xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 6e536b992ff6bc401c55631f1bc4464446496b52)
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][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][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(
254             CeedVectorSetArray(impl->e_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][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(CeedVectorSetArray(impl->q_vecs_out[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data_full[i + num_input_fields][e * Q * size]));
341       }
342     }
343 
344     // Input basis apply
345     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, false, e_data_full, impl));
346 
347     // Q function
348     if (!impl->is_identity_qf) {
349       CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
350     }
351 
352     // Output basis apply
353     CeedCallBackend(
354         CeedOperatorOutputBasis_Ref(e, Q, qf_output_fields, op_output_fields, num_input_fields, num_output_fields, op, e_data_full, impl));
355   }
356 
357   // Output restriction
358   for (CeedInt i = 0; i < num_output_fields; i++) {
359     CeedVector          vec;
360     CeedElemRestriction elem_rstr;
361 
362     // Restore Evec
363     CeedCallBackend(CeedVectorRestoreArray(impl->e_vecs_full[i + impl->num_inputs], &e_data_full[i + num_input_fields]));
364     // Get output vector
365     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
366     // Active
367     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
368     // Restrict
369     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
370     CeedCallBackend(CeedElemRestrictionApply(elem_rstr, CEED_TRANSPOSE, impl->e_vecs_full[i + impl->num_inputs], vec, request));
371   }
372 
373   // Restore input arrays
374   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, false, e_data_full, impl));
375   return CEED_ERROR_SUCCESS;
376 }
377 
378 //------------------------------------------------------------------------------
379 // Core code for assembling linear QFunction
380 //------------------------------------------------------------------------------
381 static inline int CeedOperatorLinearAssembleQFunctionCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
382                                                               CeedRequest *request) {
383   Ceed                ceed, ceed_parent;
384   CeedSize            q_size;
385   CeedInt             num_active_in, num_active_out, Q, num_elem, num_input_fields, num_output_fields, size;
386   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
387   CeedVector         *active_in;
388   CeedQFunctionField *qf_input_fields, *qf_output_fields;
389   CeedQFunction       qf;
390   CeedOperatorField  *op_input_fields, *op_output_fields;
391   CeedOperator_Ref   *impl;
392 
393   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
394   CeedCallBackend(CeedOperatorGetFallbackParentCeed(op, &ceed_parent));
395   CeedCallBackend(CeedOperatorGetData(op, &impl));
396   active_in     = impl->qf_active_in;
397   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
398   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
399   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
400   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
401   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
402   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
403 
404   // Setup
405   CeedCallBackend(CeedOperatorSetup_Ref(op));
406 
407   // Check for restriction only operator
408   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
409 
410   // Input Evecs and Restriction
411   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
412 
413   // Count number of active input fields
414   if (!num_active_in) {
415     for (CeedInt i = 0; i < num_input_fields; i++) {
416       CeedScalar *q_vec_array;
417       CeedVector  vec;
418 
419       // Get input vector
420       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
421       // Check if active input
422       if (vec == CEED_VECTOR_ACTIVE) {
423         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
424         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
425         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
426         CeedCallBackend(CeedRealloc(num_active_in + size, &active_in));
427         for (CeedInt field = 0; field < size; field++) {
428           q_size = (CeedSize)Q;
429           CeedCallBackend(CeedVectorCreate(ceed_parent, q_size, &active_in[num_active_in + field]));
430           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * Q]));
431         }
432         num_active_in += size;
433         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
434       }
435     }
436     impl->num_active_in = num_active_in;
437     impl->qf_active_in  = active_in;
438   }
439 
440   // Count number of active output fields
441   if (!num_active_out) {
442     for (CeedInt i = 0; i < num_output_fields; i++) {
443       CeedVector vec;
444 
445       // Get output vector
446       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
447       // Check if active output
448       if (vec == CEED_VECTOR_ACTIVE) {
449         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &size));
450         num_active_out += size;
451       }
452     }
453     impl->num_active_out = num_active_out;
454   }
455 
456   // Check sizes
457   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
458 
459   // Build objects if needed
460   if (build_objects) {
461     const CeedSize l_size     = (CeedSize)num_elem * Q * num_active_in * num_active_out;
462     CeedInt        strides[3] = {1, Q, num_active_in * num_active_out * Q}; /* *NOPAD* */
463 
464     // Create output restriction
465     CeedCallBackend(CeedElemRestrictionCreateStrided(ceed_parent, num_elem, Q, num_active_in * num_active_out,
466                                                      num_active_in * num_active_out * num_elem * Q, strides, rstr));
467     // Create assembled vector
468     CeedCallBackend(CeedVectorCreate(ceed_parent, l_size, assembled));
469   }
470   // Clear output vector
471   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
472   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
473 
474   // Loop through elements
475   for (CeedInt e = 0; e < num_elem; e++) {
476     // Input basis apply
477     CeedCallBackend(CeedOperatorInputBasis_Ref(e, Q, qf_input_fields, op_input_fields, num_input_fields, true, e_data_full, impl));
478 
479     // Assemble QFunction
480     for (CeedInt in = 0; in < num_active_in; in++) {
481       // Set Inputs
482       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
483       if (num_active_in > 1) {
484         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
485       }
486       if (!impl->is_identity_qf) {
487         // Set Outputs
488         for (CeedInt out = 0; out < num_output_fields; out++) {
489           CeedVector vec;
490 
491           // Get output vector
492           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
493           // Check if active output
494           if (vec == CEED_VECTOR_ACTIVE) {
495             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
496             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &size));
497             assembled_array += size * Q;  // Advance the pointer by the size of the output
498           }
499         }
500         // Apply QFunction
501         CeedCallBackend(CeedQFunctionApply(qf, Q, impl->q_vecs_in, impl->q_vecs_out));
502       } else {
503         const CeedScalar *q_vec_array;
504 
505         // Copy Identity Outputs
506         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &size));
507         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
508         for (CeedInt i = 0; i < size * Q; i++) assembled_array[i] = q_vec_array[i];
509         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
510         assembled_array += size * Q;
511       }
512     }
513   }
514 
515   // Un-set output Qvecs to prevent accidental overwrite of Assembled
516   if (!impl->is_identity_qf) {
517     for (CeedInt out = 0; out < num_output_fields; out++) {
518       CeedVector vec;
519 
520       // Get output vector
521       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
522       // Check if active output
523       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
524         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
525       }
526     }
527   }
528 
529   // Restore input arrays
530   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
531 
532   // Restore output
533   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
534   return CEED_ERROR_SUCCESS;
535 }
536 
537 //------------------------------------------------------------------------------
538 // Assemble Linear QFunction
539 //------------------------------------------------------------------------------
540 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
541   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, true, assembled, rstr, request);
542 }
543 
544 //------------------------------------------------------------------------------
545 // Update Assembled Linear QFunction
546 //------------------------------------------------------------------------------
547 static int CeedOperatorLinearAssembleQFunctionUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
548   return CeedOperatorLinearAssembleQFunctionCore_Ref(op, false, &assembled, &rstr, request);
549 }
550 
551 //------------------------------------------------------------------------------
552 // Setup Input/Output Fields
553 //------------------------------------------------------------------------------
554 static int CeedOperatorSetupFieldsAtPoints_Ref(CeedQFunction qf, CeedOperator op, bool is_input, CeedVector *e_vecs_full, CeedVector *e_vecs,
555                                                CeedVector *q_vecs, CeedInt start_e, CeedInt num_fields, CeedInt Q) {
556   Ceed                ceed;
557   CeedSize            e_size, q_size;
558   CeedInt             max_num_points, num_comp, size, P;
559   CeedQFunctionField *qf_fields;
560   CeedOperatorField  *op_fields;
561 
562   {
563     Ceed ceed_parent;
564 
565     CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
566     CeedCallBackend(CeedGetParent(ceed, &ceed_parent));
567     if (ceed_parent) ceed = ceed_parent;
568   }
569   if (is_input) {
570     CeedCallBackend(CeedOperatorGetFields(op, NULL, &op_fields, NULL, NULL));
571     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL));
572   } else {
573     CeedCallBackend(CeedOperatorGetFields(op, NULL, NULL, NULL, &op_fields));
574     CeedCallBackend(CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields));
575   }
576 
577   // Get max number of points
578   {
579     CeedInt             dim;
580     CeedElemRestriction rstr_points = NULL;
581     CeedOperator_Ref   *impl;
582 
583     CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, NULL));
584     CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
585     CeedCallBackend(CeedElemRestrictionGetNumComponents(rstr_points, &dim));
586     CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
587     CeedCallBackend(CeedOperatorGetData(op, &impl));
588     if (is_input) CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
589   }
590 
591   // Loop over fields
592   for (CeedInt i = 0; i < num_fields; i++) {
593     CeedEvalMode eval_mode;
594     CeedBasis    basis;
595 
596     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
597     if (eval_mode != CEED_EVAL_WEIGHT) {
598       CeedRestrictionType rstr_type;
599       CeedElemRestriction elem_rstr;
600 
601       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
602       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
603       CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
604       CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
605     }
606 
607     switch (eval_mode) {
608       case CEED_EVAL_NONE: {
609         CeedVector vec;
610 
611         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
612         e_size = (CeedSize)max_num_points * size;
613         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
614         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
615         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
616           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
617         } else {
618           q_size = (CeedSize)max_num_points * size;
619           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
620         }
621         break;
622       }
623       case CEED_EVAL_INTERP:
624       case CEED_EVAL_GRAD:
625       case CEED_EVAL_DIV:
626       case CEED_EVAL_CURL:
627         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
628         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
629         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
630         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
631         e_size = (CeedSize)P * num_comp;
632         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
633         q_size = (CeedSize)max_num_points * size;
634         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
635         break;
636       case CEED_EVAL_WEIGHT:  // Only on input fields
637         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
638         q_size = (CeedSize)max_num_points;
639         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
640         CeedCallBackend(
641             CeedBasisApplyAtPoints(basis, max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
642         break;
643     }
644     if (is_input && e_vecs[i]) {
645       CeedCallBackend(CeedVectorSetArray(e_vecs[i], CEED_MEM_HOST, CEED_COPY_VALUES, NULL));
646     }
647   }
648   return CEED_ERROR_SUCCESS;
649 }
650 
651 //------------------------------------------------------------------------------
652 // Setup Operator
653 //------------------------------------------------------------------------------
654 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
655   bool                is_setup_done;
656   CeedInt             Q, num_input_fields, num_output_fields;
657   CeedQFunctionField *qf_input_fields, *qf_output_fields;
658   CeedQFunction       qf;
659   CeedOperatorField  *op_input_fields, *op_output_fields;
660   CeedOperator_Ref   *impl;
661 
662   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
663   if (is_setup_done) return CEED_ERROR_SUCCESS;
664 
665   CeedCallBackend(CeedOperatorGetData(op, &impl));
666   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
667   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
668   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
669   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
670   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
671 
672   // Allocate
673   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
674 
675   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
676   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
677   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
678   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
679   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
680 
681   impl->num_inputs  = num_input_fields;
682   impl->num_outputs = num_output_fields;
683 
684   // Set up infield and outfield pointer arrays
685   // Infields
686   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
687   // Outfields
688   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
689                                                       num_output_fields, Q));
690 
691   // Identity QFunctions
692   if (impl->is_identity_qf) {
693     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
694     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
695   }
696 
697   CeedCallBackend(CeedOperatorSetSetupDone(op));
698   return CEED_ERROR_SUCCESS;
699 }
700 
701 //------------------------------------------------------------------------------
702 // Input Basis Action
703 //------------------------------------------------------------------------------
704 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
705                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
706                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
707                                                      CeedOperator_Ref *impl, CeedRequest *request) {
708   for (CeedInt i = 0; i < num_input_fields; i++) {
709     bool                is_active_input = false;
710     CeedInt             elem_size, size, num_comp;
711     CeedRestrictionType rstr_type;
712     CeedEvalMode        eval_mode;
713     CeedVector          vec;
714     CeedElemRestriction elem_rstr;
715     CeedBasis           basis;
716 
717     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
718     // Skip active input
719     is_active_input = vec == CEED_VECTOR_ACTIVE;
720     if (skip_active && is_active_input) continue;
721 
722     // Get elem_size, eval_mode, size
723     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
724     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
725     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
726     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
727     // Restrict block active input
728     if (is_active_input) {
729       if (rstr_type == CEED_RESTRICTION_POINTS) {
730         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
731       } else {
732         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
733       }
734     }
735     // Basis action
736     switch (eval_mode) {
737       case CEED_EVAL_NONE:
738         if (!is_active_input) {
739           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
740         }
741         break;
742       // Note - these basis eval modes require FEM fields
743       case CEED_EVAL_INTERP:
744       case CEED_EVAL_GRAD:
745       case CEED_EVAL_DIV:
746       case CEED_EVAL_CURL:
747         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
748         if (!is_active_input) {
749           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
750           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
751           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][e * elem_size * num_comp]));
752         }
753         CeedCallBackend(
754             CeedBasisApplyAtPoints(basis, num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
755         break;
756       case CEED_EVAL_WEIGHT:
757         break;  // No action
758     }
759   }
760   return CEED_ERROR_SUCCESS;
761 }
762 
763 //------------------------------------------------------------------------------
764 // Output Basis Action
765 //------------------------------------------------------------------------------
766 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
767                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
768                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
769                                                       CeedRequest *request) {
770   for (CeedInt i = 0; i < num_output_fields; i++) {
771     CeedRestrictionType rstr_type;
772     CeedEvalMode        eval_mode;
773     CeedVector          vec;
774     CeedElemRestriction elem_rstr;
775     CeedBasis           basis;
776 
777     // Get elem_size, eval_mode, size
778     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
779     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
780     // Basis action
781     switch (eval_mode) {
782       case CEED_EVAL_NONE:
783         break;  // No action
784       case CEED_EVAL_INTERP:
785       case CEED_EVAL_GRAD:
786       case CEED_EVAL_DIV:
787       case CEED_EVAL_CURL:
788         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
789         CeedCallBackend(
790             CeedBasisApplyAtPoints(basis, num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
791         break;
792       // LCOV_EXCL_START
793       case CEED_EVAL_WEIGHT: {
794         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
795         // LCOV_EXCL_STOP
796       }
797     }
798     // Restrict output block
799     // Get output vector
800     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
801     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
802     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
803     // Restrict
804     if (rstr_type == CEED_RESTRICTION_POINTS) {
805       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
806     } else {
807       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
808     }
809   }
810   return CEED_ERROR_SUCCESS;
811 }
812 
813 //------------------------------------------------------------------------------
814 // Operator Apply
815 //------------------------------------------------------------------------------
816 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
817   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
818   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
819   CeedVector          point_coords               = NULL;
820   CeedElemRestriction rstr_points                = NULL;
821   CeedQFunctionField *qf_input_fields, *qf_output_fields;
822   CeedQFunction       qf;
823   CeedOperatorField  *op_input_fields, *op_output_fields;
824   CeedOperator_Ref   *impl;
825 
826   CeedCallBackend(CeedOperatorGetData(op, &impl));
827   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
828   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
829   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
830   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
831 
832   // Setup
833   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
834 
835   // Point coordinates
836   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
837 
838   // Input Evecs and Restriction
839   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
840 
841   // Loop through elements
842   for (CeedInt e = 0; e < num_elem; e++) {
843     CeedInt num_points;
844 
845     // Setup points for element
846     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
847     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
848 
849     // Input basis apply
850     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
851                                                        impl->point_coords_elem, false, e_data, impl, request));
852 
853     // Q function
854     if (!impl->is_identity_qf) {
855       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
856     }
857 
858     // Output basis apply and restriction
859     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
860                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
861 
862     num_points_offset += num_points;
863   }
864 
865   // Restore input arrays
866   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
867 
868   // Cleanup point coordinates
869   CeedCallBackend(CeedVectorDestroy(&point_coords));
870   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
871   return CEED_ERROR_SUCCESS;
872 }
873 
874 //------------------------------------------------------------------------------
875 // Core code for assembling linear QFunction
876 //------------------------------------------------------------------------------
877 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
878                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
879   Ceed                ceed;
880   CeedSize            q_size;
881   CeedInt             num_active_in, num_active_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
882   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
883   CeedVector         *active_in, point_coords                           = NULL;
884   CeedQFunctionField *qf_input_fields, *qf_output_fields;
885   CeedQFunction       qf;
886   CeedOperatorField  *op_input_fields, *op_output_fields;
887   CeedOperator_Ref   *impl;
888   CeedElemRestriction rstr_points = NULL;
889 
890   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
891   CeedCallBackend(CeedOperatorGetData(op, &impl));
892   active_in     = impl->qf_active_in;
893   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
894   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
895   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
896   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
897   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
898 
899   // Setup
900   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
901 
902   // Check for restriction only operator
903   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
904 
905   // Point coordinates
906   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
907   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
908 
909   // Input Evecs and Restriction
910   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
911 
912   // Count number of active input fields
913   if (!num_active_in) {
914     for (CeedInt i = 0; i < num_input_fields; i++) {
915       CeedScalar *q_vec_array;
916       CeedInt     field_size;
917       CeedVector  vec;
918 
919       // Get input vector
920       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
921       // Check if active input
922       if (vec == CEED_VECTOR_ACTIVE) {
923         // Check that all active inputs are nodal fields
924         {
925           CeedElemRestriction elem_rstr;
926           bool                is_at_points = false;
927 
928           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
929           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
930           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
931         }
932         // Get size of active input
933         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
934         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
935         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
936         CeedCallBackend(CeedRealloc(num_active_in + field_size, &active_in));
937         for (CeedInt field = 0; field < field_size; field++) {
938           q_size = (CeedSize)max_num_points;
939           CeedCallBackend(CeedVectorCreate(ceed, q_size, &active_in[num_active_in + field]));
940           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * q_size]));
941         }
942         num_active_in += field_size;
943         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
944       }
945     }
946     impl->num_active_in = num_active_in;
947     impl->qf_active_in  = active_in;
948   }
949 
950   // Count number of active output fields
951   if (!num_active_out) {
952     for (CeedInt i = 0; i < num_output_fields; i++) {
953       CeedVector vec;
954       CeedInt    field_size;
955 
956       // Get output vector
957       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
958       // Check if active output
959       if (vec == CEED_VECTOR_ACTIVE) {
960         // Check that all active inputs are nodal fields
961         {
962           CeedElemRestriction elem_rstr;
963           bool                is_at_points = false;
964 
965           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
966           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
967           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
968         }
969         // Get size of active output
970         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
971         num_active_out += field_size;
972       }
973     }
974     impl->num_active_out = num_active_out;
975   }
976 
977   // Check sizes
978   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
979 
980   // Build objects if needed
981   if (build_objects) {
982     CeedInt        num_points_total;
983     const CeedInt *offsets;
984 
985     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
986 
987     // Create output restriction (at points)
988     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
989     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, num_active_in * num_active_out,
990                                                       num_active_in * num_active_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
991                                                       rstr));
992     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
993 
994     // Create assembled vector
995     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
996   }
997   // Clear output vector
998   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
999   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1000 
1001   // Loop through elements
1002   for (CeedInt e = 0; e < num_elem; e++) {
1003     CeedInt num_points;
1004 
1005     // Setup points for element
1006     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1007     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1008 
1009     // Input basis apply
1010     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1011                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1012 
1013     // Assemble QFunction
1014     for (CeedInt in = 0; in < num_active_in; in++) {
1015       // Set Inputs
1016       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
1017       if (num_active_in > 1) {
1018         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
1019       }
1020       if (!impl->is_identity_qf) {
1021         // Set Outputs
1022         for (CeedInt out = 0; out < num_output_fields; out++) {
1023           CeedVector vec;
1024           CeedInt    field_size;
1025 
1026           // Get output vector
1027           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1028           // Check if active output
1029           if (vec == CEED_VECTOR_ACTIVE) {
1030             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1031             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1032             assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1033           }
1034         }
1035         // Apply QFunction
1036         CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1037       } else {
1038         const CeedScalar *q_vec_array;
1039         CeedInt           field_size;
1040 
1041         // Copy Identity Outputs
1042         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1043         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
1044         for (CeedInt i = 0; i < field_size * num_points; i++) assembled_array[i] = q_vec_array[i];
1045         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
1046         assembled_array += field_size * num_points;
1047       }
1048     }
1049     num_points_offset += num_points;
1050   }
1051 
1052   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1053   if (!impl->is_identity_qf) {
1054     for (CeedInt out = 0; out < num_output_fields; out++) {
1055       CeedVector vec;
1056 
1057       // Get output vector
1058       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1059       // Check if active output
1060       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1061         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1062       }
1063     }
1064   }
1065 
1066   // Restore input arrays
1067   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1068 
1069   // Restore output
1070   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1071 
1072   // Cleanup
1073   CeedCallBackend(CeedVectorDestroy(&point_coords));
1074   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1075   return CEED_ERROR_SUCCESS;
1076 }
1077 
1078 //------------------------------------------------------------------------------
1079 // Assemble Linear QFunction
1080 //------------------------------------------------------------------------------
1081 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1082   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1083 }
1084 
1085 //------------------------------------------------------------------------------
1086 // Update Assembled Linear QFunction
1087 //------------------------------------------------------------------------------
1088 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1089                                                                  CeedRequest *request) {
1090   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1091 }
1092 
1093 //------------------------------------------------------------------------------
1094 // Assemble Operator
1095 //------------------------------------------------------------------------------
1096 
1097 //------------------------------------------------------------------------------
1098 // Operator Destroy
1099 //------------------------------------------------------------------------------
1100 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1101   CeedOperator_Ref *impl;
1102 
1103   CeedCallBackend(CeedOperatorGetData(op, &impl));
1104   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1105     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1106   }
1107   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1108   CeedCallBackend(CeedFree(&impl->input_states));
1109 
1110   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1111     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1112     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1113   }
1114   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1115   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1116 
1117   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1118     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1119     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1120   }
1121   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1122   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1123   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1124 
1125   // QFunction assembly
1126   for (CeedInt i = 0; i < impl->num_active_in; i++) {
1127     CeedCallBackend(CeedVectorDestroy(&impl->qf_active_in[i]));
1128   }
1129   CeedCallBackend(CeedFree(&impl->qf_active_in));
1130 
1131   CeedCallBackend(CeedFree(&impl));
1132   return CEED_ERROR_SUCCESS;
1133 }
1134 
1135 //------------------------------------------------------------------------------
1136 // Operator Create
1137 //------------------------------------------------------------------------------
1138 int CeedOperatorCreate_Ref(CeedOperator op) {
1139   Ceed              ceed;
1140   CeedOperator_Ref *impl;
1141 
1142   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1143   CeedCallBackend(CeedCalloc(1, &impl));
1144   CeedCallBackend(CeedOperatorSetData(op, impl));
1145   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1146   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1147   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1148   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1149   return CEED_ERROR_SUCCESS;
1150 }
1151 
1152 //------------------------------------------------------------------------------
1153 // Operator Create At Points
1154 //------------------------------------------------------------------------------
1155 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1156   Ceed              ceed;
1157   CeedOperator_Ref *impl;
1158 
1159   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1160   CeedCallBackend(CeedCalloc(1, &impl));
1161   CeedCallBackend(CeedOperatorSetData(op, impl));
1162   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1163   CeedCallBackend(
1164       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1165   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1166   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1167   return CEED_ERROR_SUCCESS;
1168 }
1169 
1170 //------------------------------------------------------------------------------
1171