == CEED_VECTOR_ACTIVE) {
514         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
515         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
516         qf_size_in += field_size;
517       }
518       CeedCallBackend(CeedVectorDestroy(&vec));
519     }
520     CeedCheck(qf_size_in > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
521     impl->qf_size_in = qf_size_in;
522   }
523 
524   // Count number of active output fields
525   if (qf_size_out == 0) {
526     for (CeedInt i = 0; i < num_output_fields; i++) {
527       CeedInt    field_size;
528       CeedVector vec;
529 
530       // Get output vector
531       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
532       // Check if active output
533       if (vec == CEED_VECTOR_ACTIVE) {
534         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
535         qf_size_out += field_size;
536       }
537       CeedCallBackend(CeedVectorDestroy(&vec));
538     }
539     CeedCheck(qf_size_out > 0, CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
540     impl->qf_size_out = qf_size_out;
541   }
542 
543   // Build objects if needed
544   if (build_objects) {
545     const CeedSize l_size     = (CeedSize)num_elem * Q * qf_size_in * qf_size_out;
546     CeedInt        strides[3] = {1, Q, qf_size_in * qf_size_out * Q}; /* *NOPAD* */
547 
548     // Create output restriction
549     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, qf_size_in * qf_size_out,
550                                                      (CeedSize)qf_size_in * (CeedSize)qf_size_out * (CeedSize)num_elem * (CeedSize)Q, strides, rstr));
551     // Create assembled vector
552     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
553   }
554   // Clear output vector
555   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
556   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
557 
558   // Loop through elements
559   for (CeedInt e = 0; e < num_elem; e++) {
560     // Input basis apply
561     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
562 
563     // Assemble QFunction
564 
565     for (CeedInt i = 0; i < num_input_fields; i++) {
566       bool       is_active;
567       CeedInt    field_size;
568       CeedVector vec;
569 
570       // Set Inputs
571       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
572       is_active = vec == CEED_VECTOR_ACTIVE;
573       CeedCallBackend(CeedVectorDestroy(&vec));
574       if (!is_active) continue;
575       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
576       for (CeedInt field = 0; field < field_size; field++) {
577         // Set current portion of input to 1.0
578         {
579           CeedScalar *array;
580 
581           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
582           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 1.0;
583           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
584         }
585 
586         if (!impl->is_identity_qf) {
587           // Set Outputs
588           for (CeedInt out = 0; out < num_output_fields; out++) {
589             CeedVector vec;
590 
591             // Get output vector
592             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
593             // Check if active output
594             if (vec == CEED_VECTOR_ACTIVE) {
595               CeedInt field_size;
596 
597               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
598               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
599               assembled_array += field_size * Q;  // Advance the pointer by the size of the output
600             }
601             CeedCallBackend(CeedVectorDestroy(&vec));
602           }
603           // Apply QFunction
604           CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
605         } else {
606           CeedInt           field_size;
607           const CeedScalar *array;
608 
609           // Copy Identity Outputs
610           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
611           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
612           for (CeedInt j = 0; j < field_size * Q; j++) assembled_array[j] = array[j];
613           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
614           assembled_array += field_size * Q;
615         }
616         // Reset input to 0.0
617         {
618           CeedScalar *array;
619 
620           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
621           for (CeedInt j = 0; j < Q; j++) array[field * Q + j] = 0.0;
622           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
623         }
624       }
625     }
626   }
627 
628   // Un-set output Qvecs to prevent accidental overwrite of Assembled
629   if (!impl->is_identity_qf) {
630     for (CeedInt out = 0; out < num_output_fields; out++) {
631       CeedVector vec;
632 
633       // Get output vector
634       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
635       // Check if active output
636       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
637         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
638       }
639       CeedCallBackend(CeedVectorDestroy(&vec));
640     }
641   }
642 
643   // Restore input arrays
644   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
645 
646   // Restore output
647   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
648   CeedCallBackend(CeedDestroy(&ceed_parent));
649   return CEED_ERROR_SUCCESS;
650 }
651 
652 //------------------------------------------------------------------------------
653 // Assemble Linear QFunction
654 //------------------------------------------------------------------------------
655 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
656   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
657 }
658 
659 //------------------------------------------------------------------------------
660 // Update Assembled Linear QFunction
661 //------------------------------------------------------------------------------
662 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
663   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
664 }
665 
666 //------------------------------------------------------------------------------
667 // Setup Input/Output Fields
668 //------------------------------------------------------------------------------
669 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, bool *skip_rstr, bool *apply_add_basis,
670                                                CeedVector *e_vecs_full, CeedVector *e_vecs, CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields,
671                                                CeedInt Q) {
672   Ceed                ceed;
673   CeedSize            e_size, q_size;
674   CeedInt             max_num_points, num_comp, size, P;
675   CeedQFunctionField *qf_fields;
676   CeedOperatorField  *op_fields;
677 
678   {
679     Ceed ceed_parent;
680 
681     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
682     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
683     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
684     CeedCallBackend(CeedDestroy(&ceed_parent));
685   }
686   if (is_input) {
687     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
688     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
689   } else {
690     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
691     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
692   }
693 
694   // Get max number of points
695   {
696     CeedInt             dim;
697     CeedElemRestriction rstr_points = NULL;
698     CeedOperator_Ref   *impl;
699 
700     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
701     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
702     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
703     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
704     CeedCallBackend(CeedOperatorGetData(op, &impl));
705     if (is_input) {
706       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
707       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
708     }
709   }
710 
711   // Loop over fields
712   for (CeedInt i = 0; i < num_fields; i++) {
713     CeedEvalMode eval_mode;
714     CeedBasis    basis;
715 
716     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
717     if (eval_mode != CEED_EVAL_WEIGHT) {
718       CeedElemRestriction elem_rstr;
719 
720       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
721       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
722       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
723       CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
724     }
725 
726     switch (eval_mode) {
727       case CEED_EVAL_NONE: {
728         CeedVector vec;
729 
730         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
731         e_size = (CeedSize)max_num_points * size;
732         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
733         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
734         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
735           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
736         } else {
737           q_size = (CeedSize)max_num_points * size;
738           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
739         }
740         CeedCallBackend(CeedVectorDestroy(&vec));
741         break;
742       }
743       case CEED_EVAL_INTERP:
744       case CEED_EVAL_GRAD:
745       case CEED_EVAL_DIV:
746       case CEED_EVAL_CURL:
747         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
748         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
749         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
750         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
751         e_size = (CeedSize)P * num_comp;
752         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
753         q_size = (CeedSize)max_num_points * size;
754         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
755         CeedCallBackend(CeedBasisDestroy(&basis));
756         break;
757       case CEED_EVAL_WEIGHT:  // Only on input fields
758         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
759         q_size = (CeedSize)max_num_points;
760         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
761         CeedCallBackend(
762             CeedBasisApplyAtPoints(basis, 1, &max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
763         CeedCallBackend(CeedBasisDestroy(&basis));
764         break;
765     }
766     // Initialize full arrays for E-vectors and Q-vectors
767     if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
768     if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
769   }
770   // Drop duplicate restrictions
771   if (is_input) {
772     for (CeedInt i = 0; i < num_fields; i++) {
773       CeedVector          vec_i;
774       CeedElemRestriction rstr_i;
775 
776       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
777       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
778       for (CeedInt j = i + 1; j < num_fields; j++) {
779         CeedVector          vec_j;
780         CeedElemRestriction rstr_j;
781 
782         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
783         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
784         if (vec_i == vec_j && rstr_i == rstr_j) {
785           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
786           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
787           skip_rstr[j] = true;
788         }
789         CeedCallBackend(CeedVectorDestroy(&vec_j));
790         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
791       }
792       CeedCallBackend(CeedVectorDestroy(&vec_i));
793       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
794     }
795   } else {
796     for (CeedInt i = num_fields - 1; i >= 0; i--) {
797       CeedVector          vec_i;
798       CeedElemRestriction rstr_i;
799 
800       CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec_i));
801       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &rstr_i));
802       for (CeedInt j = i - 1; j >= 0; j--) {
803         CeedVector          vec_j;
804         CeedElemRestriction rstr_j;
805 
806         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[j], &vec_j));
807         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[j], &rstr_j));
808         if (vec_i == vec_j && rstr_i == rstr_j) {
809           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &e_vecs[j]));
810           CeedCallBackend(CeedVectorReferenceCopy(e_vecs_full[i + start_e], &e_vecs_full[j + start_e]));
811           skip_rstr[j]       = true;
812           apply_add_basis[i] = true;
813         }
814         CeedCallBackend(CeedVectorDestroy(&vec_j));
815         CeedCallBackend(CeedElemRestrictionDestroy(&rstr_j));
816       }
817       CeedCallBackend(CeedVectorDestroy(&vec_i));
818       CeedCallBackend(CeedElemRestrictionDestroy(&rstr_i));
819     }
820   }
821   CeedCallBackend(CeedDestroy(&ceed));
822   return CEED_ERROR_SUCCESS;
823 }
824 
825 //------------------------------------------------------------------------------
826 // Setup Operator
827 //------------------------------------------------------------------------------
828 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
829   bool                is_setup_done;
830   CeedInt             Q, num_input_fields, num_output_fields;
831   CeedQFunctionField *qf_input_fields, *qf_output_fields;
832   CeedQFunction       qf;
833   CeedOperatorField  *op_input_fields, *op_output_fields;
834   CeedOperator_Ref   *impl;
835 
836   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
837   if (is_setup_done) return CEED_ERROR_SUCCESS;
838 
839   CeedCallBackend(CeedOperatorGetData(op, &impl));
840   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
841   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
842   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
843   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
844   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
845 
846   // Allocate
847   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
848 
849   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_in));
850   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->skip_rstr_out));
851   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->apply_add_basis_out));
852   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
853   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
854   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
855   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
856   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
857 
858   impl->num_inputs  = num_input_fields;
859   impl->num_outputs = num_output_fields;
860 
861   // Set up infield and outfield pointer arrays
862   // Infields
863   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->skip_rstr_in, NULL, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0,
864                                                       num_input_fields, Q));
865   // Outfields
866   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->skip_rstr_out, impl->apply_add_basis_out, impl->e_vecs_full,
867                                                       impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
868 
869   // Identity QFunctions
870   if (impl->is_identity_qf) {
871     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
872     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
873   }
874 
875   CeedCallBackend(CeedOperatorSetSetupDone(op));
876   return CEED_ERROR_SUCCESS;
877 }
878 
879 //------------------------------------------------------------------------------
880 // Input Basis Action
881 //------------------------------------------------------------------------------
882 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
883                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
884                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
885                                                      CeedOperator_Ref *impl, CeedRequest *request) {
886   for (CeedInt i = 0; i < num_input_fields; i++) {
887     bool                is_active;
888     CeedInt             elem_size, size, num_comp;
889     CeedRestrictionType rstr_type;
890     CeedEvalMode        eval_mode;
891     CeedVector          vec;
892     CeedElemRestriction elem_rstr;
893     CeedBasis           basis;
894 
895     // Skip active input
896     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
897     is_active = vec == CEED_VECTOR_ACTIVE;
898     CeedCallBackend(CeedVectorDestroy(&vec));
899     if (skip_active && is_active) continue;
900 
901     // Get elem_size, eval_mode, size
902     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
903     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
904     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
905     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
906     // Restrict block active input
907     if (is_active && !impl->skip_rstr_in[i]) {
908       if (rstr_type == CEED_RESTRICTION_POINTS) {
909         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
910       } else {
911         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
912       }
913     }
914     // Basis action
915     switch (eval_mode) {
916       case CEED_EVAL_NONE:
917         if (!is_active) {
918           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
919         }
920         break;
921       // Note - these basis eval modes require FEM fields
922       case CEED_EVAL_INTERP:
923       case CEED_EVAL_GRAD:
924       case CEED_EVAL_DIV:
925       case CEED_EVAL_CURL:
926         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
927         if (!is_active) {
928           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
929           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
930           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
931         }
932         CeedCallBackend(
933             CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
934         CeedCallBackend(CeedBasisDestroy(&basis));
935         break;
936       case CEED_EVAL_WEIGHT:
937         break;  // No action
938     }
939     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
940   }
941   return CEED_ERROR_SUCCESS;
942 }
943 
944 //------------------------------------------------------------------------------
945 // Output Basis Action
946 //------------------------------------------------------------------------------
947 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
948                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
949                                                       bool *apply_add_basis, bool *skip_rstr, CeedOperator op, CeedVector out_vec,
950                                                       CeedVector point_coords_elem, CeedOperator_Ref *impl, CeedRequest *request) {
951   for (CeedInt i = 0; i < num_output_fields; i++) {
952     bool                is_active;
953     CeedRestrictionType rstr_type;
954     CeedEvalMode        eval_mode;
955     CeedVector          vec;
956     CeedElemRestriction elem_rstr;
957     CeedBasis           basis;
958 
959     // Get elem_size, eval_mode, size
960     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
961     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
962     // Basis action
963     switch (eval_mode) {
964       case CEED_EVAL_NONE:
965         break;  // No action
966       case CEED_EVAL_INTERP:
967       case CEED_EVAL_GRAD:
968       case CEED_EVAL_DIV:
969       case CEED_EVAL_CURL:
970         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
971         if (apply_add_basis[i]) {
972           CeedCallBackend(CeedBasisApplyAddAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i],
973                                                     impl->e_vecs_out[i]));
974         } else {
975           CeedCallBackend(
976               CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
977         }
978         CeedCallBackend(CeedBasisDestroy(&basis));
979         break;
980       // LCOV_EXCL_START
981       case CEED_EVAL_WEIGHT: {
982         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
983         // LCOV_EXCL_STOP
984       }
985     }
986     // Restrict output block
987     if (skip_rstr[i]) {
988       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
989       continue;
990     }
991 
992     // Get output vector
993     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
994     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
995     is_active = vec == CEED_VECTOR_ACTIVE;
996     if (is_active) vec = out_vec;
997     // Restrict
998     if (rstr_type == CEED_RESTRICTION_POINTS) {
999       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1000     } else {
1001       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
1002     }
1003     if (!is_active) CeedCallBackend(CeedVectorDestroy(&vec));
1004     CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1005   }
1006   return CEED_ERROR_SUCCESS;
1007 }
1008 
1009 //------------------------------------------------------------------------------
1010 // Operator Apply
1011 //------------------------------------------------------------------------------
1012 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
1013   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
1014   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1015   CeedVector          point_coords               = NULL;
1016   CeedElemRestriction rstr_points                = NULL;
1017   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1018   CeedQFunction       qf;
1019   CeedOperatorField  *op_input_fields, *op_output_fields;
1020   CeedOperator_Ref   *impl;
1021 
1022   CeedCallBackend(CeedOperatorGetData(op, &impl));
1023   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1024   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1025   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1026   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1027 
1028   // Setup
1029   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1030 
1031   // Point coordinates
1032   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1033 
1034   // Input Evecs and Restriction
1035   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1036 
1037   // Loop through elements
1038   for (CeedInt e = 0; e < num_elem; e++) {
1039     CeedInt num_points;
1040 
1041     // Setup points for element
1042     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1043     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1044 
1045     // Input basis apply
1046     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1047                                                        impl->point_coords_elem, false, e_data, impl, request));
1048 
1049     // Q function
1050     if (!impl->is_identity_qf) {
1051       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1052     }
1053 
1054     // Output basis apply and restriction
1055     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1056                                                         num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1057                                                         impl->point_coords_elem, impl, request));
1058 
1059     num_points_offset += num_points;
1060   }
1061 
1062   // Restore input arrays
1063   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1064 
1065   // Cleanup point coordinates
1066   CeedCallBackend(CeedVectorDestroy(&point_coords));
1067   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1068   return CEED_ERROR_SUCCESS;
1069 }
1070 
1071 //------------------------------------------------------------------------------
1072 // Core code for assembling linear QFunction
1073 //------------------------------------------------------------------------------
1074 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
1075                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
1076   Ceed                ceed;
1077   CeedInt             qf_size_in, qf_size_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
1078   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
1079   CeedVector          point_coords = NULL;
1080   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1081   CeedQFunction       qf;
1082   CeedOperatorField  *op_input_fields, *op_output_fields;
1083   CeedOperator_Ref   *impl;
1084   CeedElemRestriction rstr_points = NULL;
1085 
1086   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1087   CeedCallBackend(CeedOperatorGetData(op, &impl));
1088   qf_size_in  = impl->qf_size_in;
1089   qf_size_out = impl->qf_size_out;
1090   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1091   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1092   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1093   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1094 
1095   // Setup
1096   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1097 
1098   // Check for restriction only operator
1099   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
1100 
1101   // Point coordinates
1102   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1103   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
1104 
1105   // Input Evecs and Restriction
1106   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
1107 
1108   // Count number of active input fields
1109   if (qf_size_in == 0) {
1110     for (CeedInt i = 0; i < num_input_fields; i++) {
1111       CeedInt    field_size;
1112       CeedVector vec;
1113 
1114       // Get input vector
1115       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1116       // Check if active input
1117       if (vec == CEED_VECTOR_ACTIVE) {
1118         // Check that all active inputs are nodal fields
1119         {
1120           CeedElemRestriction elem_rstr;
1121           bool                is_at_points = false;
1122 
1123           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1124           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1125           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1126           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1127         }
1128         // Get size of active input
1129         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1130         qf_size_in += field_size;
1131       }
1132       CeedCallBackend(CeedVectorDestroy(&vec));
1133     }
1134     CeedCheck(qf_size_in, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1135     impl->qf_size_in = qf_size_in;
1136   }
1137 
1138   // Count number of active output fields
1139   if (qf_size_out == 0) {
1140     for (CeedInt i = 0; i < num_output_fields; i++) {
1141       CeedInt    field_size;
1142       CeedVector vec;
1143 
1144       // Get output vector
1145       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
1146       // Check if active output
1147       if (vec == CEED_VECTOR_ACTIVE) {
1148         // Check that all active inputs are nodal fields
1149         {
1150           CeedElemRestriction elem_rstr;
1151           bool                is_at_points = false;
1152 
1153           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
1154           CeedCallBackend(CeedElemRestrictionIsAtPoints(elem_rstr, &is_at_points));
1155           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1156           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
1157         }
1158         // Get size of active output
1159         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
1160         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1161         qf_size_out += field_size;
1162       }
1163       CeedCallBackend(CeedVectorDestroy(&vec));
1164     }
1165     CeedCheck(qf_size_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1166     impl->qf_size_out = qf_size_out;
1167   }
1168 
1169   // Build objects if needed
1170   if (build_objects) {
1171     CeedInt        num_points_total;
1172     const CeedInt *offsets;
1173 
1174     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1175 
1176     // Create output restriction (at points)
1177     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1178     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, qf_size_in * qf_size_out,
1179                                                       qf_size_in * qf_size_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets, rstr));
1180     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1181 
1182     // Create assembled vector
1183     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1184   }
1185   // Clear output vector
1186   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1187   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1188 
1189   // Loop through elements
1190   for (CeedInt e = 0; e < num_elem; e++) {
1191     CeedInt num_points;
1192 
1193     // Setup points for element
1194     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1195     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1196 
1197     // Input basis apply
1198     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1199                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1200 
1201     // Assemble QFunction
1202     for (CeedInt i = 0; i < num_input_fields; i++) {
1203       bool       is_active;
1204       CeedInt    field_size;
1205       CeedVector vec;
1206 
1207       // Get input vector
1208       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1209       is_active = vec == CEED_VECTOR_ACTIVE;
1210       CeedCallBackend(CeedVectorDestroy(&vec));
1211       // Check if active input
1212       if (!is_active) continue;
1213       // Get size of active input
1214       CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
1215       for (CeedInt field = 0; field < field_size; field++) {
1216         // Set current portion of input to 1.0
1217         {
1218           CeedScalar *array;
1219 
1220           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1221           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 1.0;
1222           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1223         }
1224 
1225         if (!impl->is_identity_qf) {
1226           // Set Outputs
1227           for (CeedInt out = 0; out < num_output_fields; out++) {
1228             CeedVector vec;
1229             CeedInt    field_size;
1230 
1231             // Get output vector
1232             CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1233             // Check if active output
1234             if (vec == CEED_VECTOR_ACTIVE) {
1235               CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1236               CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1237               assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1238             }
1239             CeedCallBackend(CeedVectorDestroy(&vec));
1240           }
1241           // Apply QFunction
1242           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1243         } else {
1244           const CeedScalar *array;
1245           CeedInt           field_size;
1246 
1247           // Copy Identity Outputs
1248           CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1249           CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &array));
1250           for (CeedInt j = 0; j < field_size * num_points; j++) assembled_array[j] = array[j];
1251           CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &array));
1252           assembled_array += field_size * num_points;
1253         }
1254         // Reset input to 0.0
1255         {
1256           CeedScalar *array;
1257 
1258           CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &array));
1259           for (CeedInt j = 0; j < num_points; j++) array[field * num_points + j] = 0.0;
1260           CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &array));
1261         }
1262       }
1263     }
1264     num_points_offset += num_points;
1265   }
1266 
1267   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1268   if (!impl->is_identity_qf) {
1269     for (CeedInt out = 0; out < num_output_fields; out++) {
1270       CeedVector vec;
1271 
1272       // Get output vector
1273       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1274       // Check if active output
1275       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1276         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1277       }
1278       CeedCallBackend(CeedVectorDestroy(&vec));
1279     }
1280   }
1281 
1282   // Restore input arrays
1283   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1284 
1285   // Restore output
1286   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1287 
1288   // Cleanup
1289   CeedCallBackend(CeedDestroy(&ceed));
1290   CeedCallBackend(CeedVectorDestroy(&point_coords));
1291   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1292   return CEED_ERROR_SUCCESS;
1293 }
1294 
1295 //------------------------------------------------------------------------------
1296 // Assemble Linear QFunction
1297 //------------------------------------------------------------------------------
1298 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1299   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1300 }
1301 
1302 //------------------------------------------------------------------------------
1303 // Update Assembled Linear QFunction
1304 //------------------------------------------------------------------------------
1305 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1306                                                                  CeedRequest *request) {
1307   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1308 }
1309 
1310 //------------------------------------------------------------------------------
1311 // Assemble Operator Diagonal AtPoints
1312 //------------------------------------------------------------------------------
1313 static int CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref(CeedOperator op, CeedVector assembled, CeedRequest *request) {
1314   CeedInt             num_points_offset = 0, num_input_fields, num_output_fields, num_elem, num_comp_active = 1;
1315   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
1316   Ceed                ceed;
1317   CeedVector          point_coords = NULL, in_vec, out_vec;
1318   CeedElemRestriction rstr_points  = NULL;
1319   CeedQFunctionField *qf_input_fields, *qf_output_fields;
1320   CeedQFunction       qf;
1321   CeedOperatorField  *op_input_fields, *op_output_fields;
1322   CeedOperator_Ref   *impl;
1323 
1324   CeedCallBackend(CeedOperatorGetData(op, &impl));
1325   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
1326   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
1327   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
1328   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
1329 
1330   // Setup
1331   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
1332 
1333   // Ceed
1334   {
1335     Ceed ceed_parent;
1336 
1337     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1338     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
1339     CeedCallBackend(CeedReferenceCopy(ceed_parent, &ceed));
1340     CeedCallBackend(CeedDestroy(&ceed_parent));
1341   }
1342 
1343   // Point coordinates
1344   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
1345 
1346   // Input and output vectors
1347   {
1348     CeedSize input_size, output_size;
1349 
1350     CeedCallBackend(CeedOperatorGetActiveVectorLengths(op, &input_size, &output_size));
1351     CeedCallBackend(CeedVectorCreate(ceed, input_size, &in_vec));
1352     CeedCallBackend(CeedVectorCreate(ceed, output_size, &out_vec));
1353     CeedCallBackend(CeedVectorSetValue(out_vec, 0.0));
1354   }
1355 
1356   // Clear input Qvecs
1357   for (CeedInt i = 0; i < num_input_fields; i++) {
1358     bool       is_active;
1359     CeedVector vec;
1360 
1361     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1362     is_active = vec == CEED_VECTOR_ACTIVE;
1363     CeedCallBackend(CeedVectorDestroy(&vec));
1364     if (!is_active) continue;
1365     CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1366   }
1367 
1368   // Input Evecs and Restriction
1369   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
1370 
1371   // Loop through elements
1372   for (CeedInt e = 0; e < num_elem; e++) {
1373     CeedInt num_points, e_vec_size = 0;
1374 
1375     // Setup points for element
1376     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1377     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1378 
1379     // Input basis apply for non-active bases
1380     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
1381                                                        impl->point_coords_elem, true, e_data, impl, request));
1382 
1383     // Loop over points on element
1384     for (CeedInt i = 0; i < num_input_fields; i++) {
1385       bool                is_active_at_points = true, is_active;
1386       CeedInt             elem_size_active    = 1;
1387       CeedRestrictionType rstr_type;
1388       CeedVector          vec;
1389       CeedElemRestriction elem_rstr;
1390 
1391       // -- Skip non-active input
1392       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
1393       is_active = vec == CEED_VECTOR_ACTIVE;
1394       CeedCallBackend(CeedVectorDestroy(&vec));
1395       if (!is_active) continue;
1396 
1397       // -- Get active restriction type
1398       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
1399       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1400       is_active_at_points = rstr_type == CEED_RESTRICTION_POINTS;
1401       if (!is_active_at_points) CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size_active));
1402       else elem_size_active = num_points;
1403       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp_active));
1404       CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1405 
1406       e_vec_size = elem_size_active * num_comp_active;
1407       for (CeedInt s = 0; s < e_vec_size; s++) {
1408         CeedEvalMode eval_mode;
1409         CeedBasis    basis;
1410 
1411         // -- Update unit vector
1412         {
1413           CeedScalar *array;
1414 
1415           if (s == 0) CeedCallBackend(CeedVectorSetValue(impl->e_vecs_in[i], 0.0));
1416           CeedCallBackend(CeedVectorGetArray(impl->e_vecs_in[i], CEED_MEM_HOST, &array));
1417           array[s] = 1.0;
1418           if (s > 0) array[s - 1] = 0.0;
1419           CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_in[i], &array));
1420         }
1421         // -- Basis action
1422         CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
1423         switch (eval_mode) {
1424           case CEED_EVAL_NONE:
1425             break;
1426           // Note - these basis eval modes require FEM fields
1427           case CEED_EVAL_INTERP:
1428           case CEED_EVAL_GRAD:
1429           case CEED_EVAL_DIV:
1430           case CEED_EVAL_CURL:
1431             CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
1432             CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_NOTRANSPOSE, eval_mode, impl->point_coords_elem, impl->e_vecs_in[i],
1433                                                    impl->q_vecs_in[i]));
1434             CeedCallBackend(CeedBasisDestroy(&basis));
1435             break;
1436           case CEED_EVAL_WEIGHT:
1437             break;  // No action
1438         }
1439 
1440         // -- Q function
1441         if (!impl->is_identity_qf) {
1442           CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1443         }
1444 
1445         // -- Output basis apply and restriction
1446         CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
1447                                                             num_output_fields, impl->apply_add_basis_out, impl->skip_rstr_out, op, out_vec,
1448                                                             impl->point_coords_elem, impl, request));
1449 
1450         // -- Grab diagonal value
1451         for (CeedInt j = 0; j < num_output_fields; j++) {
1452           bool                is_active;
1453           CeedInt             elem_size = 0;
1454           CeedRestrictionType rstr_type;
1455           CeedEvalMode        eval_mode;
1456           CeedVector          vec;
1457           CeedElemRestriction elem_rstr;
1458           CeedBasis           basis;
1459 
1460           // ---- Skip non-active output
1461           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[j], &vec));
1462           is_active = vec == CEED_VECTOR_ACTIVE;
1463           CeedCallBackend(CeedVectorDestroy(&vec));
1464           if (!is_active) continue;
1465 
1466           // ---- Check if elem size matches
1467           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[j], &elem_rstr));
1468           CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
1469           if (is_active_at_points && rstr_type != CEED_RESTRICTION_POINTS) {
1470             CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1471             continue;
1472           }
1473           if (rstr_type == CEED_RESTRICTION_POINTS) {
1474             CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, e, &elem_size));
1475           } else {
1476             CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
1477           }
1478           {
1479             CeedInt num_comp = 0;
1480 
1481             CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
1482             if (e_vec_size != num_comp * elem_size) {
1483               CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1484               continue;
1485             }
1486           }
1487 
1488           // ---- Basis action
1489           CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[j], &eval_mode));
1490           switch (eval_mode) {
1491             case CEED_EVAL_NONE:
1492               break;  // No action
1493             case CEED_EVAL_INTERP:
1494             case CEED_EVAL_GRAD:
1495             case CEED_EVAL_DIV:
1496             case CEED_EVAL_CURL:
1497               CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[j], &basis));
1498               CeedCallBackend(CeedBasisApplyAtPoints(basis, 1, &num_points, CEED_TRANSPOSE, eval_mode, impl->point_coords_elem, impl->q_vecs_out[j],
1499                                                      impl->e_vecs_out[j]));
1500               CeedCallBackend(CeedBasisDestroy(&basis));
1501               break;
1502             // LCOV_EXCL_START
1503             case CEED_EVAL_WEIGHT: {
1504               return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
1505               // LCOV_EXCL_STOP
1506             }
1507           }
1508           // ---- Update output vector
1509           {
1510             CeedScalar *array, current_value = 0.0;
1511 
1512             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1513             current_value = array[s];
1514             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1515             CeedCallBackend(CeedVectorSetValue(impl->e_vecs_out[j], 0.0));
1516             CeedCallBackend(CeedVectorGetArray(impl->e_vecs_out[j], CEED_MEM_HOST, &array));
1517             array[s] = current_value;
1518             CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_out[j], &array));
1519           }
1520           // ---- Restrict output block
1521           if (rstr_type == CEED_RESTRICTION_POINTS) {
1522             CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1523           } else {
1524             CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[j], assembled, request));
1525           }
1526           CeedCallBackend(CeedElemRestrictionDestroy(&elem_rstr));
1527         }
1528         // -- Reset unit vector
1529         if (s == e_vec_size - 1) CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
1530       }
1531     }
1532     num_points_offset += num_points;
1533   }
1534 
1535   // Restore input arrays
1536   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
1537 
1538   // Cleanup
1539   CeedCallBackend(CeedDestroy(&ceed));
1540   CeedCallBackend(CeedVectorDestroy(&in_vec));
1541   CeedCallBackend(CeedVectorDestroy(&out_vec));
1542   CeedCallBackend(CeedVectorDestroy(&point_coords));
1543   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1544   return CEED_ERROR_SUCCESS;
1545 }
1546 
1547 //------------------------------------------------------------------------------
1548 // Operator Destroy
1549 //------------------------------------------------------------------------------
1550 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1551   CeedOperator_Ref *impl;
1552 
1553   CeedCallBackend(CeedOperatorGetData(op, &impl));
1554   CeedCallBackend(CeedFree(&impl->skip_rstr_in));
1555   CeedCallBackend(CeedFree(&impl->skip_rstr_out));
1556   CeedCallBackend(CeedFree(&impl->e_data_out_indices));
1557   CeedCallBackend(CeedFree(&impl->apply_add_basis_out));
1558   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1559     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1560   }
1561   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1562   CeedCallBackend(CeedFree(&impl->input_states));
1563 
1564   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1565     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1566     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1567   }
1568   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1569   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1570 
1571   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1572     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1573     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1574   }
1575   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1576   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1577   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1578 
1579   CeedCallBackend(CeedFree(&impl));
1580   return CEED_ERROR_SUCCESS;
1581 }
1582 
1583 //------------------------------------------------------------------------------
1584 // Operator Create
1585 //------------------------------------------------------------------------------
1586 int CeedOperatorCreate_Ref(CeedOperator op) {
1587   Ceed              ceed;
1588   CeedOperator_Ref *impl;
1589 
1590   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1591   CeedCallBackend(CeedCalloc(1, &impl));
1592   CeedCallBackend(CeedOperatorSetData(op, impl));
1593   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1594   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1595   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1596   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1597   CeedCallBackend(CeedDestroy(&ceed));
1598   return CEED_ERROR_SUCCESS;
1599 }
1600 
1601 //------------------------------------------------------------------------------
1602 // Operator Create At Points
1603 //------------------------------------------------------------------------------
1604 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1605   Ceed              ceed;
1606   CeedOperator_Ref *impl;
1607 
1608   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1609   CeedCallBackend(CeedCalloc(1, &impl));
1610   CeedCallBackend(CeedOperatorSetData(op, impl));
1611   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1612   CeedCallBackend(
1613       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1614   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal", CeedOperatorLinearAssembleAddDiagonalAtPoints_Ref));
1615   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1616   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1617   CeedCallBackend(CeedDestroy(&ceed));
1618   return CEED_ERROR_SUCCESS;
1619 }
1620 
1621 //------------------------------------------------------------------------------
1622