xref: /libCEED/backends/ref/ceed-ref-operator.c (revision a267acd12487b2c23311fe9e8f7b0c3e959135b1)
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   CeedSize            e_size, q_size;
23   CeedInt             num_comp, size, P;
24   CeedQFunctionField *qf_fields;
25   CeedOperatorField  *op_fields;
26 
27   {
28     Ceed ceed_parent;
29 
30     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
31     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
32     if (ceed_parent) ceed = ceed_parent;
33   }
34   if (is_input) {
35     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
36     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
37   } else {
38     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
39     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
40   }
41 
42   // Loop over fields
43   for (CeedInt i = 0; i < num_fields; i++) {
44     CeedEvalMode        eval_mode;
45     CeedElemRestriction elem_rstr;
46     CeedBasis           basis;
47 
48     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
49     if (eval_mode != CEED_EVAL_WEIGHT) {
50       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
51       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
52     }
53 
54     switch (eval_mode) {
55       case CEED_EVAL_NONE:
56         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
57         q_size = (CeedSize)Q * size;
58         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
59         break;
60       case CEED_EVAL_INTERP:
61       case CEED_EVAL_GRAD:
62       case CEED_EVAL_DIV:
63       case CEED_EVAL_CURL:
64         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
65         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
66         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
67         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
68         e_size = (CeedSize)P * num_comp;
69         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
70         q_size = (CeedSize)Q * size;
71         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
72         break;
73       case CEED_EVAL_WEIGHT:  // Only on input fields
74         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
75         q_size = (CeedSize)Q;
76         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
77         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, q_vecs[i]));
78         break;
79     }
80   }
81   return CEED_ERROR_SUCCESS;
82 }
83 
84 //------------------------------------------------------------------------------
85 // Setup Operator
86 //------------------------------------------------------------------------------/*
87 static int CeedOperatorSetup_Ref(CeedOperator op) {
88   bool                is_setup_done;
89   CeedInt             Q, num_input_fields, num_output_fields;
90   CeedQFunctionField *qf_input_fields, *qf_output_fields;
91   CeedQFunction       qf;
92   CeedOperatorField  *op_input_fields, *op_output_fields;
93   CeedOperator_Ref   *impl;
94 
95   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
96   if (is_setup_done) return CEED_ERROR_SUCCESS;
97 
98   CeedCallBackend(CeedOperatorGetData(op, &impl));
99   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
100   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
101   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
102   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
103   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
104 
105   // Allocate
106   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
107 
108   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
109   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
110   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
111   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
112   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
113 
114   impl->num_inputs  = num_input_fields;
115   impl->num_outputs = num_output_fields;
116 
117   // Set up infield and outfield e_vecs and q_vecs
118   // Infields
119   CeedCallBackend(CeedOperatorSetupFields_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
120   // Outfields
121   CeedCallBackend(
122       CeedOperatorSetupFields_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields, num_output_fields, Q));
123 
124   // Identity QFunctions
125   if (impl->is_identity_qf) {
126     CeedEvalMode        in_mode, out_mode;
127     CeedQFunctionField *in_fields, *out_fields;
128 
129     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &in_fields, NULL, &out_fields));
130     CeedCallBackend(CeedQFunctionFieldGetEvalMode(in_fields[0], &in_mode));
131     CeedCallBackend(CeedQFunctionFieldGetEvalMode(out_fields[0], &out_mode));
132 
133     if (in_mode == CEED_EVAL_NONE && out_mode == CEED_EVAL_NONE) {
134       impl->is_identity_rstr_op = true;
135     } else {
136       CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
137     }
138   }
139 
140   CeedCallBackend(CeedOperatorSetSetupDone(op));
141   return CEED_ERROR_SUCCESS;
142 }
143 
144 //------------------------------------------------------------------------------
145 // Setup Operator Inputs
146 //------------------------------------------------------------------------------
147 static inline int CeedOperatorSetupInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
148                                               CeedVector in_vec, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
149                                               CeedOperator_Ref *impl, CeedRequest *request) {
150   for (CeedInt i = 0; i < num_input_fields; i++) {
151     uint64_t            state;
152     CeedEvalMode        eval_mode;
153     CeedVector          vec;
154     CeedElemRestriction elem_rstr;
155 
156     // Get input vector
157     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
158     if (vec == CEED_VECTOR_ACTIVE) {
159       if (skip_active) continue;
160       else vec = in_vec;
161     }
162 
163     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
164     // Restrict and Evec
165     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
166     } else {
167       // Restrict
168       CeedCallBackend(CeedVectorGetState(vec, &state));
169       // Skip restriction if input is unchanged
170       if (state != impl->input_states[i] || vec == in_vec) {
171         CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
172         CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, vec, impl->e_vecs_full[i], request));
173         impl->input_states[i] = state;
174       }
175       // Get evec
176       CeedCallBackend(CeedVectorGetArrayRead(impl->e_vecs_full[i], CEED_MEM_HOST, (const CeedScalar **)&e_data_full[i]));
177     }
178   }
179   return CEED_ERROR_SUCCESS;
180 }
181 
182 //------------------------------------------------------------------------------
183 // Input Basis Action
184 //------------------------------------------------------------------------------
185 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
186                                              CeedInt num_input_fields, const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX],
187                                              CeedOperator_Ref *impl) {
188   for (CeedInt i = 0; i < num_input_fields; i++) {
189     CeedInt             elem_size, size, num_comp;
190     CeedEvalMode        eval_mode;
191     CeedElemRestriction elem_rstr;
192     CeedBasis           basis;
193 
194     // Skip active input
195     if (skip_active) {
196       CeedVector vec;
197 
198       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
199       if (vec == CEED_VECTOR_ACTIVE) continue;
200     }
201     // Get elem_size, eval_mode, size
202     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
203     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
204     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
205     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
206     // Basis action
207     switch (eval_mode) {
208       case CEED_EVAL_NONE:
209         CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * Q * size]));
210         break;
211       case CEED_EVAL_INTERP:
212       case CEED_EVAL_GRAD:
213       case CEED_EVAL_DIV:
214       case CEED_EVAL_CURL:
215         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
216         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
217         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i][(CeedSize)e * elem_size * num_comp]));
218         CeedCallBackend(CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, eval_mode, impl->e_vecs_in[i], impl->q_vecs_in[i]));
219         break;
220       case CEED_EVAL_WEIGHT:
221         break;  // No action
222     }
223   }
224   return CEED_ERROR_SUCCESS;
225 }
226 
227 //------------------------------------------------------------------------------
228 // Output Basis Action
229 //------------------------------------------------------------------------------
230 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q, CeedQFunctionField *qf_output_fields, CeedOperatorField *op_output_fields,
231                                               CeedInt num_input_fields, CeedInt num_output_fields, CeedOperator op,
232                                               CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
233   for (CeedInt i = 0; i < num_output_fields; i++) {
234     CeedInt             elem_size, num_comp;
235     CeedEvalMode        eval_mode;
236     CeedElemRestriction elem_rstr;
237     CeedBasis           basis;
238 
239     // Get elem_size, eval_mode
240     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
241     CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
242     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
243     // Basis action
244     switch (eval_mode) {
245       case CEED_EVAL_NONE:
246         break;  // No action
247       case CEED_EVAL_INTERP:
248       case CEED_EVAL_GRAD:
249       case CEED_EVAL_DIV:
250       case CEED_EVAL_CURL:
251         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
252         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
253         CeedCallBackend(CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER,
254                                            &e_data_full[i + num_input_fields][(CeedSize)e * elem_size * num_comp]));
255         CeedCallBackend(CeedBasisApply(basis, 1, CEED_TRANSPOSE, eval_mode, impl->q_vecs_out[i], impl->e_vecs_out[i]));
256         break;
257       // LCOV_EXCL_START
258       case CEED_EVAL_WEIGHT: {
259         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
260         // LCOV_EXCL_STOP
261       }
262     }
263   }
264   return CEED_ERROR_SUCCESS;
265 }
266 
267 //------------------------------------------------------------------------------
268 // Restore Input Vectors
269 //------------------------------------------------------------------------------
270 static inline int CeedOperatorRestoreInputs_Ref(CeedInt num_input_fields, CeedQFunctionField *qf_input_fields, CeedOperatorField *op_input_fields,
271                                                 const bool skip_active, CeedScalar *e_data_full[2 * CEED_FIELD_MAX], CeedOperator_Ref *impl) {
272   for (CeedInt i = 0; i < num_input_fields; i++) {
273     CeedEvalMode eval_mode;
274 
275     // Skip active inputs
276     if (skip_active) {
277       CeedVector vec;
278 
279       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
280       if (vec == CEED_VECTOR_ACTIVE) continue;
281     }
282     // Restore input
283     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
284     if (eval_mode == CEED_EVAL_WEIGHT) {  // Skip
285     } else {
286       CeedCallBackend(CeedVectorRestoreArrayRead(impl->e_vecs_full[i], (const CeedScalar **)&e_data_full[i]));
287     }
288   }
289   return CEED_ERROR_SUCCESS;
290 }
291 
292 //------------------------------------------------------------------------------
293 // Operator Apply
294 //------------------------------------------------------------------------------
295 static int CeedOperatorApplyAdd_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
296   CeedInt             Q, num_elem, num_input_fields, num_output_fields, size;
297   CeedEvalMode        eval_mode;
298   CeedScalar         *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
299   CeedQFunctionField *qf_input_fields, *qf_output_fields;
300   CeedQFunction       qf;
301   CeedOperatorField  *op_input_fields, *op_output_fields;
302   CeedOperator_Ref   *impl;
303 
304   CeedCallBackend(CeedOperatorGetData(op, &impl));
305   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
306   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
307   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
308   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
309   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
310 
311   // Setup
312   CeedCallBackend(CeedOperatorSetup_Ref(op));
313 
314   // Restriction only operator
315   if (impl->is_identity_rstr_op) {
316     CeedElemRestriction elem_rstr;
317 
318     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[0], &elem_rstr));
319     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_full[0], request));
320     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[0], &elem_rstr));
321     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[0], out_vec, request));
322     return CEED_ERROR_SUCCESS;
323   }
324 
325   // Input Evecs and Restriction
326   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, in_vec, false, e_data_full, impl, request));
327 
328   // Output Evecs
329   for (CeedInt i = 0; i < num_output_fields; i++) {
330     CeedCallBackend(CeedVectorGetArrayWrite(impl->e_vecs_full[i + impl->num_inputs], CEED_MEM_HOST, &e_data_full[i + num_input_fields]));
331   }
332 
333   // Loop through elements
334   for (CeedInt e = 0; e < num_elem; e++) {
335     // Output pointers
336     for (CeedInt i = 0; i < num_output_fields; i++) {
337       CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
338       if (eval_mode == CEED_EVAL_NONE) {
339         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
340         CeedCallBackend(
341             CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][(CeedSize)e * Q * size]));
342       }
343     }
344 
345     // Input basis apply
346     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
347 
348     // Q function
349     if (!impl->is_identity_qf) {
350       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
351     }
352 
353     // Output basis apply
354     CeedCallBackend(
355         CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields, op, e_data_full, impl));
356   }
357 
358   // Output restriction
359   for (CeedInt i = 0; i < num_output_fields; i++) {
360     CeedVector          vec;
361     CeedElemRestriction elem_rstr;
362 
363     // Restore Evec
364     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
365     // Get output vector
366     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
367     // Active
368     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
369     // Restrict
370     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
371     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
372   }
373 
374   // Restore input arrays
375   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
376   return CEED_ERROR_SUCCESS;
377 }
378 
379 //------------------------------------------------------------------------------
380 // Core code for assembling linear QFunction
381 //------------------------------------------------------------------------------
382 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
383                                                               CeedRequest *request) {
384   Ceed                ceed, ceed_parent;
385   CeedSize            q_size;
386   CeedInt             num_active_in, num_active_out, Q, num_elem, num_input_fields, num_output_fields, size;
387   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
388   CeedVector         *active_in;
389   CeedQFunctionField *qf_input_fields, *qf_output_fields;
390   CeedQFunction       qf;
391   CeedOperatorField  *op_input_fields, *op_output_fields;
392   CeedOperator_Ref   *impl;
393 
394   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
395   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
396   CeedCallBackend(CeedOperatorGetData(op, &impl));
397   active_in     = impl->qf_active_in;
398   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
399   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
400   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
401   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
402   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
403   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
404 
405   // Setup
406   CeedCallBackend(CeedOperatorSetup_Ref(op));
407 
408   // Check for restriction only operator
409   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
410 
411   // Input Evecs and Restriction
412   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
413 
414   // Count number of active input fields
415   if (!num_active_in) {
416     for (CeedInt i = 0; i < num_input_fields; i++) {
417       CeedScalar *q_vec_array;
418       CeedVector  vec;
419 
420       // Get input vector
421       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
422       // Check if active input
423       if (vec == CEED_VECTOR_ACTIVE) {
424         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
425         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
426         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
427         CeedCallBackend(CeedRealloc(num_active_in + size, &active_in));
428         for (CeedInt field = 0; field < size; field++) {
429           q_size = (CeedSize)Q;
430           CeedCallBackend(CeedVectorCreate(ceed_parent, q_size, &active_in[num_active_in + field]));
431           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * Q]));
432         }
433         num_active_in += size;
434         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
435       }
436     }
437     impl->num_active_in = num_active_in;
438     impl->qf_active_in  = active_in;
439   }
440 
441   // Count number of active output fields
442   if (!num_active_out) {
443     for (CeedInt i = 0; i < num_output_fields; i++) {
444       CeedVector vec;
445 
446       // Get output vector
447       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
448       // Check if active output
449       if (vec == CEED_VECTOR_ACTIVE) {
450         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
451         num_active_out += size;
452       }
453     }
454     impl->num_active_out = num_active_out;
455   }
456 
457   // Check sizes
458   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
459 
460   // Build objects if needed
461   if (build_objects) {
462     const CeedSize l_size     = (CeedSize)num_elem * Q * num_active_in * num_active_out;
463     CeedInt        strides[3] = {1, Q, num_active_in * num_active_out * Q}; /* *NOPAD* */
464 
465     // Create output restriction
466     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, num_active_in * num_active_out,
467                                                      num_active_in * num_active_out * num_elem * Q, strides, rstr));
468     // Create assembled vector
469     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
470   }
471   // Clear output vector
472   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
473   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
474 
475   // Loop through elements
476   for (CeedInt e = 0; e < num_elem; e++) {
477     // Input basis apply
478     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
479 
480     // Assemble QFunction
481     for (CeedInt in = 0; in < num_active_in; in++) {
482       // Set Inputs
483       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
484       if (num_active_in > 1) {
485         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
486       }
487       if (!impl->is_identity_qf) {
488         // Set Outputs
489         for (CeedInt out = 0; out < num_output_fields; out++) {
490           CeedVector vec;
491 
492           // Get output vector
493           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
494           // Check if active output
495           if (vec == CEED_VECTOR_ACTIVE) {
496             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
497             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &size));
498             assembled_array += size * Q;  // Advance the pointer by the size of the output
499           }
500         }
501         // Apply QFunction
502         CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
503       } else {
504         const CeedScalar *q_vec_array;
505 
506         // Copy Identity Outputs
507         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &size));
508         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
509         for (CeedInt i = 0; i < size * Q; i++) assembled_array[i] = q_vec_array[i];
510         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
511         assembled_array += size * Q;
512       }
513     }
514   }
515 
516   // Un-set output Qvecs to prevent accidental overwrite of Assembled
517   if (!impl->is_identity_qf) {
518     for (CeedInt out = 0; out < num_output_fields; out++) {
519       CeedVector vec;
520 
521       // Get output vector
522       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
523       // Check if active output
524       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
525         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
526       }
527     }
528   }
529 
530   // Restore input arrays
531   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
532 
533   // Restore output
534   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
535   return CEED_ERROR_SUCCESS;
536 }
537 
538 //------------------------------------------------------------------------------
539 // Assemble Linear QFunction
540 //------------------------------------------------------------------------------
541 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
542   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
543 }
544 
545 //------------------------------------------------------------------------------
546 // Update Assembled Linear QFunction
547 //------------------------------------------------------------------------------
548 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
549   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
550 }
551 
552 //------------------------------------------------------------------------------
553 // Setup Input/Output Fields
554 //------------------------------------------------------------------------------
555 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
556                                                CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
557   Ceed                ceed;
558   CeedSize            e_size, q_size;
559   CeedInt             e_size_padding = 0, max_num_points, num_comp, size, P;
560   CeedQFunctionField *qf_fields;
561   CeedOperatorField  *op_fields;
562 
563   {
564     Ceed ceed_parent;
565 
566     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
567     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
568     if (ceed_parent) ceed = ceed_parent;
569   }
570   if (is_input) {
571     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
572     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
573   } else {
574     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
575     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
576   }
577 
578   // Get max number of points
579   {
580     CeedInt             dim;
581     CeedElemRestriction rstr_points = NULL;
582     CeedOperator_Ref   *impl;
583 
584     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
585     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
586     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
587     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
588     CeedCallBackend(CeedOperatorGetData(op, &impl));
589     if (is_input) {
590       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
591       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
592     }
593   }
594 
595   // Loop over fields
596   for (CeedInt i = 0; i < num_fields; i++) {
597     CeedEvalMode eval_mode;
598     CeedBasis    basis;
599 
600     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
601     if (eval_mode != CEED_EVAL_WEIGHT) {
602       CeedElemRestriction elem_rstr;
603       CeedSize            e_size;
604       bool                is_at_points;
605 
606       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
607       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
608       CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
609       if (is_at_points) {
610         CeedCallBackend(CeedElemRestrictionGetEVectorSize(elem_rstr, &e_size));
611         if (e_size_padding == 0) {
612           CeedInt num_points, num_elem;
613 
614           CeedCallBackend(CeedElemRestrictionGetNumElements(elem_rstr, &num_elem));
615           CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, num_elem - 1, &num_points));
616           e_size_padding = (max_num_points - num_points) * num_comp;
617         }
618         CeedCallBackend(CeedVectorCreate(ceed, e_size + e_size_padding, &e_vecs_full[i + start_e]));
619         CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
620       } else {
621         CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
622       }
623     }
624 
625     switch (eval_mode) {
626       case CEED_EVAL_NONE: {
627         CeedVector vec;
628 
629         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
630         e_size = (CeedSize)max_num_points * size;
631         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
632         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
633         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
634           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
635         } else {
636           q_size = (CeedSize)max_num_points * size;
637           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
638         }
639         break;
640       }
641       case CEED_EVAL_INTERP:
642       case CEED_EVAL_GRAD:
643       case CEED_EVAL_DIV:
644       case CEED_EVAL_CURL:
645         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
646         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
647         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
648         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
649         e_size = (CeedSize)P * num_comp;
650         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
651         q_size = (CeedSize)max_num_points * size;
652         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
653         break;
654       case CEED_EVAL_WEIGHT:  // Only on input fields
655         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
656         q_size = (CeedSize)max_num_points;
657         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
658         CeedCallBackend(
659             CeedBasisApplyAtPoints(basis, max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
660         break;
661     }
662     // Initialize full arrays for E-vectors and Q-vectors
663     if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
664     if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
665   }
666   return CEED_ERROR_SUCCESS;
667 }
668 
669 //------------------------------------------------------------------------------
670 // Setup Operator
671 //------------------------------------------------------------------------------
672 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
673   bool                is_setup_done;
674   CeedInt             Q, num_input_fields, num_output_fields;
675   CeedQFunctionField *qf_input_fields, *qf_output_fields;
676   CeedQFunction       qf;
677   CeedOperatorField  *op_input_fields, *op_output_fields;
678   CeedOperator_Ref   *impl;
679 
680   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
681   if (is_setup_done) return CEED_ERROR_SUCCESS;
682 
683   CeedCallBackend(CeedOperatorGetData(op, &impl));
684   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
685   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
686   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
687   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
688   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
689 
690   // Allocate
691   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
692 
693   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
694   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
695   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
696   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
697   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
698 
699   impl->num_inputs  = num_input_fields;
700   impl->num_outputs = num_output_fields;
701 
702   // Set up infield and outfield pointer arrays
703   // Infields
704   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
705   // Outfields
706   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
707                                                       num_output_fields, Q));
708 
709   // Identity QFunctions
710   if (impl->is_identity_qf) {
711     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
712     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
713   }
714 
715   CeedCallBackend(CeedOperatorSetSetupDone(op));
716   return CEED_ERROR_SUCCESS;
717 }
718 
719 //------------------------------------------------------------------------------
720 // Input Basis Action
721 //------------------------------------------------------------------------------
722 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
723                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
724                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
725                                                      CeedOperator_Ref *impl, CeedRequest *request) {
726   for (CeedInt i = 0; i < num_input_fields; i++) {
727     bool                is_active_input = false;
728     CeedInt             elem_size, size, num_comp;
729     CeedRestrictionType rstr_type;
730     CeedEvalMode        eval_mode;
731     CeedVector          vec;
732     CeedElemRestriction elem_rstr;
733     CeedBasis           basis;
734 
735     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
736     // Skip active input
737     is_active_input = vec == CEED_VECTOR_ACTIVE;
738     if (skip_active && is_active_input) continue;
739 
740     // Get elem_size, eval_mode, size
741     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
742     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
743     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
744     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
745     // Restrict block active input
746     if (is_active_input) {
747       if (rstr_type == CEED_RESTRICTION_POINTS) {
748         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
749       } else {
750         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
751       }
752     }
753     // Basis action
754     switch (eval_mode) {
755       case CEED_EVAL_NONE:
756         if (!is_active_input) {
757           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
758         }
759         break;
760       // Note - these basis eval modes require FEM fields
761       case CEED_EVAL_INTERP:
762       case CEED_EVAL_GRAD:
763       case CEED_EVAL_DIV:
764       case CEED_EVAL_CURL:
765         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
766         if (!is_active_input) {
767           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
768           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
769           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][(CeedSize)e * elem_size * num_comp]));
770         }
771         CeedCallBackend(
772             CeedBasisApplyAtPoints(basis, num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
773         break;
774       case CEED_EVAL_WEIGHT:
775         break;  // No action
776     }
777   }
778   return CEED_ERROR_SUCCESS;
779 }
780 
781 //------------------------------------------------------------------------------
782 // Output Basis Action
783 //------------------------------------------------------------------------------
784 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
785                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
786                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
787                                                       CeedRequest *request) {
788   for (CeedInt i = 0; i < num_output_fields; i++) {
789     CeedRestrictionType rstr_type;
790     CeedEvalMode        eval_mode;
791     CeedVector          vec;
792     CeedElemRestriction elem_rstr;
793     CeedBasis           basis;
794 
795     // Get elem_size, eval_mode, size
796     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
797     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
798     // Basis action
799     switch (eval_mode) {
800       case CEED_EVAL_NONE:
801         break;  // No action
802       case CEED_EVAL_INTERP:
803       case CEED_EVAL_GRAD:
804       case CEED_EVAL_DIV:
805       case CEED_EVAL_CURL:
806         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
807         CeedCallBackend(
808             CeedBasisApplyAtPoints(basis, num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
809         break;
810       // LCOV_EXCL_START
811       case CEED_EVAL_WEIGHT: {
812         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
813         // LCOV_EXCL_STOP
814       }
815     }
816     // Restrict output block
817     // Get output vector
818     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
819     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
820     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
821     // Restrict
822     if (rstr_type == CEED_RESTRICTION_POINTS) {
823       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
824     } else {
825       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
826     }
827   }
828   return CEED_ERROR_SUCCESS;
829 }
830 
831 //------------------------------------------------------------------------------
832 // Operator Apply
833 //------------------------------------------------------------------------------
834 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
835   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
836   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
837   CeedVector          point_coords               = NULL;
838   CeedElemRestriction rstr_points                = NULL;
839   CeedQFunctionField *qf_input_fields, *qf_output_fields;
840   CeedQFunction       qf;
841   CeedOperatorField  *op_input_fields, *op_output_fields;
842   CeedOperator_Ref   *impl;
843 
844   CeedCallBackend(CeedOperatorGetData(op, &impl));
845   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
846   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
847   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
848   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
849 
850   // Setup
851   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
852 
853   // Point coordinates
854   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
855 
856   // Input Evecs and Restriction
857   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
858 
859   // Loop through elements
860   for (CeedInt e = 0; e < num_elem; e++) {
861     CeedInt num_points;
862 
863     // Setup points for element
864     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
865     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
866 
867     // Input basis apply
868     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
869                                                        impl->point_coords_elem, false, e_data, impl, request));
870 
871     // Q function
872     if (!impl->is_identity_qf) {
873       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
874     }
875 
876     // Output basis apply and restriction
877     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
878                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
879 
880     num_points_offset += num_points;
881   }
882 
883   // Restore input arrays
884   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
885 
886   // Cleanup point coordinates
887   CeedCallBackend(CeedVectorDestroy(&point_coords));
888   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
889   return CEED_ERROR_SUCCESS;
890 }
891 
892 //------------------------------------------------------------------------------
893 // Core code for assembling linear QFunction
894 //------------------------------------------------------------------------------
895 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
896                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
897   Ceed                ceed;
898   CeedSize            q_size;
899   CeedInt             num_active_in, num_active_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
900   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
901   CeedVector         *active_in, point_coords                           = NULL;
902   CeedQFunctionField *qf_input_fields, *qf_output_fields;
903   CeedQFunction       qf;
904   CeedOperatorField  *op_input_fields, *op_output_fields;
905   CeedOperator_Ref   *impl;
906   CeedElemRestriction rstr_points = NULL;
907 
908   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
909   CeedCallBackend(CeedOperatorGetData(op, &impl));
910   active_in     = impl->qf_active_in;
911   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
912   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
913   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
914   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
915   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
916 
917   // Setup
918   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
919 
920   // Check for restriction only operator
921   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
922 
923   // Point coordinates
924   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
925   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
926 
927   // Input Evecs and Restriction
928   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
929 
930   // Count number of active input fields
931   if (!num_active_in) {
932     for (CeedInt i = 0; i < num_input_fields; i++) {
933       CeedScalar *q_vec_array;
934       CeedInt     field_size;
935       CeedVector  vec;
936 
937       // Get input vector
938       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
939       // Check if active input
940       if (vec == CEED_VECTOR_ACTIVE) {
941         // Check that all active inputs are nodal fields
942         {
943           CeedElemRestriction elem_rstr;
944           bool                is_at_points = false;
945 
946           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
947           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
948           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
949         }
950         // Get size of active input
951         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
952         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
953         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
954         CeedCallBackend(CeedRealloc(num_active_in + field_size, &active_in));
955         for (CeedInt field = 0; field < field_size; field++) {
956           q_size = (CeedSize)max_num_points;
957           CeedCallBackend(CeedVectorCreate(ceed, q_size, &active_in[num_active_in + field]));
958           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * q_size]));
959         }
960         num_active_in += field_size;
961         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
962       }
963     }
964     impl->num_active_in = num_active_in;
965     impl->qf_active_in  = active_in;
966   }
967 
968   // Count number of active output fields
969   if (!num_active_out) {
970     for (CeedInt i = 0; i < num_output_fields; i++) {
971       CeedVector vec;
972       CeedInt    field_size;
973 
974       // Get output vector
975       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
976       // Check if active output
977       if (vec == CEED_VECTOR_ACTIVE) {
978         // Check that all active inputs are nodal fields
979         {
980           CeedElemRestriction elem_rstr;
981           bool                is_at_points = false;
982 
983           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
984           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
985           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
986         }
987         // Get size of active output
988         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
989         num_active_out += field_size;
990       }
991     }
992     impl->num_active_out = num_active_out;
993   }
994 
995   // Check sizes
996   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
997 
998   // Build objects if needed
999   if (build_objects) {
1000     CeedInt        num_points_total;
1001     const CeedInt *offsets;
1002 
1003     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1004 
1005     // Create output restriction (at points)
1006     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1007     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, num_active_in * num_active_out,
1008                                                       num_active_in * num_active_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
1009                                                       rstr));
1010     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1011 
1012     // Create assembled vector
1013     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1014   }
1015   // Clear output vector
1016   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1017   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1018 
1019   // Loop through elements
1020   for (CeedInt e = 0; e < num_elem; e++) {
1021     CeedInt num_points;
1022 
1023     // Setup points for element
1024     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1025     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1026 
1027     // Input basis apply
1028     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1029                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1030 
1031     // Assemble QFunction
1032     for (CeedInt in = 0; in < num_active_in; in++) {
1033       // Set Inputs
1034       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
1035       if (num_active_in > 1) {
1036         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
1037       }
1038       if (!impl->is_identity_qf) {
1039         // Set Outputs
1040         for (CeedInt out = 0; out < num_output_fields; out++) {
1041           CeedVector vec;
1042           CeedInt    field_size;
1043 
1044           // Get output vector
1045           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1046           // Check if active output
1047           if (vec == CEED_VECTOR_ACTIVE) {
1048             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1049             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1050             assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1051           }
1052         }
1053         // Apply QFunction
1054         CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1055       } else {
1056         const CeedScalar *q_vec_array;
1057         CeedInt           field_size;
1058 
1059         // Copy Identity Outputs
1060         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1061         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
1062         for (CeedInt i = 0; i < field_size * num_points; i++) assembled_array[i] = q_vec_array[i];
1063         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
1064         assembled_array += field_size * num_points;
1065       }
1066     }
1067     num_points_offset += num_points;
1068   }
1069 
1070   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1071   if (!impl->is_identity_qf) {
1072     for (CeedInt out = 0; out < num_output_fields; out++) {
1073       CeedVector vec;
1074 
1075       // Get output vector
1076       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1077       // Check if active output
1078       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1079         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1080       }
1081     }
1082   }
1083 
1084   // Restore input arrays
1085   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1086 
1087   // Restore output
1088   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1089 
1090   // Cleanup
1091   CeedCallBackend(CeedVectorDestroy(&point_coords));
1092   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1093   return CEED_ERROR_SUCCESS;
1094 }
1095 
1096 //------------------------------------------------------------------------------
1097 // Assemble Linear QFunction
1098 //------------------------------------------------------------------------------
1099 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1100   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1101 }
1102 
1103 //------------------------------------------------------------------------------
1104 // Update Assembled Linear QFunction
1105 //------------------------------------------------------------------------------
1106 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1107                                                                  CeedRequest *request) {
1108   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1109 }
1110 
1111 //------------------------------------------------------------------------------
1112 // Assemble Operator
1113 //------------------------------------------------------------------------------
1114 
1115 //------------------------------------------------------------------------------
1116 // Operator Destroy
1117 //------------------------------------------------------------------------------
1118 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1119   CeedOperator_Ref *impl;
1120 
1121   CeedCallBackend(CeedOperatorGetData(op, &impl));
1122   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1123     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1124   }
1125   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1126   CeedCallBackend(CeedFree(&impl->input_states));
1127 
1128   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1129     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1130     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1131   }
1132   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1133   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1134 
1135   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1136     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1137     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1138   }
1139   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1140   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1141   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1142 
1143   // QFunction assembly
1144   for (CeedInt i = 0; i < impl->num_active_in; i++) {
1145     CeedCallBackend(CeedVectorDestroy(&impl->qf_active_in[i]));
1146   }
1147   CeedCallBackend(CeedFree(&impl->qf_active_in));
1148 
1149   CeedCallBackend(CeedFree(&impl));
1150   return CEED_ERROR_SUCCESS;
1151 }
1152 
1153 //------------------------------------------------------------------------------
1154 // Operator Create
1155 //------------------------------------------------------------------------------
1156 int CeedOperatorCreate_Ref(CeedOperator op) {
1157   Ceed              ceed;
1158   CeedOperator_Ref *impl;
1159 
1160   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1161   CeedCallBackend(CeedCalloc(1, &impl));
1162   CeedCallBackend(CeedOperatorSetData(op, impl));
1163   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1164   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1165   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1166   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1167   return CEED_ERROR_SUCCESS;
1168 }
1169 
1170 //------------------------------------------------------------------------------
1171 // Operator Create At Points
1172 //------------------------------------------------------------------------------
1173 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1174   Ceed              ceed;
1175   CeedOperator_Ref *impl;
1176 
1177   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1178   CeedCallBackend(CeedCalloc(1, &impl));
1179   CeedCallBackend(CeedOperatorSetData(op, impl));
1180   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1181   CeedCallBackend(
1182       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1183   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1184   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1185   return CEED_ERROR_SUCCESS;
1186 }
1187 
1188 //------------------------------------------------------------------------------
1189