xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 6efa0d72b0004d844b67396ef4fa3300cbbcc0f4)
1 // Copyright (c) 2017-2022, Lawrence Livermore National Security, LLC and other CEED contributors.
2 // All Rights Reserved. See the top-level LICENSE and NOTICE files for details.
3 //
4 // SPDX-License-Identifier: BSD-2-Clause
5 //
6 // This file is part of CEED:  http://github.com/ceed
7 
8 #include <ceed.h>
9 #include <ceed/backend.h>
10 #include <stdbool.h>
11 #include <stddef.h>
12 #include <stdint.h>
13 
14 #include "ceed-ref.h"
15 
16 //------------------------------------------------------------------------------
17 // Setup Input/Output Fields
18 //------------------------------------------------------------------------------
19 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
20                                        CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
21   Ceed                ceed;
22   bool                is_at_points;
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     if (ceed_parent) ceed = ceed_parent;
34   }
35   CeedCallBackend(CeedOperatorIsAtPoints(op, &is_at_points));
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     }
55 
56     switch (eval_mode) {
57       case CEED_EVAL_NONE:
58         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
59         q_size = (CeedSize)Q * size;
60         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
61         break;
62       case CEED_EVAL_INTERP:
63       case CEED_EVAL_GRAD:
64       case CEED_EVAL_DIV:
65       case CEED_EVAL_CURL:
66         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
67         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
68         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
69         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
70         e_size = (CeedSize)P * num_comp;
71         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
72         q_size = (CeedSize)Q * size;
73         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
74         break;
75       case CEED_EVAL_WEIGHT:  // Only on input fields
76         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
77         q_size = (CeedSize)Q;
78         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
79         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_vecs[i]));
80         break;
81     }
82   }
83   return CEED_ERROR_SUCCESS;
84 }
85 
86 //------------------------------------------------------------------------------
87 // Setup Operator
88 //------------------------------------------------------------------------------/*
89 static int CeedOperatorSetup_Ref(CeedOperator op) {
90   bool                is_setup_done;
91   CeedInt             Q, num_input_fields, num_output_fields;
92   CeedQFunctionField *qf_input_fields, *qf_output_fields;
93   CeedQFunction       qf;
94   CeedOperatorField  *op_input_fields, *op_output_fields;
95   CeedOperator_Ref   *impl;
96 
97   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
98   if (is_setup_done) return CEED_ERROR_SUCCESS;
99 
100   CeedCallBackend(CeedOperatorGetData(op, &impl));
101   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
102   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
103   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
104   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
105   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
106 
107   // Allocate
108   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
109 
110   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
111   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
112   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
113   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
114   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
115 
116   impl->num_inputs  = num_input_fields;
117   impl->num_outputs = num_output_fields;
118 
119   // Set up infield and outfield e_vecs and q_vecs
120   // Infields
121   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
122   // Outfields
123   CeedCallBackend(
124       CeedOperatorSetupFields_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
125 
126   // Identity QFunctions
127   if (impl->is_identity_qf) {
128     CeedEvalMode        in_mode, out_mode;
129     CeedQFunctionField *in_fields, *out_fields;
130 
131     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
132     CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
133     CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));
134 
135     if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
136       impl->is_identity_rstr_op = true;
137     } else {
138       CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
139     }
140   }
141 
142   CeedCallBackend(CeedOperatorSetSetupDone(op));
143   return CEED_ERROR_SUCCESS;
144 }
145 
146 //------------------------------------------------------------------------------
147 // Setup Operator Inputs
148 //------------------------------------------------------------------------------
149 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
150                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
151                                               CeedOperator_Ref *impl, CeedRequest *request) {
152   for (CeedInt i = 0; i < num_input_fields; i++) {
153     uint64_t            state;
154     CeedEvalMode        eval_mode;
155     CeedVector          vec;
156     CeedElemRestriction elem_rstr;
157 
158     // Get input vector
159     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
160     if (vec == CEED_VECTOR_ACTIVE) {
161       if (skip_active) continue;
162       else vec = in_vec;
163     }
164 
165     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
166     // Restrict and Evec
167     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
168     } else {
169       // Restrict
170       CeedCallBackend(CeedVectorGetState(vec, &state));
171       // Skip restriction if input is unchanged
172       if (state != impl->input_states[i] || vec == in_vec) {
173         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
174         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
175         impl->input_states[i] = state;
176       }
177       // Get evec
178       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
179     }
180   }
181   return CEED_ERROR_SUCCESS;
182 }
183 
184 //------------------------------------------------------------------------------
185 // Input Basis Action
186 //------------------------------------------------------------------------------
187 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
188                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
189                                              CeedOperator_Ref *impl) {
190   for (CeedInt i = 0; i < num_input_fields; i++) {
191     CeedInt             elem_size, size, num_comp;
192     CeedEvalMode        eval_mode;
193     CeedElemRestriction elem_rstr;
194     CeedBasis           basis;
195 
196     // Skip active input
197     if (skip_active) {
198       CeedVector vec;
199 
200       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
201       if (vec == CEED_VECTOR_ACTIVE) continue;
202     }
203     // Get elem_size, eval_mode, size
204     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
205     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
206     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
207     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
208     // Basis action
209     switch (eval_mode) {
210       case CEED_EVAL_NONE:
211         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][e * Q * size]));
212         break;
213       case CEED_EVAL_INTERP:
214       case CEED_EVAL_GRAD:
215       case CEED_EVAL_DIV:
216       case CEED_EVAL_CURL:
217         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
218         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
219         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][e * elem_size * num_comp]));
220         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
221         break;
222       case CEED_EVAL_WEIGHT:
223         break;  // No action
224     }
225   }
226   return CEED_ERROR_SUCCESS;
227 }
228 
229 //------------------------------------------------------------------------------
230 // Output Basis Action
231 //------------------------------------------------------------------------------
232 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
233                                               CeedInt num_input_fields, CeedInt num_output_fields, CeedOperator op,
234                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
235   for (CeedInt i = 0; i < num_output_fields; i++) {
236     CeedInt             elem_size, num_comp;
237     CeedEvalMode        eval_mode;
238     CeedElemRestriction elem_rstr;
239     CeedBasis           basis;
240 
241     // Get elem_size, eval_mode
242     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
243     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
244     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
245     // Basis action
246     switch (eval_mode) {
247       case CEED_EVAL_NONE:
248         break;  // No action
249       case CEED_EVAL_INTERP:
250       case CEED_EVAL_GRAD:
251       case CEED_EVAL_DIV:
252       case CEED_EVAL_CURL:
253         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
254         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
255         CeedCallBackend(
256             CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][e * elem_size * num_comp]));
257         CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
258         break;
259       // LCOV_EXCL_START
260       case CEED_EVAL_WEIGHT: {
261         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
262         // LCOV_EXCL_STOP
263       }
264     }
265   }
266   return CEED_ERROR_SUCCESS;
267 }
268 
269 //------------------------------------------------------------------------------
270 // Restore Input Vectors
271 //------------------------------------------------------------------------------
272 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
273                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
274   for (CeedInt i = 0; i < num_input_fields; i++) {
275     CeedEvalMode eval_mode;
276 
277     // Skip active inputs
278     if (skip_active) {
279       CeedVector vec;
280 
281       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
282       if (vec == CEED_VECTOR_ACTIVE) continue;
283     }
284     // Restore input
285     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
286     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
287     } else {
288       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
289     }
290   }
291   return CEED_ERROR_SUCCESS;
292 }
293 
294 //------------------------------------------------------------------------------
295 // Operator Apply
296 //------------------------------------------------------------------------------
297 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
298   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
299   CeedEvalMode        eval_mode;
300   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
301   CeedQFunctionField *qf_input_fields, *qf_output_fields;
302   CeedQFunction       qf;
303   CeedOperatorField  *op_input_fields, *op_output_fields;
304   CeedOperator_Ref   *impl;
305 
306   CeedCallBackend(CeedOperatorGetData(op, &impl));
307   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
308   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
309   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
310   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
311   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
312 
313   // Setup
314   CeedCallBackend(CeedOperatorSetup_Ref(op));
315 
316   // Restriction only operator
317   if (impl->is_identity_rstr_op) {
318     CeedElemRestriction elem_rstr;
319 
320     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
321     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
322     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
323     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
324     return CEED_ERROR_SUCCESS;
325   }
326 
327   // Input Evecs and Restriction
328   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
329 
330   // Output Evecs
331   for (CeedInt i = 0; i < num_output_fields; i++) {
332     CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
333   }
334 
335   // Loop through elements
336   for (CeedInt e = 0; e < num_elem; e++) {
337     // Output pointers
338     for (CeedInt i = 0; i < num_output_fields; i++) {
339       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
340       if (eval_mode == CEED_EVAL_NONE) {
341         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
342         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][e * Q * size]));
343       }
344     }
345 
346     // Input basis apply
347     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
348 
349     // Q function
350     if (!impl->is_identity_qf) {
351       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
352     }
353 
354     // Output basis apply
355     CeedCallBackend(
356         CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields, op, e_data_full, impl));
357   }
358 
359   // Output restriction
360   for (CeedInt i = 0; i < num_output_fields; i++) {
361     CeedVector          vec;
362     CeedElemRestriction elem_rstr;
363 
364     // Restore Evec
365     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
366     // Get output vector
367     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
368     // Active
369     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
370     // Restrict
371     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
372     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
373   }
374 
375   // Restore input arrays
376   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
377   return CEED_ERROR_SUCCESS;
378 }
379 
380 //------------------------------------------------------------------------------
381 // Core code for assembling linear QFunction
382 //------------------------------------------------------------------------------
383 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
384                                                               CeedRequest *request) {
385   Ceed                ceed, ceed_parent;
386   CeedSize            q_size;
387   CeedInt             num_active_in, num_active_out, Q, num_elem, num_input_fields, num_output_fields, size;
388   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
389   CeedVector         *active_in;
390   CeedQFunctionField *qf_input_fields, *qf_output_fields;
391   CeedQFunction       qf;
392   CeedOperatorField  *op_input_fields, *op_output_fields;
393   CeedOperator_Ref   *impl;
394 
395   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
396   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
397   CeedCallBackend(CeedOperatorGetData(op, &impl));
398   active_in     = impl->qf_active_in;
399   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
400   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
401   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
402   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
403   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
404   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
405 
406   // Setup
407   CeedCallBackend(CeedOperatorSetup_Ref(op));
408 
409   // Check for restriction only operator
410   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
411 
412   // Input Evecs and Restriction
413   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
414 
415   // Count number of active input fields
416   if (!num_active_in) {
417     for (CeedInt i = 0; i < num_input_fields; i++) {
418       CeedScalar *q_vec_array;
419       CeedVector  vec;
420 
421       // Get input vector
422       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
423       // Check if active input
424       if (vec == CEED_VECTOR_ACTIVE) {
425         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
426         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
427         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
428         CeedCallBackend(CeedRealloc(num_active_in + size, &active_in));
429         for (CeedInt field = 0; field < size; field++) {
430           q_size = (CeedSize)Q;
431           CeedCallBackend(CeedVectorCreate(ceed_parent, q_size, &active_in[num_active_in + field]));
432           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * Q]));
433         }
434         num_active_in += size;
435         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
436       }
437     }
438     impl->num_active_in = num_active_in;
439     impl->qf_active_in  = active_in;
440   }
441 
442   // Count number of active output fields
443   if (!num_active_out) {
444     for (CeedInt i = 0; i < num_output_fields; i++) {
445       CeedVector vec;
446 
447       // Get output vector
448       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
449       // Check if active output
450       if (vec == CEED_VECTOR_ACTIVE) {
451         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
452         num_active_out += size;
453       }
454     }
455     impl->num_active_out = num_active_out;
456   }
457 
458   // Check sizes
459   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
460 
461   // Build objects if needed
462   if (build_objects) {
463     const CeedSize l_size     = (CeedSize)num_elem * Q * num_active_in * num_active_out;
464     CeedInt        strides[3] = {1, Q, num_active_in * num_active_out * Q}; /* *NOPAD* */
465 
466     // Create output restriction
467     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, num_active_in * num_active_out,
468                                                      num_active_in * num_active_out * num_elem * Q, strides, rstr));
469     // Create assembled vector
470     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
471   }
472   // Clear output vector
473   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
474   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
475 
476   // Loop through elements
477   for (CeedInt e = 0; e < num_elem; e++) {
478     // Input basis apply
479     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
480 
481     // Assemble QFunction
482     for (CeedInt in = 0; in < num_active_in; in++) {
483       // Set Inputs
484       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
485       if (num_active_in > 1) {
486         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
487       }
488       if (!impl->is_identity_qf) {
489         // Set Outputs
490         for (CeedInt out = 0; out < num_output_fields; out++) {
491           CeedVector vec;
492 
493           // Get output vector
494           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
495           // Check if active output
496           if (vec == CEED_VECTOR_ACTIVE) {
497             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
498             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &size));
499             assembled_array += size * Q;  // Advance the pointer by the size of the output
500           }
501         }
502         // Apply QFunction
503         CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
504       } else {
505         const CeedScalar *q_vec_array;
506 
507         // Copy Identity Outputs
508         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &size));
509         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
510         for (CeedInt i = 0; i < size * Q; i++) assembled_array[i] = q_vec_array[i];
511         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
512         assembled_array += size * Q;
513       }
514     }
515   }
516 
517   // Un-set output Qvecs to prevent accidental overwrite of Assembled
518   if (!impl->is_identity_qf) {
519     for (CeedInt out = 0; out < num_output_fields; out++) {
520       CeedVector vec;
521 
522       // Get output vector
523       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
524       // Check if active output
525       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
526         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
527       }
528     }
529   }
530 
531   // Restore input arrays
532   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
533 
534   // Restore output
535   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
536   return CEED_ERROR_SUCCESS;
537 }
538 
539 //------------------------------------------------------------------------------
540 // Assemble Linear QFunction
541 //------------------------------------------------------------------------------
542 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
543   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
544 }
545 
546 //------------------------------------------------------------------------------
547 // Update Assembled Linear QFunction
548 //------------------------------------------------------------------------------
549 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
550   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
551 }
552 
553 //------------------------------------------------------------------------------
554 // Setup Input/Output Fields
555 //------------------------------------------------------------------------------
556 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
557                                                CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
558   Ceed                ceed;
559   CeedSize            e_size, q_size;
560   CeedInt             e_size_padding = 0, max_num_points, num_comp, size, P;
561   CeedQFunctionField *qf_fields;
562   CeedOperatorField  *op_fields;
563 
564   {
565     Ceed ceed_parent;
566 
567     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
568     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
569     if (ceed_parent) ceed = ceed_parent;
570   }
571   if (is_input) {
572     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
573     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
574   } else {
575     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
576     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
577   }
578 
579   // Get max number of points
580   {
581     CeedInt             dim;
582     CeedElemRestriction rstr_points = NULL;
583     CeedOperator_Ref   *impl;
584 
585     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
586     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
587     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
588     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
589     CeedCallBackend(CeedOperatorGetData(op, &impl));
590     if (is_input) {
591       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
592       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
593     }
594   }
595 
596   // Loop over fields
597   for (CeedInt i = 0; i < num_fields; i++) {
598     CeedEvalMode eval_mode;
599     CeedBasis    basis;
600 
601     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
602     if (eval_mode != CEED_EVAL_WEIGHT) {
603       CeedElemRestriction elem_rstr;
604       CeedSize            e_size;
605       bool                is_at_points;
606 
607       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
608       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
609       CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
610       if (is_at_points) {
611         CeedCallBackend(CeedElemRestrictionGetEVectorSize(elem_rstr, &e_size));
612         if (e_size_padding == 0) {
613           CeedInt num_points, num_elem;
614 
615           CeedCallBackend(CeedElemRestrictionGetNumElements(elem_rstr, &num_elem));
616           CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, num_elem - 1, &num_points));
617           e_size_padding = (max_num_points - num_points) * num_comp;
618         }
619         CeedCallBackend(CeedVectorCreate(ceed, e_size + e_size_padding, &e_vecs_full[i + start_e]));
620         CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
621       } else {
622         CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
623       }
624     }
625 
626     switch (eval_mode) {
627       case CEED_EVAL_NONE: {
628         CeedVector vec;
629 
630         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
631         e_size = (CeedSize)max_num_points * size;
632         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
633         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
634         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
635           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
636           CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
637         } else {
638           q_size = (CeedSize)max_num_points * size;
639           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
640         }
641         break;
642       }
643       case CEED_EVAL_INTERP:
644       case CEED_EVAL_GRAD:
645       case CEED_EVAL_DIV:
646       case CEED_EVAL_CURL:
647         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
648         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
649         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
650         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
651         e_size = (CeedSize)P * num_comp;
652         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
653         q_size = (CeedSize)max_num_points * size;
654         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
655         CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
656         break;
657       case CEED_EVAL_WEIGHT:  // Only on input fields
658         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
659         q_size = (CeedSize)max_num_points;
660         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
661         CeedCallBackend(
662             CeedBasisApplyAtPoints(basis, max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
663         break;
664     }
665     if (is_input && e_vecs[i]) {
666       CeedCallBackend(CeedVectorSetArray(e_vecs[i], CEED_MEM_HOST, CEED_COPY_VALUES, NULL));
667     }
668   }
669   return CEED_ERROR_SUCCESS;
670 }
671 
672 //------------------------------------------------------------------------------
673 // Setup Operator
674 //------------------------------------------------------------------------------
675 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
676   bool                is_setup_done;
677   CeedInt             Q, num_input_fields, num_output_fields;
678   CeedQFunctionField *qf_input_fields, *qf_output_fields;
679   CeedQFunction       qf;
680   CeedOperatorField  *op_input_fields, *op_output_fields;
681   CeedOperator_Ref   *impl;
682 
683   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
684   if (is_setup_done) return CEED_ERROR_SUCCESS;
685 
686   CeedCallBackend(CeedOperatorGetData(op, &impl));
687   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
688   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
689   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
690   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
691   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
692 
693   // Allocate
694   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
695 
696   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
697   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
698   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
699   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
700   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
701 
702   impl->num_inputs  = num_input_fields;
703   impl->num_outputs = num_output_fields;
704 
705   // Set up infield and outfield pointer arrays
706   // Infields
707   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
708   // Outfields
709   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
710                                                       num_output_fields, Q));
711 
712   // Identity QFunctions
713   if (impl->is_identity_qf) {
714     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
715     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
716   }
717 
718   CeedCallBackend(CeedOperatorSetSetupDone(op));
719   return CEED_ERROR_SUCCESS;
720 }
721 
722 //------------------------------------------------------------------------------
723 // Input Basis Action
724 //------------------------------------------------------------------------------
725 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
726                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
727                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
728                                                      CeedOperator_Ref *impl, CeedRequest *request) {
729   for (CeedInt i = 0; i < num_input_fields; i++) {
730     bool                is_active_input = false;
731     CeedInt             elem_size, size, num_comp;
732     CeedRestrictionType rstr_type;
733     CeedEvalMode        eval_mode;
734     CeedVector          vec;
735     CeedElemRestriction elem_rstr;
736     CeedBasis           basis;
737 
738     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
739     // Skip active input
740     is_active_input = vec == CEED_VECTOR_ACTIVE;
741     if (skip_active && is_active_input) continue;
742 
743     // Get elem_size, eval_mode, size
744     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
745     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
746     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
747     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
748     // Restrict block active input
749     if (is_active_input) {
750       if (rstr_type == CEED_RESTRICTION_POINTS) {
751         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
752       } else {
753         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
754       }
755     }
756     // Basis action
757     switch (eval_mode) {
758       case CEED_EVAL_NONE:
759         if (!is_active_input) {
760           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
761         }
762         break;
763       // Note - these basis eval modes require FEM fields
764       case CEED_EVAL_INTERP:
765       case CEED_EVAL_GRAD:
766       case CEED_EVAL_DIV:
767       case CEED_EVAL_CURL:
768         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
769         if (!is_active_input) {
770           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
771           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
772           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][e * elem_size * num_comp]));
773         }
774         CeedCallBackend(
775             CeedBasisApplyAtPoints(basis, num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
776         break;
777       case CEED_EVAL_WEIGHT:
778         break;  // No action
779     }
780   }
781   return CEED_ERROR_SUCCESS;
782 }
783 
784 //------------------------------------------------------------------------------
785 // Output Basis Action
786 //------------------------------------------------------------------------------
787 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
788                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
789                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
790                                                       CeedRequest *request) {
791   for (CeedInt i = 0; i < num_output_fields; i++) {
792     CeedRestrictionType rstr_type;
793     CeedEvalMode        eval_mode;
794     CeedVector          vec;
795     CeedElemRestriction elem_rstr;
796     CeedBasis           basis;
797 
798     // Get elem_size, eval_mode, size
799     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
800     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
801     // Basis action
802     switch (eval_mode) {
803       case CEED_EVAL_NONE:
804         break;  // No action
805       case CEED_EVAL_INTERP:
806       case CEED_EVAL_GRAD:
807       case CEED_EVAL_DIV:
808       case CEED_EVAL_CURL:
809         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
810         CeedCallBackend(
811             CeedBasisApplyAtPoints(basis, num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
812         break;
813       // LCOV_EXCL_START
814       case CEED_EVAL_WEIGHT: {
815         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
816         // LCOV_EXCL_STOP
817       }
818     }
819     // Restrict output block
820     // Get output vector
821     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
822     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
823     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
824     // Restrict
825     if (rstr_type == CEED_RESTRICTION_POINTS) {
826       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
827     } else {
828       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
829     }
830   }
831   return CEED_ERROR_SUCCESS;
832 }
833 
834 //------------------------------------------------------------------------------
835 // Operator Apply
836 //------------------------------------------------------------------------------
837 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
838   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
839   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
840   CeedVector          point_coords               = NULL;
841   CeedElemRestriction rstr_points                = NULL;
842   CeedQFunctionField *qf_input_fields, *qf_output_fields;
843   CeedQFunction       qf;
844   CeedOperatorField  *op_input_fields, *op_output_fields;
845   CeedOperator_Ref   *impl;
846 
847   CeedCallBackend(CeedOperatorGetData(op, &impl));
848   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
849   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
850   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
851   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
852 
853   // Setup
854   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
855 
856   // Point coordinates
857   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
858 
859   // Input Evecs and Restriction
860   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
861 
862   // Loop through elements
863   for (CeedInt e = 0; e < num_elem; e++) {
864     CeedInt num_points;
865 
866     // Setup points for element
867     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
868     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
869 
870     // Input basis apply
871     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
872                                                        impl->point_coords_elem, false, e_data, impl, request));
873 
874     // Q function
875     if (!impl->is_identity_qf) {
876       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
877     }
878 
879     // Output basis apply and restriction
880     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
881                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
882 
883     num_points_offset += num_points;
884   }
885 
886   // Restore input arrays
887   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
888 
889   // Cleanup point coordinates
890   CeedCallBackend(CeedVectorDestroy(&point_coords));
891   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
892   return CEED_ERROR_SUCCESS;
893 }
894 
895 //------------------------------------------------------------------------------
896 // Core code for assembling linear QFunction
897 //------------------------------------------------------------------------------
898 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
899                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
900   Ceed                ceed;
901   CeedSize            q_size;
902   CeedInt             num_active_in, num_active_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
903   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
904   CeedVector         *active_in, point_coords                           = NULL;
905   CeedQFunctionField *qf_input_fields, *qf_output_fields;
906   CeedQFunction       qf;
907   CeedOperatorField  *op_input_fields, *op_output_fields;
908   CeedOperator_Ref   *impl;
909   CeedElemRestriction rstr_points = NULL;
910 
911   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
912   CeedCallBackend(CeedOperatorGetData(op, &impl));
913   active_in     = impl->qf_active_in;
914   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
915   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
916   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
917   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
918   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
919 
920   // Setup
921   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
922 
923   // Check for restriction only operator
924   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
925 
926   // Point coordinates
927   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
928   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
929 
930   // Input Evecs and Restriction
931   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
932 
933   // Count number of active input fields
934   if (!num_active_in) {
935     for (CeedInt i = 0; i < num_input_fields; i++) {
936       CeedScalar *q_vec_array;
937       CeedInt     field_size;
938       CeedVector  vec;
939 
940       // Get input vector
941       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
942       // Check if active input
943       if (vec == CEED_VECTOR_ACTIVE) {
944         // Check that all active inputs are nodal fields
945         {
946           CeedElemRestriction elem_rstr;
947           bool                is_at_points = false;
948 
949           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
950           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
951           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
952         }
953         // Get size of active input
954         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
955         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
956         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
957         CeedCallBackend(CeedRealloc(num_active_in + field_size, &active_in));
958         for (CeedInt field = 0; field < field_size; field++) {
959           q_size = (CeedSize)max_num_points;
960           CeedCallBackend(CeedVectorCreate(ceed, q_size, &active_in[num_active_in + field]));
961           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * q_size]));
962         }
963         num_active_in += field_size;
964         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
965       }
966     }
967     impl->num_active_in = num_active_in;
968     impl->qf_active_in  = active_in;
969   }
970 
971   // Count number of active output fields
972   if (!num_active_out) {
973     for (CeedInt i = 0; i < num_output_fields; i++) {
974       CeedVector vec;
975       CeedInt    field_size;
976 
977       // Get output vector
978       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
979       // Check if active output
980       if (vec == CEED_VECTOR_ACTIVE) {
981         // Check that all active inputs are nodal fields
982         {
983           CeedElemRestriction elem_rstr;
984           bool                is_at_points = false;
985 
986           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
987           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
988           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
989         }
990         // Get size of active output
991         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
992         num_active_out += field_size;
993       }
994     }
995     impl->num_active_out = num_active_out;
996   }
997 
998   // Check sizes
999   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
1000 
1001   // Build objects if needed
1002   if (build_objects) {
1003     CeedInt        num_points_total;
1004     const CeedInt *offsets;
1005 
1006     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1007 
1008     // Create output restriction (at points)
1009     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1010     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, num_active_in * num_active_out,
1011                                                       num_active_in * num_active_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
1012                                                       rstr));
1013     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1014 
1015     // Create assembled vector
1016     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1017   }
1018   // Clear output vector
1019   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1020   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1021 
1022   // Loop through elements
1023   for (CeedInt e = 0; e < num_elem; e++) {
1024     CeedInt num_points;
1025 
1026     // Setup points for element
1027     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1028     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1029 
1030     // Input basis apply
1031     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1032                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1033 
1034     // Assemble QFunction
1035     for (CeedInt in = 0; in < num_active_in; in++) {
1036       // Set Inputs
1037       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
1038       if (num_active_in > 1) {
1039         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
1040       }
1041       if (!impl->is_identity_qf) {
1042         // Set Outputs
1043         for (CeedInt out = 0; out < num_output_fields; out++) {
1044           CeedVector vec;
1045           CeedInt    field_size;
1046 
1047           // Get output vector
1048           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1049           // Check if active output
1050           if (vec == CEED_VECTOR_ACTIVE) {
1051             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1052             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1053             assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1054           }
1055         }
1056         // Apply QFunction
1057         CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1058       } else {
1059         const CeedScalar *q_vec_array;
1060         CeedInt           field_size;
1061 
1062         // Copy Identity Outputs
1063         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1064         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
1065         for (CeedInt i = 0; i < field_size * num_points; i++) assembled_array[i] = q_vec_array[i];
1066         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
1067         assembled_array += field_size * num_points;
1068       }
1069     }
1070     num_points_offset += num_points;
1071   }
1072 
1073   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1074   if (!impl->is_identity_qf) {
1075     for (CeedInt out = 0; out < num_output_fields; out++) {
1076       CeedVector vec;
1077 
1078       // Get output vector
1079       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1080       // Check if active output
1081       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1082         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1083       }
1084     }
1085   }
1086 
1087   // Restore input arrays
1088   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1089 
1090   // Restore output
1091   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1092 
1093   // Cleanup
1094   CeedCallBackend(CeedVectorDestroy(&point_coords));
1095   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1096   return CEED_ERROR_SUCCESS;
1097 }
1098 
1099 //------------------------------------------------------------------------------
1100 // Assemble Linear QFunction
1101 //------------------------------------------------------------------------------
1102 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1103   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1104 }
1105 
1106 //------------------------------------------------------------------------------
1107 // Update Assembled Linear QFunction
1108 //------------------------------------------------------------------------------
1109 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1110                                                                  CeedRequest *request) {
1111   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1112 }
1113 
1114 //------------------------------------------------------------------------------
1115 // Assemble Operator
1116 //------------------------------------------------------------------------------
1117 
1118 //------------------------------------------------------------------------------
1119 // Operator Destroy
1120 //------------------------------------------------------------------------------
1121 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1122   CeedOperator_Ref *impl;
1123 
1124   CeedCallBackend(CeedOperatorGetData(op, &impl));
1125   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1126     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1127   }
1128   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1129   CeedCallBackend(CeedFree(&impl->input_states));
1130 
1131   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1132     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1133     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1134   }
1135   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1136   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1137 
1138   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1139     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1140     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1141   }
1142   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1143   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1144   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1145 
1146   // QFunction assembly
1147   for (CeedInt i = 0; i < impl->num_active_in; i++) {
1148     CeedCallBackend(CeedVectorDestroy(&impl->qf_active_in[i]));
1149   }
1150   CeedCallBackend(CeedFree(&impl->qf_active_in));
1151 
1152   CeedCallBackend(CeedFree(&impl));
1153   return CEED_ERROR_SUCCESS;
1154 }
1155 
1156 //------------------------------------------------------------------------------
1157 // Operator Create
1158 //------------------------------------------------------------------------------
1159 int CeedOperatorCreate_Ref(CeedOperator op) {
1160   Ceed              ceed;
1161   CeedOperator_Ref *impl;
1162 
1163   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1164   CeedCallBackend(CeedCalloc(1, &impl));
1165   CeedCallBackend(CeedOperatorSetData(op, impl));
1166   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1167   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1168   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1169   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1170   return CEED_ERROR_SUCCESS;
1171 }
1172 
1173 //------------------------------------------------------------------------------
1174 // Operator Create At Points
1175 //------------------------------------------------------------------------------
1176 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1177   Ceed              ceed;
1178   CeedOperator_Ref *impl;
1179 
1180   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1181   CeedCallBackend(CeedCalloc(1, &impl));
1182   CeedCallBackend(CeedOperatorSetData(op, impl));
1183   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1184   CeedCallBackend(
1185       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1186   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1187   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1188   return CEED_ERROR_SUCCESS;
1189 }
1190 
1191 //------------------------------------------------------------------------------
1192