xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 297a0f4635bd3c3ec6107d4eee9658e9384f4572)
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             e_size_padding = 0, 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) {
589       CeedCallBackend(CeedVectorCreate(ceed, dim * max_num_points, &impl->point_coords_elem));
590       CeedCallBackend(CeedVectorSetValue(impl->point_coords_elem, 0.0));
591     }
592   }
593 
594   // Loop over fields
595   for (CeedInt i = 0; i < num_fields; i++) {
596     CeedEvalMode eval_mode;
597     CeedBasis    basis;
598 
599     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode));
600     if (eval_mode != CEED_EVAL_WEIGHT) {
601       CeedElemRestriction elem_rstr;
602       CeedSize            e_size;
603       bool                is_at_points;
604 
605       CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_fields[i], &elem_rstr));
606       CeedCallBackend(CeedElemRestrictionGetNumComponents(elem_rstr, &num_comp));
607       CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
608       if (is_at_points) {
609         CeedCallBackend(CeedElemRestrictionGetEVectorSize(elem_rstr, &e_size));
610         if (e_size_padding == 0) {
611           CeedInt num_points, num_elem;
612 
613           CeedCallBackend(CeedElemRestrictionGetNumElements(elem_rstr, &num_elem));
614           CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(elem_rstr, num_elem - 1, &num_points));
615           e_size_padding = (max_num_points - num_points) * num_comp;
616         }
617         CeedCallBackend(CeedVectorCreate(ceed, e_size + e_size_padding, &e_vecs_full[i + start_e]));
618         CeedCallBackend(CeedVectorSetValue(e_vecs_full[i + start_e], 0.0));
619       } else {
620         CeedCallBackend(CeedElemRestrictionCreateVector(elem_rstr, NULL, &e_vecs_full[i + start_e]));
621       }
622     }
623 
624     switch (eval_mode) {
625       case CEED_EVAL_NONE: {
626         CeedVector vec;
627 
628         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
629         e_size = (CeedSize)max_num_points * size;
630         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
631         CeedCallBackend(CeedOperatorFieldGetVector(op_fields[i], &vec));
632         if (vec == CEED_VECTOR_ACTIVE || !is_input) {
633           CeedCallBackend(CeedVectorReferenceCopy(e_vecs[i], &q_vecs[i]));
634         } else {
635           q_size = (CeedSize)max_num_points * size;
636           CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
637         }
638         break;
639       }
640       case CEED_EVAL_INTERP:
641       case CEED_EVAL_GRAD:
642       case CEED_EVAL_DIV:
643       case CEED_EVAL_CURL:
644         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
645         CeedCallBackend(CeedQFunctionFieldGetSize(qf_fields[i], &size));
646         CeedCallBackend(CeedBasisGetNumNodes(basis, &P));
647         CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
648         e_size = (CeedSize)P * num_comp;
649         CeedCallBackend(CeedVectorCreate(ceed, e_size, &e_vecs[i]));
650         q_size = (CeedSize)max_num_points * size;
651         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
652         break;
653       case CEED_EVAL_WEIGHT:  // Only on input fields
654         CeedCallBackend(CeedOperatorFieldGetBasis(op_fields[i], &basis));
655         q_size = (CeedSize)max_num_points;
656         CeedCallBackend(CeedVectorCreate(ceed, q_size, &q_vecs[i]));
657         CeedCallBackend(
658             CeedBasisApplyAtPoints(basis, max_num_points, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT, CEED_VECTOR_NONE, CEED_VECTOR_NONE, q_vecs[i]));
659         break;
660     }
661     if (e_vecs[i]) CeedCallBackend(CeedVectorSetValue(e_vecs[i], 0.0));
662     if (eval_mode != CEED_EVAL_WEIGHT) CeedCallBackend(CeedVectorSetValue(q_vecs[i], 0.0));
663   }
664   return CEED_ERROR_SUCCESS;
665 }
666 
667 //------------------------------------------------------------------------------
668 // Setup Operator
669 //------------------------------------------------------------------------------
670 static int CeedOperatorSetupAtPoints_Ref(CeedOperator op) {
671   bool                is_setup_done;
672   CeedInt             Q, num_input_fields, num_output_fields;
673   CeedQFunctionField *qf_input_fields, *qf_output_fields;
674   CeedQFunction       qf;
675   CeedOperatorField  *op_input_fields, *op_output_fields;
676   CeedOperator_Ref   *impl;
677 
678   CeedCallBackend(CeedOperatorIsSetupDone(op, &is_setup_done));
679   if (is_setup_done) return CEED_ERROR_SUCCESS;
680 
681   CeedCallBackend(CeedOperatorGetData(op, &impl));
682   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
683   CeedCallBackend(CeedOperatorGetNumQuadraturePoints(op, &Q));
684   CeedCallBackend(CeedQFunctionIsIdentity(qf, &impl->is_identity_qf));
685   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
686   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
687 
688   // Allocate
689   CeedCallBackend(CeedCalloc(num_input_fields + num_output_fields, &impl->e_vecs_full));
690 
691   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->input_states));
692   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_in));
693   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->e_vecs_out));
694   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_in));
695   CeedCallBackend(CeedCalloc(CEED_FIELD_MAX, &impl->q_vecs_out));
696 
697   impl->num_inputs  = num_input_fields;
698   impl->num_outputs = num_output_fields;
699 
700   // Set up infield and outfield pointer arrays
701   // Infields
702   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, true, impl->e_vecs_full, impl->e_vecs_in, impl->q_vecs_in, 0, num_input_fields, Q));
703   // Outfields
704   CeedCallBackend(CeedOperatorSetupFieldsAtPoints_Ref(qf, op, false, impl->e_vecs_full, impl->e_vecs_out, impl->q_vecs_out, num_input_fields,
705                                                       num_output_fields, Q));
706 
707   // Identity QFunctions
708   if (impl->is_identity_qf) {
709     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->q_vecs_out[0]));
710     CeedCallBackend(CeedVectorReferenceCopy(impl->q_vecs_in[0], &impl->e_vecs_out[0]));
711   }
712 
713   CeedCallBackend(CeedOperatorSetSetupDone(op));
714   return CEED_ERROR_SUCCESS;
715 }
716 
717 //------------------------------------------------------------------------------
718 // Input Basis Action
719 //------------------------------------------------------------------------------
720 static inline int CeedOperatorInputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_input_fields,
721                                                      CeedOperatorField *op_input_fields, CeedInt num_input_fields, CeedVector in_vec,
722                                                      CeedVector point_coords_elem, bool skip_active, CeedScalar *e_data[2 * CEED_FIELD_MAX],
723                                                      CeedOperator_Ref *impl, CeedRequest *request) {
724   for (CeedInt i = 0; i < num_input_fields; i++) {
725     bool                is_active_input = false;
726     CeedInt             elem_size, size, num_comp;
727     CeedRestrictionType rstr_type;
728     CeedEvalMode        eval_mode;
729     CeedVector          vec;
730     CeedElemRestriction elem_rstr;
731     CeedBasis           basis;
732 
733     CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
734     // Skip active input
735     is_active_input = vec == CEED_VECTOR_ACTIVE;
736     if (skip_active && is_active_input) continue;
737 
738     // Get elem_size, eval_mode, size
739     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
740     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
741     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_input_fields[i], &eval_mode));
742     CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &size));
743     // Restrict block active input
744     if (is_active_input) {
745       if (rstr_type == CEED_RESTRICTION_POINTS) {
746         CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
747       } else {
748         CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_NOTRANSPOSE, in_vec, impl->e_vecs_in[i], request));
749       }
750     }
751     // Basis action
752     switch (eval_mode) {
753       case CEED_EVAL_NONE:
754         if (!is_active_input) {
755           CeedCallBackend(CeedVectorSetArray(impl->q_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][num_points_offset * size]));
756         }
757         break;
758       // Note - these basis eval modes require FEM fields
759       case CEED_EVAL_INTERP:
760       case CEED_EVAL_GRAD:
761       case CEED_EVAL_DIV:
762       case CEED_EVAL_CURL:
763         CeedCallBackend(CeedOperatorFieldGetBasis(op_input_fields[i], &basis));
764         if (!is_active_input) {
765           CeedCallBackend(CeedBasisGetNumComponents(basis, &num_comp));
766           CeedCallBackend(CeedElemRestrictionGetElementSize(elem_rstr, &elem_size));
767           CeedCallBackend(CeedVectorSetArray(impl->e_vecs_in[i], CEED_MEM_HOST, CEED_USE_POINTER, &e_data[i][e * elem_size * num_comp]));
768         }
769         CeedCallBackend(
770             CeedBasisApplyAtPoints(basis, num_points, CEED_NOTRANSPOSE, eval_mode, point_coords_elem, impl->e_vecs_in[i], impl->q_vecs_in[i]));
771         break;
772       case CEED_EVAL_WEIGHT:
773         break;  // No action
774     }
775   }
776   return CEED_ERROR_SUCCESS;
777 }
778 
779 //------------------------------------------------------------------------------
780 // Output Basis Action
781 //------------------------------------------------------------------------------
782 static inline int CeedOperatorOutputBasisAtPoints_Ref(CeedInt e, CeedInt num_points_offset, CeedInt num_points, CeedQFunctionField *qf_output_fields,
783                                                       CeedOperatorField *op_output_fields, CeedInt num_input_fields, CeedInt num_output_fields,
784                                                       CeedOperator op, CeedVector out_vec, CeedVector point_coords_elem, CeedOperator_Ref *impl,
785                                                       CeedRequest *request) {
786   for (CeedInt i = 0; i < num_output_fields; i++) {
787     CeedRestrictionType rstr_type;
788     CeedEvalMode        eval_mode;
789     CeedVector          vec;
790     CeedElemRestriction elem_rstr;
791     CeedBasis           basis;
792 
793     // Get elem_size, eval_mode, size
794     CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
795     CeedCallBackend(CeedQFunctionFieldGetEvalMode(qf_output_fields[i], &eval_mode));
796     // Basis action
797     switch (eval_mode) {
798       case CEED_EVAL_NONE:
799         break;  // No action
800       case CEED_EVAL_INTERP:
801       case CEED_EVAL_GRAD:
802       case CEED_EVAL_DIV:
803       case CEED_EVAL_CURL:
804         CeedCallBackend(CeedOperatorFieldGetBasis(op_output_fields[i], &basis));
805         CeedCallBackend(
806             CeedBasisApplyAtPoints(basis, num_points, CEED_TRANSPOSE, eval_mode, point_coords_elem, impl->q_vecs_out[i], impl->e_vecs_out[i]));
807         break;
808       // LCOV_EXCL_START
809       case CEED_EVAL_WEIGHT: {
810         return CeedError(CeedOperatorReturnCeed(op), CEED_ERROR_BACKEND, "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
811         // LCOV_EXCL_STOP
812       }
813     }
814     // Restrict output block
815     // Get output vector
816     CeedCallBackend(CeedElemRestrictionGetType(elem_rstr, &rstr_type));
817     CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
818     if (vec == CEED_VECTOR_ACTIVE) vec = out_vec;
819     // Restrict
820     if (rstr_type == CEED_RESTRICTION_POINTS) {
821       CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
822     } else {
823       CeedCallBackend(CeedElemRestrictionApplyBlock(elem_rstr, e, CEED_TRANSPOSE, impl->e_vecs_out[i], vec, request));
824     }
825   }
826   return CEED_ERROR_SUCCESS;
827 }
828 
829 //------------------------------------------------------------------------------
830 // Operator Apply
831 //------------------------------------------------------------------------------
832 static int CeedOperatorApplyAddAtPoints_Ref(CeedOperator op, CeedVector in_vec, CeedVector out_vec, CeedRequest *request) {
833   CeedInt             num_points_offset          = 0, num_input_fields, num_output_fields, num_elem;
834   CeedScalar         *e_data[2 * CEED_FIELD_MAX] = {0};
835   CeedVector          point_coords               = NULL;
836   CeedElemRestriction rstr_points                = NULL;
837   CeedQFunctionField *qf_input_fields, *qf_output_fields;
838   CeedQFunction       qf;
839   CeedOperatorField  *op_input_fields, *op_output_fields;
840   CeedOperator_Ref   *impl;
841 
842   CeedCallBackend(CeedOperatorGetData(op, &impl));
843   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
844   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
845   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
846   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
847 
848   // Setup
849   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
850 
851   // Point coordinates
852   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
853 
854   // Input Evecs and Restriction
855   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data, impl, request));
856 
857   // Loop through elements
858   for (CeedInt e = 0; e < num_elem; e++) {
859     CeedInt num_points;
860 
861     // Setup points for element
862     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
863     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
864 
865     // Input basis apply
866     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, in_vec,
867                                                        impl->point_coords_elem, false, e_data, impl, request));
868 
869     // Q function
870     if (!impl->is_identity_qf) {
871       CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
872     }
873 
874     // Output basis apply and restriction
875     CeedCallBackend(CeedOperatorOutputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_output_fields, op_output_fields, num_input_fields,
876                                                         num_output_fields, op, out_vec, impl->point_coords_elem, impl, request));
877 
878     num_points_offset += num_points;
879   }
880 
881   // Restore input arrays
882   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data, impl));
883 
884   // Cleanup point coordinates
885   CeedCallBackend(CeedVectorDestroy(&point_coords));
886   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
887   return CEED_ERROR_SUCCESS;
888 }
889 
890 //------------------------------------------------------------------------------
891 // Core code for assembling linear QFunction
892 //------------------------------------------------------------------------------
893 static inline int CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(CeedOperator op, bool build_objects, CeedVector *assembled,
894                                                                       CeedElemRestriction *rstr, CeedRequest *request) {
895   Ceed                ceed;
896   CeedSize            q_size;
897   CeedInt             num_active_in, num_active_out, max_num_points, num_elem, num_input_fields, num_output_fields, num_points_offset = 0;
898   CeedScalar         *assembled_array, *e_data_full[2 * CEED_FIELD_MAX] = {NULL};
899   CeedVector         *active_in, point_coords                           = NULL;
900   CeedQFunctionField *qf_input_fields, *qf_output_fields;
901   CeedQFunction       qf;
902   CeedOperatorField  *op_input_fields, *op_output_fields;
903   CeedOperator_Ref   *impl;
904   CeedElemRestriction rstr_points = NULL;
905 
906   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
907   CeedCallBackend(CeedOperatorGetData(op, &impl));
908   active_in     = impl->qf_active_in;
909   num_active_in = impl->num_active_in, num_active_out = impl->num_active_out;
910   CeedCallBackend(CeedOperatorGetQFunction(op, &qf));
911   CeedCallBackend(CeedOperatorGetNumElements(op, &num_elem));
912   CeedCallBackend(CeedQFunctionGetFields(qf, NULL, &qf_input_fields, NULL, &qf_output_fields));
913   CeedCallBackend(CeedOperatorGetFields(op, &num_input_fields, &op_input_fields, &num_output_fields, &op_output_fields));
914 
915   // Setup
916   CeedCallBackend(CeedOperatorSetupAtPoints_Ref(op));
917 
918   // Check for restriction only operator
919   CeedCheck(!impl->is_identity_rstr_op, ceed, CEED_ERROR_BACKEND, "Assembling restriction only operators is not supported");
920 
921   // Point coordinates
922   CeedCallBackend(CeedOperatorAtPointsGetPoints(op, &rstr_points, &point_coords));
923   CeedCallBackend(CeedElemRestrictionGetMaxPointsInElement(rstr_points, &max_num_points));
924 
925   // Input Evecs and Restriction
926   CeedCallBackend(CeedOperatorSetupInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, NULL, true, e_data_full, impl, request));
927 
928   // Count number of active input fields
929   if (!num_active_in) {
930     for (CeedInt i = 0; i < num_input_fields; i++) {
931       CeedScalar *q_vec_array;
932       CeedInt     field_size;
933       CeedVector  vec;
934 
935       // Get input vector
936       CeedCallBackend(CeedOperatorFieldGetVector(op_input_fields[i], &vec));
937       // Check if active input
938       if (vec == CEED_VECTOR_ACTIVE) {
939         // Check that all active inputs are nodal fields
940         {
941           CeedElemRestriction elem_rstr;
942           bool                is_at_points = false;
943 
944           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_input_fields[i], &elem_rstr));
945           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
946           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
947         }
948         // Get size of active input
949         CeedCallBackend(CeedQFunctionFieldGetSize(qf_input_fields[i], &field_size));
950         CeedCallBackend(CeedVectorSetValue(impl->q_vecs_in[i], 0.0));
951         CeedCallBackend(CeedVectorGetArray(impl->q_vecs_in[i], CEED_MEM_HOST, &q_vec_array));
952         CeedCallBackend(CeedRealloc(num_active_in + field_size, &active_in));
953         for (CeedInt field = 0; field < field_size; field++) {
954           q_size = (CeedSize)max_num_points;
955           CeedCallBackend(CeedVectorCreate(ceed, q_size, &active_in[num_active_in + field]));
956           CeedCallBackend(CeedVectorSetArray(active_in[num_active_in + field], CEED_MEM_HOST, CEED_USE_POINTER, &q_vec_array[field * q_size]));
957         }
958         num_active_in += field_size;
959         CeedCallBackend(CeedVectorRestoreArray(impl->q_vecs_in[i], &q_vec_array));
960       }
961     }
962     impl->num_active_in = num_active_in;
963     impl->qf_active_in  = active_in;
964   }
965 
966   // Count number of active output fields
967   if (!num_active_out) {
968     for (CeedInt i = 0; i < num_output_fields; i++) {
969       CeedVector vec;
970       CeedInt    field_size;
971 
972       // Get output vector
973       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[i], &vec));
974       // Check if active output
975       if (vec == CEED_VECTOR_ACTIVE) {
976         // Check that all active inputs are nodal fields
977         {
978           CeedElemRestriction elem_rstr;
979           bool                is_at_points = false;
980 
981           CeedCallBackend(CeedOperatorFieldGetElemRestriction(op_output_fields[i], &elem_rstr));
982           CeedCallBackend(CeedElemRestrictionIsPoints(elem_rstr, &is_at_points));
983           CeedCheck(!is_at_points, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction with active input at points");
984         }
985         // Get size of active output
986         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[i], &field_size));
987         num_active_out += field_size;
988       }
989     }
990     impl->num_active_out = num_active_out;
991   }
992 
993   // Check sizes
994   CeedCheck(num_active_in > 0 && num_active_out > 0, ceed, CEED_ERROR_BACKEND, "Cannot assemble QFunction without active inputs and outputs");
995 
996   // Build objects if needed
997   if (build_objects) {
998     CeedInt        num_points_total;
999     const CeedInt *offsets;
1000 
1001     CeedCallBackend(CeedElemRestrictionGetNumPoints(rstr_points, &num_points_total));
1002 
1003     // Create output restriction (at points)
1004     CeedCallBackend(CeedElemRestrictionGetOffsets(rstr_points, CEED_MEM_HOST, &offsets));
1005     CeedCallBackend(CeedElemRestrictionCreateAtPoints(ceed, num_elem, num_points_total, num_active_in * num_active_out,
1006                                                       num_active_in * num_active_out * num_points_total, CEED_MEM_HOST, CEED_COPY_VALUES, offsets,
1007                                                       rstr));
1008     CeedCallBackend(CeedElemRestrictionRestoreOffsets(rstr_points, &offsets));
1009 
1010     // Create assembled vector
1011     CeedCallBackend(CeedElemRestrictionCreateVector(*rstr, assembled, NULL));
1012   }
1013   // Clear output vector
1014   CeedCallBackend(CeedVectorSetValue(*assembled, 0.0));
1015   CeedCallBackend(CeedVectorGetArray(*assembled, CEED_MEM_HOST, &assembled_array));
1016 
1017   // Loop through elements
1018   for (CeedInt e = 0; e < num_elem; e++) {
1019     CeedInt num_points;
1020 
1021     // Setup points for element
1022     CeedCallBackend(CeedElemRestrictionApplyAtPointsInElement(rstr_points, e, CEED_NOTRANSPOSE, point_coords, impl->point_coords_elem, request));
1023     CeedCallBackend(CeedElemRestrictionGetNumPointsInElement(rstr_points, e, &num_points));
1024 
1025     // Input basis apply
1026     CeedCallBackend(CeedOperatorInputBasisAtPoints_Ref(e, num_points_offset, num_points, qf_input_fields, op_input_fields, num_input_fields, NULL,
1027                                                        impl->point_coords_elem, true, e_data_full, impl, request));
1028 
1029     // Assemble QFunction
1030     for (CeedInt in = 0; in < num_active_in; in++) {
1031       // Set Inputs
1032       CeedCallBackend(CeedVectorSetValue(active_in[in], 1.0));
1033       if (num_active_in > 1) {
1034         CeedCallBackend(CeedVectorSetValue(active_in[(in + num_active_in - 1) % num_active_in], 0.0));
1035       }
1036       if (!impl->is_identity_qf) {
1037         // Set Outputs
1038         for (CeedInt out = 0; out < num_output_fields; out++) {
1039           CeedVector vec;
1040           CeedInt    field_size;
1041 
1042           // Get output vector
1043           CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1044           // Check if active output
1045           if (vec == CEED_VECTOR_ACTIVE) {
1046             CeedCallBackend(CeedVectorSetArray(impl->q_vecs_out[out], CEED_MEM_HOST, CEED_USE_POINTER, assembled_array));
1047             CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[out], &field_size));
1048             assembled_array += field_size * num_points;  // Advance the pointer by the size of the output
1049           }
1050         }
1051         // Apply QFunction
1052         CeedCallBackend(CeedQFunctionApply(qf, num_points, impl->q_vecs_in, impl->q_vecs_out));
1053       } else {
1054         const CeedScalar *q_vec_array;
1055         CeedInt           field_size;
1056 
1057         // Copy Identity Outputs
1058         CeedCallBackend(CeedQFunctionFieldGetSize(qf_output_fields[0], &field_size));
1059         CeedCallBackend(CeedVectorGetArrayRead(impl->q_vecs_out[0], CEED_MEM_HOST, &q_vec_array));
1060         for (CeedInt i = 0; i < field_size * num_points; i++) assembled_array[i] = q_vec_array[i];
1061         CeedCallBackend(CeedVectorRestoreArrayRead(impl->q_vecs_out[0], &q_vec_array));
1062         assembled_array += field_size * num_points;
1063       }
1064     }
1065     num_points_offset += num_points;
1066   }
1067 
1068   // Un-set output Qvecs to prevent accidental overwrite of Assembled
1069   if (!impl->is_identity_qf) {
1070     for (CeedInt out = 0; out < num_output_fields; out++) {
1071       CeedVector vec;
1072 
1073       // Get output vector
1074       CeedCallBackend(CeedOperatorFieldGetVector(op_output_fields[out], &vec));
1075       // Check if active output
1076       if (vec == CEED_VECTOR_ACTIVE && num_elem > 0) {
1077         CeedCallBackend(CeedVectorTakeArray(impl->q_vecs_out[out], CEED_MEM_HOST, NULL));
1078       }
1079     }
1080   }
1081 
1082   // Restore input arrays
1083   CeedCallBackend(CeedOperatorRestoreInputs_Ref(num_input_fields, qf_input_fields, op_input_fields, true, e_data_full, impl));
1084 
1085   // Restore output
1086   CeedCallBackend(CeedVectorRestoreArray(*assembled, &assembled_array));
1087 
1088   // Cleanup
1089   CeedCallBackend(CeedVectorDestroy(&point_coords));
1090   CeedCallBackend(CeedElemRestrictionDestroy(&rstr_points));
1091   return CEED_ERROR_SUCCESS;
1092 }
1093 
1094 //------------------------------------------------------------------------------
1095 // Assemble Linear QFunction
1096 //------------------------------------------------------------------------------
1097 static int CeedOperatorLinearAssembleQFunctionAtPoints_Ref(CeedOperator op, CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
1098   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, true, assembled, rstr, request);
1099 }
1100 
1101 //------------------------------------------------------------------------------
1102 // Update Assembled Linear QFunction
1103 //------------------------------------------------------------------------------
1104 static int CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref(CeedOperator op, CeedVector assembled, CeedElemRestriction rstr,
1105                                                                  CeedRequest *request) {
1106   return CeedOperatorLinearAssembleQFunctionAtPointsCore_Ref(op, false, &assembled, &rstr, request);
1107 }
1108 
1109 //------------------------------------------------------------------------------
1110 // Assemble Operator
1111 //------------------------------------------------------------------------------
1112 
1113 //------------------------------------------------------------------------------
1114 // Operator Destroy
1115 //------------------------------------------------------------------------------
1116 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1117   CeedOperator_Ref *impl;
1118 
1119   CeedCallBackend(CeedOperatorGetData(op, &impl));
1120   for (CeedInt i = 0; i < impl->num_inputs + impl->num_outputs; i++) {
1121     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_full[i]));
1122   }
1123   CeedCallBackend(CeedFree(&impl->e_vecs_full));
1124   CeedCallBackend(CeedFree(&impl->input_states));
1125 
1126   for (CeedInt i = 0; i < impl->num_inputs; i++) {
1127     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_in[i]));
1128     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_in[i]));
1129   }
1130   CeedCallBackend(CeedFree(&impl->e_vecs_in));
1131   CeedCallBackend(CeedFree(&impl->q_vecs_in));
1132 
1133   for (CeedInt i = 0; i < impl->num_outputs; i++) {
1134     CeedCallBackend(CeedVectorDestroy(&impl->e_vecs_out[i]));
1135     CeedCallBackend(CeedVectorDestroy(&impl->q_vecs_out[i]));
1136   }
1137   CeedCallBackend(CeedFree(&impl->e_vecs_out));
1138   CeedCallBackend(CeedFree(&impl->q_vecs_out));
1139   CeedCallBackend(CeedVectorDestroy(&impl->point_coords_elem));
1140 
1141   // QFunction assembly
1142   for (CeedInt i = 0; i < impl->num_active_in; i++) {
1143     CeedCallBackend(CeedVectorDestroy(&impl->qf_active_in[i]));
1144   }
1145   CeedCallBackend(CeedFree(&impl->qf_active_in));
1146 
1147   CeedCallBackend(CeedFree(&impl));
1148   return CEED_ERROR_SUCCESS;
1149 }
1150 
1151 //------------------------------------------------------------------------------
1152 // Operator Create
1153 //------------------------------------------------------------------------------
1154 int CeedOperatorCreate_Ref(CeedOperator op) {
1155   Ceed              ceed;
1156   CeedOperator_Ref *impl;
1157 
1158   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1159   CeedCallBackend(CeedCalloc(1, &impl));
1160   CeedCallBackend(CeedOperatorSetData(op, impl));
1161   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunction_Ref));
1162   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionUpdate_Ref));
1163   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAdd_Ref));
1164   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1165   return CEED_ERROR_SUCCESS;
1166 }
1167 
1168 //------------------------------------------------------------------------------
1169 // Operator Create At Points
1170 //------------------------------------------------------------------------------
1171 int CeedOperatorCreateAtPoints_Ref(CeedOperator op) {
1172   Ceed              ceed;
1173   CeedOperator_Ref *impl;
1174 
1175   CeedCallBackend(CeedOperatorGetCeed(op, &ceed));
1176   CeedCallBackend(CeedCalloc(1, &impl));
1177   CeedCallBackend(CeedOperatorSetData(op, impl));
1178   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction", CeedOperatorLinearAssembleQFunctionAtPoints_Ref));
1179   CeedCallBackend(
1180       CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunctionUpdate", CeedOperatorLinearAssembleQFunctionAtPointsUpdate_Ref));
1181   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd", CeedOperatorApplyAddAtPoints_Ref));
1182   CeedCallBackend(CeedSetBackendFunction(ceed, "Operator", op, "Destroy", CeedOperatorDestroy_Ref));
1183   return CEED_ERROR_SUCCESS;
1184 }
1185 
1186 //------------------------------------------------------------------------------
1187