xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 713f43c3136a96a13935ed58fa5dd016f047cd4d) 
1 // Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC.
2 // Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707.
3 // All Rights reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 #include "ceed-ref.h"
18 
19 static int CeedOperatorDestroy_Ref(CeedOperator op) {
20   int ierr;
21   CeedOperator_Ref *impl;
22   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
23 
24   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
25     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
26   }
27   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
28   ierr = CeedFree(&impl->edata); CeedChk(ierr);
29   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
30 
31   for (CeedInt i=0; i<impl->numein; i++) {
32     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
33     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
34   }
35   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
36   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
37 
38   for (CeedInt i=0; i<impl->numeout; i++) {
39     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
40     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
41   }
42   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
43   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
44 
45   ierr = CeedFree(&impl); CeedChk(ierr);
46   return 0;
47 }
48 
49 /*
50   Setup infields or outfields
51  */
52 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op,
53                                        bool inOrOut,
54                                        CeedVector *fullevecs, CeedVector *evecs,
55                                        CeedVector *qvecs, CeedInt starte,
56                                        CeedInt numfields, CeedInt Q) {
57   CeedInt dim, ierr, size, P;
58   Ceed ceed;
59   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
60   CeedBasis basis;
61   CeedElemRestriction Erestrict;
62   CeedOperatorField *opfields;
63   CeedQFunctionField *qffields;
64   if (inOrOut) {
65     ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
66     ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
67   } else {
68     ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
69     ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
70   }
71 
72   // Loop over fields
73   for (CeedInt i=0; i<numfields; i++) {
74     CeedEvalMode emode;
75     ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
76 
77     if (emode != CEED_EVAL_WEIGHT) {
78       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
79       CeedChk(ierr);
80       ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
81                                              &fullevecs[i+starte]);
82       CeedChk(ierr);
83     }
84 
85     switch(emode) {
86     case CEED_EVAL_NONE:
87       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
88       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
89       break;
90     case CEED_EVAL_INTERP:
91       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
92       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
93       CeedChk(ierr);
94       ierr = CeedVectorCreate(ceed, P*size, &evecs[i]); CeedChk(ierr);
95       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
96       break;
97     case CEED_EVAL_GRAD:
98       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
99       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
100       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
101       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
102       CeedChk(ierr);
103       ierr = CeedVectorCreate(ceed, P*size/dim, &evecs[i]); CeedChk(ierr);
104       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
105       break;
106     case CEED_EVAL_WEIGHT: // Only on input fields
107       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
108       ierr = CeedVectorCreate(ceed, Q, &qvecs[i]); CeedChk(ierr);
109       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
110                             CEED_VECTOR_NONE, qvecs[i]); CeedChk(ierr);
111       break;
112     case CEED_EVAL_DIV:
113       break; // Not implemented
114     case CEED_EVAL_CURL:
115       break; // Not implemented
116     }
117   }
118   return 0;
119 }
120 
121 /*
122   CeedOperator needs to connect all the named fields (be they active or passive)
123   to the named inputs and outputs of its CeedQFunction.
124  */
125 static int CeedOperatorSetup_Ref(CeedOperator op) {
126   int ierr;
127   bool setupdone;
128   ierr = CeedOperatorGetSetupStatus(op, &setupdone); CeedChk(ierr);
129   if (setupdone) return 0;
130   Ceed ceed;
131   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
132   CeedOperator_Ref *impl;
133   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
134   CeedQFunction qf;
135   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
136   CeedInt Q, numinputfields, numoutputfields;
137   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
138   ierr = CeedQFunctionGetIdentityStatus(qf, &impl->identityqf); CeedChk(ierr);
139   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
140   CeedChk(ierr);
141   CeedOperatorField *opinputfields, *opoutputfields;
142   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
143   CeedChk(ierr);
144   CeedQFunctionField *qfinputfields, *qfoutputfields;
145   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
146   CeedChk(ierr);
147 
148   // Allocate
149   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
150   CeedChk(ierr);
151   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->edata);
152   CeedChk(ierr);
153 
154   ierr = CeedCalloc(16, &impl->inputstate); CeedChk(ierr);
155   ierr = CeedCalloc(16, &impl->evecsin); CeedChk(ierr);
156   ierr = CeedCalloc(16, &impl->evecsout); CeedChk(ierr);
157   ierr = CeedCalloc(16, &impl->qvecsin); CeedChk(ierr);
158   ierr = CeedCalloc(16, &impl->qvecsout); CeedChk(ierr);
159 
160   impl->numein = numinputfields; impl->numeout = numoutputfields;
161 
162   // Set up infield and outfield evecs and qvecs
163   // Infields
164   ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->evecs,
165                                      impl->evecsin, impl->qvecsin, 0,
166                                      numinputfields, Q);
167   CeedChk(ierr);
168   // Outfields
169   ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->evecs,
170                                      impl->evecsout, impl->qvecsout,
171                                      numinputfields, numoutputfields, Q);
172   CeedChk(ierr);
173 
174   // Identity QFunctions
175   if (impl->identityqf) {
176     CeedEvalMode inmode, outmode;
177     CeedQFunctionField *infields, *outfields;
178     ierr = CeedQFunctionGetFields(qf, &infields, &outfields); CeedChk(ierr);
179 
180     for (CeedInt i=0; i<numinputfields; i++) {
181       ierr = CeedQFunctionFieldGetEvalMode(infields[i], &inmode);
182       CeedChk(ierr);
183       ierr = CeedQFunctionFieldGetEvalMode(outfields[i], &outmode);
184       CeedChk(ierr);
185 
186       ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
187       impl->qvecsout[i] = impl->qvecsin[i];
188       ierr = CeedVectorAddReference(impl->qvecsin[i]); CeedChk(ierr);
189     }
190   }
191 
192   ierr = CeedOperatorSetSetupDone(op); CeedChk(ierr);
193 
194   return 0;
195 }
196 
197 // Setup Input fields
198 static inline int CeedOperatorSetupInputs_Ref(CeedInt numinputfields,
199     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
200     CeedVector invec, const bool skipactive, CeedOperator_Ref *impl,
201     CeedRequest *request) {
202   CeedInt ierr;
203   CeedEvalMode emode;
204   CeedVector vec;
205   CeedElemRestriction Erestrict;
206   CeedTransposeMode lmode;
207   uint64_t state;
208 
209   for (CeedInt i=0; i<numinputfields; i++) {
210     // Get input vector
211     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
212     if (vec == CEED_VECTOR_ACTIVE) {
213       if (skipactive)
214         continue;
215       else
216         vec = invec;
217     }
218 
219     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
220     CeedChk(ierr);
221     // Restrict and Evec
222     if (emode == CEED_EVAL_WEIGHT) { // Skip
223     } else {
224       // Restrict
225       ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
226       // Skip restriction if input is unchanged
227       if (state != impl->inputstate[i] || vec == invec) {
228         ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
229         CeedChk(ierr);
230         ierr = CeedOperatorFieldGetLMode(opinputfields[i], &lmode);
231         CeedChk(ierr);
232         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE,
233                                         lmode, vec, impl->evecs[i],
234                                         request); CeedChk(ierr);
235         impl->inputstate[i] = state;
236       }
237       // Get evec
238       ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
239                                     (const CeedScalar **) &impl->edata[i]);
240       CeedChk(ierr);
241     }
242   }
243   return 0;
244 }
245 
246 // Input basis action
247 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
248     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
249     CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
250   CeedInt ierr;
251   CeedInt dim, elemsize, size;
252   CeedElemRestriction Erestrict;
253   CeedEvalMode emode;
254   CeedBasis basis;
255 
256   for (CeedInt i=0; i<numinputfields; i++) {
257     // Skip active input
258     if (skipactive) {
259       CeedVector vec;
260       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
261       if (vec == CEED_VECTOR_ACTIVE)
262         continue;
263     }
264     // Get elemsize, emode, size
265     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
266     CeedChk(ierr);
267     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
268     CeedChk(ierr);
269     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
270     CeedChk(ierr);
271     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
272     // Basis action
273     switch(emode) {
274     case CEED_EVAL_NONE:
275       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
276                                 CEED_USE_POINTER,
277                                 &impl->edata[i][e*Q*size]); CeedChk(ierr);
278       break;
279     case CEED_EVAL_INTERP:
280       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
281       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
282                                 CEED_USE_POINTER,
283                                 &impl->edata[i][e*elemsize*size]);
284       CeedChk(ierr);
285       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
286                             CEED_EVAL_INTERP, impl->evecsin[i],
287                             impl->qvecsin[i]); CeedChk(ierr);
288       break;
289     case CEED_EVAL_GRAD:
290       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
291       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
292       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
293                                 CEED_USE_POINTER,
294                                 &impl->edata[i][e*elemsize*size/dim]);
295       CeedChk(ierr);
296       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
297                             CEED_EVAL_GRAD, impl->evecsin[i],
298                             impl->qvecsin[i]); CeedChk(ierr);
299       break;
300     case CEED_EVAL_WEIGHT:
301       break;  // No action
302     case CEED_EVAL_DIV:
303     case CEED_EVAL_CURL: {
304       // LCOV_EXCL_START
305       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
306       CeedChk(ierr);
307       Ceed ceed;
308       ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
309       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
310       // LCOV_EXCL_STOP
311       break; // Not implemented
312     }
313     }
314   }
315   return 0;
316 }
317 
318 // Output basis action
319 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
320     CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
321     CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
322     CeedOperator_Ref *impl) {
323   CeedInt ierr;
324   CeedInt dim, elemsize, size;
325   CeedElemRestriction Erestrict;
326   CeedEvalMode emode;
327   CeedBasis basis;
328 
329   for (CeedInt i=0; i<numoutputfields; i++) {
330     // Get elemsize, emode, size
331     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
332     CeedChk(ierr);
333     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
334     CeedChk(ierr);
335     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
336     CeedChk(ierr);
337     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
338     // Basis action
339     switch(emode) {
340     case CEED_EVAL_NONE:
341       break; // No action
342     case CEED_EVAL_INTERP:
343       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
344       CeedChk(ierr);
345       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
346                                 CEED_USE_POINTER,
347                                 &impl->edata[i + numinputfields][e*elemsize*size]);
348       CeedChk(ierr);
349       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
350                             CEED_EVAL_INTERP, impl->qvecsout[i],
351                             impl->evecsout[i]); CeedChk(ierr);
352       break;
353     case CEED_EVAL_GRAD:
354       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
355       CeedChk(ierr);
356       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
357       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
358                                 CEED_USE_POINTER,
359                                 &impl->edata[i + numinputfields][e*elemsize*size/dim]);
360       CeedChk(ierr);
361       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
362                             CEED_EVAL_GRAD, impl->qvecsout[i],
363                             impl->evecsout[i]); CeedChk(ierr);
364       break;
365     case CEED_EVAL_WEIGHT: {
366       // LCOV_EXCL_START
367       Ceed ceed;
368       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
369       return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
370                        "evaluation mode");
371       // LCOV_EXCL_STOP
372       break; // Should not occur
373     }
374     case CEED_EVAL_DIV:
375     case CEED_EVAL_CURL: {
376       // LCOV_EXCL_START
377       Ceed ceed;
378       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
379       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
380       // LCOV_EXCL_STOP
381       break; // Not implemented
382     }
383     }
384   }
385   return 0;
386 }
387 
388 // Restore Inputs
389 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
390     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
391     const bool skipactive, CeedOperator_Ref *impl) {
392   CeedInt ierr;
393   CeedEvalMode emode;
394 
395   for (CeedInt i=0; i<numinputfields; i++) {
396     // Skip active inputs
397     if (skipactive) {
398       CeedVector vec;
399       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
400       if (vec == CEED_VECTOR_ACTIVE)
401         continue;
402     }
403     // Restore input
404     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
405     CeedChk(ierr);
406     if (emode == CEED_EVAL_WEIGHT) { // Skip
407     } else {
408       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
409                                         (const CeedScalar **) &impl->edata[i]);
410       CeedChk(ierr);
411     }
412   }
413   return 0;
414 }
415 
416 // Apply Operator
417 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
418                                  CeedVector outvec, CeedRequest *request) {
419   int ierr;
420   CeedOperator_Ref *impl;
421   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
422   CeedQFunction qf;
423   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
424   CeedInt Q, numelements, numinputfields, numoutputfields, size;
425   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
426   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
427   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
428   CeedChk(ierr);
429   CeedTransposeMode lmode;
430   CeedOperatorField *opinputfields, *opoutputfields;
431   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
432   CeedChk(ierr);
433   CeedQFunctionField *qfinputfields, *qfoutputfields;
434   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
435   CeedChk(ierr);
436   CeedEvalMode emode;
437   CeedVector vec;
438   CeedElemRestriction Erestrict;
439 
440   // Setup
441   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
442 
443   // Input Evecs and Restriction
444   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
445                                      opinputfields, invec, false, impl,
446                                      request); CeedChk(ierr);
447 
448   // Output Evecs
449   for (CeedInt i=0; i<numoutputfields; i++) {
450     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
451                               &impl->edata[i + numinputfields]); CeedChk(ierr);
452   }
453 
454   // Loop through elements
455   for (CeedInt e=0; e<numelements; e++) {
456     // Output pointers
457     for (CeedInt i=0; i<numoutputfields; i++) {
458       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
459       CeedChk(ierr);
460       if (emode == CEED_EVAL_NONE) {
461         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
462         CeedChk(ierr);
463         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
464                                   CEED_USE_POINTER,
465                                   &impl->edata[i + numinputfields][e*Q*size]);
466         CeedChk(ierr);
467       }
468     }
469 
470     // Input basis apply
471     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
472                                       numinputfields, false, impl);
473     CeedChk(ierr);
474 
475     // Q function
476     if (!impl->identityqf) {
477       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
478       CeedChk(ierr);
479     }
480 
481     // Output basis apply
482     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
483                                        numinputfields, numoutputfields, op, impl);
484     CeedChk(ierr);
485   }
486 
487   // Output restriction
488   for (CeedInt i=0; i<numoutputfields; i++) {
489     // Restore evec
490     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
491                                   &impl->edata[i + numinputfields]);
492     CeedChk(ierr);
493     // Get output vector
494     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
495     // Active
496     if (vec == CEED_VECTOR_ACTIVE)
497       vec = outvec;
498     // Restrict
499     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
500     CeedChk(ierr);
501     ierr = CeedOperatorFieldGetLMode(opoutputfields[i], &lmode); CeedChk(ierr);
502     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
503                                     lmode, impl->evecs[i+impl->numein], vec,
504                                     request); CeedChk(ierr);
505   }
506 
507   // Restore input arrays
508   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
509                                        opinputfields, false, impl);
510   CeedChk(ierr);
511 
512   return 0;
513 }
514 
515 // Assemble Linear QFunction
516 static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
517     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
518   int ierr;
519   CeedOperator_Ref *impl;
520   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
521   CeedQFunction qf;
522   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
523   CeedInt Q, numelements, numinputfields, numoutputfields, size;
524   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
525   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
526   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
527   CeedChk(ierr);
528   CeedOperatorField *opinputfields, *opoutputfields;
529   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
530   CeedChk(ierr);
531   CeedQFunctionField *qfinputfields, *qfoutputfields;
532   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
533   CeedChk(ierr);
534   CeedVector vec;
535   CeedInt numactivein = 0, numactiveout = 0;
536   CeedVector *activein = NULL;
537   CeedScalar *a, *tmp;
538   Ceed ceed, ceedparent;
539   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
540   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
541   ceedparent = ceedparent ? ceedparent : ceed;
542 
543   // Setup
544   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
545 
546   // Check for identity
547   if (impl->identityqf)
548     // LCOV_EXCL_START
549     return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
550   // LCOV_EXCL_STOP
551 
552   // Input Evecs and Restriction
553   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
554                                      opinputfields, NULL, true, impl, request);
555   CeedChk(ierr);
556 
557   // Count number of active input fields
558   for (CeedInt i=0; i<numinputfields; i++) {
559     // Get input vector
560     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
561     // Check if active input
562     if (vec == CEED_VECTOR_ACTIVE) {
563       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
564       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
565       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
566       CeedChk(ierr);
567       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
568       for (CeedInt field=0; field<size; field++) {
569         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
570         CeedChk(ierr);
571         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
572                                   CEED_USE_POINTER, &tmp[field*Q]);
573         CeedChk(ierr);
574       }
575       numactivein += size;
576       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
577     }
578   }
579 
580   // Count number of active output fields
581   for (CeedInt i=0; i<numoutputfields; i++) {
582     // Get output vector
583     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
584     // Check if active output
585     if (vec == CEED_VECTOR_ACTIVE) {
586       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
587       numactiveout += size;
588     }
589   }
590 
591   // Check sizes
592   if (!numactivein || !numactiveout)
593     // LCOV_EXCL_START
594     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
595                      "and outputs");
596   // LCOV_EXCL_STOP
597 
598   // Create output restriction
599   ierr = CeedElemRestrictionCreateIdentity(ceedparent, numelements, Q,
600          numelements*Q, numactivein*numactiveout, rstr); CeedChk(ierr);
601   // Create assembled vector
602   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
603                           assembled); CeedChk(ierr);
604   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
605   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
606 
607   // Loop through elements
608   for (CeedInt e=0; e<numelements; e++) {
609     // Input basis apply
610     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
611                                       numinputfields, true, impl);
612     CeedChk(ierr);
613 
614     // Assemble QFunction
615     for (CeedInt in=0; in<numactivein; in++) {
616       // Set Inputs
617       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
618       if (numactivein > 1) {
619         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
620                                   0.0); CeedChk(ierr);
621       }
622       // Set Outputs
623       for (CeedInt out=0; out<numoutputfields; out++) {
624         // Get output vector
625         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
626         CeedChk(ierr);
627         // Check if active output
628         if (vec == CEED_VECTOR_ACTIVE) {
629           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
630                              CEED_USE_POINTER, a); CeedChk(ierr);
631           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
632           CeedChk(ierr);
633           a += size*Q; // Advance the pointer by the size of the output
634         }
635       }
636       // Apply QFunction
637       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
638       CeedChk(ierr);
639     }
640   }
641 
642   // Un-set output Qvecs to prevent accidental overwrite of Assembled
643   for (CeedInt out=0; out<numoutputfields; out++) {
644     // Get output vector
645     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
646     CeedChk(ierr);
647     // Check if active output
648     if (vec == CEED_VECTOR_ACTIVE) {
649       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
650                          NULL); CeedChk(ierr);
651     }
652   }
653 
654   // Restore input arrays
655   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
656                                        opinputfields, true, impl);
657   CeedChk(ierr);
658 
659   // Restore output
660   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
661 
662   // Cleanup
663   for (CeedInt i=0; i<numactivein; i++) {
664     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
665   }
666   ierr = CeedFree(&activein); CeedChk(ierr);
667 
668   return 0;
669 }
670 
671 // Assemble Linear Diagonal
672 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
673     CeedVector *assembled, CeedRequest *request) {
674   int ierr;
675 
676   // Assemble QFunction
677   CeedQFunction qf;
678   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
679   CeedInt numinputfields, numoutputfields;
680   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
681   CeedChk(ierr);
682   CeedVector assembledqf;
683   CeedElemRestriction rstr;
684   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
685   CeedChk(ierr);
686   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
687 
688   // Determine active input basis
689   CeedOperatorField *opfields;
690   CeedQFunctionField *qffields;
691   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
692   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
693   CeedInt numemodein = 0, ncomp, dim = 1;
694   CeedEvalMode *emodein = NULL;
695   CeedBasis basisin = NULL;
696   CeedElemRestriction rstrin = NULL;
697   for (CeedInt i=0; i<numinputfields; i++) {
698     CeedVector vec;
699     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
700     if (vec == CEED_VECTOR_ACTIVE) {
701       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin);
702       CeedChk(ierr);
703       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
704       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
705       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
706       CeedChk(ierr);
707       CeedEvalMode emode;
708       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
709       CeedChk(ierr);
710       switch (emode) {
711       case CEED_EVAL_NONE:
712       case CEED_EVAL_INTERP:
713         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
714         emodein[numemodein] = emode;
715         numemodein += 1;
716         break;
717       case CEED_EVAL_GRAD:
718         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
719         for (CeedInt d=0; d<dim; d++)
720           emodein[numemodein+d] = emode;
721         numemodein += dim;
722         break;
723       case CEED_EVAL_WEIGHT:
724       case CEED_EVAL_DIV:
725       case CEED_EVAL_CURL:
726         break; // Caught by QF Assembly
727       }
728     }
729   }
730 
731   // Determine active output basis
732   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
733   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
734   CeedInt numemodeout = 0;
735   CeedEvalMode *emodeout = NULL;
736   CeedBasis basisout = NULL;
737   CeedElemRestriction rstrout = NULL;
738   CeedTransposeMode lmodeout = CEED_NOTRANSPOSE;
739   for (CeedInt i=0; i<numoutputfields; i++) {
740     CeedVector vec;
741     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
742     if (vec == CEED_VECTOR_ACTIVE) {
743       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout);
744       CeedChk(ierr);
745       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
746       CeedChk(ierr);
747       ierr = CeedOperatorFieldGetLMode(opfields[i], &lmodeout);
748       CeedChk(ierr);
749       CeedEvalMode emode;
750       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
751       CeedChk(ierr);
752       switch (emode) {
753       case CEED_EVAL_NONE:
754       case CEED_EVAL_INTERP:
755         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
756         emodeout[numemodeout] = emode;
757         numemodeout += 1;
758         break;
759       case CEED_EVAL_GRAD:
760         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
761         for (CeedInt d=0; d<dim; d++)
762           emodeout[numemodeout+d] = emode;
763         numemodeout += dim;
764         break;
765       case CEED_EVAL_WEIGHT:
766       case CEED_EVAL_DIV:
767       case CEED_EVAL_CURL:
768         break; // Caught by QF Assembly
769       }
770     }
771   }
772 
773   // Create diagonal vector
774   CeedVector elemdiag;
775   ierr = CeedElemRestrictionCreateVector(rstrin, assembled, &elemdiag);
776   CeedChk(ierr);
777 
778   // Assemble element operator diagonals
779   CeedScalar *elemdiagarray, *assembledqfarray;
780   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
781   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
782   CeedChk(ierr);
783   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
784   CeedChk(ierr);
785   CeedInt nelem, nnodes, nqpts;
786   ierr = CeedElemRestrictionGetNumElements(rstrin, &nelem); CeedChk(ierr);
787   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
788   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
789   // Compute the diagonal of B^T D B
790   // Each node, qpt pair
791   CeedScalar *interpin, *interpout, *gradin, *gradout;
792   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
793   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
794   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
795   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
796   // Each element and component
797   CeedPragmaSIMD
798   for (CeedInt e=0; e<nelem; e++) {
799     CeedPragmaSIMD
800     for (CeedInt q=0; q<nqpts; q++) {
801       CeedPragmaSIMD
802       for (CeedInt n=0; n<nnodes; n++) {
803         CeedInt dout = -1;
804         // Each basis eval mode pair
805         for (CeedInt eout=0; eout<numemodeout; eout++) {
806           CeedScalar bt = 0.0;
807           if (emodeout[eout] == CEED_EVAL_GRAD)
808             dout += 1;
809           switch (emodeout[eout]) {
810           case CEED_EVAL_NONE:
811             if (n == q)
812               bt = 1.0;
813             break;
814           case CEED_EVAL_INTERP:
815             bt = interpout[q*nnodes+n];
816             break;
817           case CEED_EVAL_GRAD:
818             bt = gradout[(dout*nqpts+q)*nnodes+n];
819             break;
820           case CEED_EVAL_WEIGHT:
821           case CEED_EVAL_DIV:
822           case CEED_EVAL_CURL:
823             break; // Caught by QF Assembly
824           }
825           CeedInt din = -1;
826           for (CeedInt ein=0; ein<numemodein; ein++) {
827             CeedScalar b = 0.0;
828             if (emodein[ein] == CEED_EVAL_GRAD)
829               din += 1;
830             switch (emodein[ein]) {
831             case CEED_EVAL_NONE:
832               if (n == q)
833                 b = 1.0;
834               break;
835             case CEED_EVAL_INTERP:
836               b = interpin[q*nnodes+n];
837               break;
838             case CEED_EVAL_GRAD:
839               b = gradin[(din*nqpts+q)*nnodes+n];
840               break;
841             case CEED_EVAL_WEIGHT:
842             case CEED_EVAL_DIV:
843             case CEED_EVAL_CURL:
844               break; // Caught by QF Assembly
845             }
846             for (CeedInt cout=0; cout<ncomp; cout++) {
847               CeedScalar db = 0.0;
848               for (CeedInt cin=0; cin<ncomp; cin++)
849                 db += assembledqfarray[((((e*numemodein+ein)*ncomp+cin)*
850                                          numemodeout+eout)*ncomp+cout)*nqpts+q]*b;
851               elemdiagarray[(e*ncomp+cout)*nnodes+n] += bt * db;
852             }
853           }
854         }
855       }
856     }
857   }
858 
859   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
860   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
861 
862   // Assemble local operator diagonal
863   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
864   ierr = CeedElemRestrictionApply(rstrout, CEED_TRANSPOSE, lmodeout, elemdiag,
865                                   *assembled, request); CeedChk(ierr);
866 
867   // Cleanup
868   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
869   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
870   ierr = CeedFree(&emodein); CeedChk(ierr);
871   ierr = CeedFree(&emodeout); CeedChk(ierr);
872 
873   return 0;
874 }
875 
876 // Create FDM Element Inverse
877 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
878     CeedOperator *fdminv,
879     CeedRequest *request) {
880   int ierr;
881   Ceed ceed, ceedparent;
882   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
883   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
884   ceedparent = ceedparent ? ceedparent : ceed;
885   CeedQFunction qf;
886   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
887 
888   // Determine active input basis
889   bool interp = false, grad = false;
890   CeedBasis basis = NULL;
891   CeedElemRestriction rstr = NULL;
892   CeedOperatorField *opfields;
893   CeedQFunctionField *qffields;
894   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
895   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
896   CeedInt numinputfields;
897   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
898   for (CeedInt i=0; i<numinputfields; i++) {
899     CeedVector vec;
900     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
901     if (vec == CEED_VECTOR_ACTIVE) {
902       CeedEvalMode emode;
903       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
904       interp = interp || emode == CEED_EVAL_INTERP;
905       grad = grad || emode == CEED_EVAL_GRAD;
906       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
907       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
908       CeedChk(ierr);
909     }
910   }
911   if (!basis)
912     return CeedError(ceed, 1, "No active field set");
913   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, nnodes = 1;
914   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
915   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
916   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
917   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
918   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
919   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
920   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
921   ierr = CeedElemRestrictionGetNumNodes(rstr, &nnodes); CeedChk(ierr);
922 
923   // Build and diagonalize 1D Mass and Laplacian
924   bool tensorbasis;
925   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
926   if (!tensorbasis)
927     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
928                      "bases");
929   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
930   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
931   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
932   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
933   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
934   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
935   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
936   // -- Mass
937   CeedScalar *interp1d, *grad1d, *qweight1d;
938   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
939   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
940   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
941   for (CeedInt i=0; i<Q1d; i++)
942     for (CeedInt j=0; j<P1d; j++)
943       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
944   ierr = CeedMatrixMultiply(ceed, work, interp1d, mass, P1d, P1d, Q1d);
945   CeedChk(ierr);
946   // -- Laplacian
947   for (CeedInt i=0; i<Q1d; i++)
948     for (CeedInt j=0; j<P1d; j++)
949       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
950   ierr = CeedMatrixMultiply(ceed, work, grad1d, laplace, P1d, P1d, Q1d);
951   CeedChk(ierr);
952   // -- Diagonalize
953   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
954   CeedChk(ierr);
955   ierr = CeedFree(&work); CeedChk(ierr);
956   ierr = CeedFree(&mass); CeedChk(ierr);
957   ierr = CeedFree(&laplace); CeedChk(ierr);
958   for (CeedInt i=0; i<P1d; i++)
959     for (CeedInt j=0; j<P1d; j++)
960       x2[i+j*P1d] = x[j+i*P1d];
961   ierr = CeedFree(&x); CeedChk(ierr);
962 
963   // Assemble QFunction
964   CeedVector assembled;
965   CeedElemRestriction rstr_qf;
966   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
967           request); CeedChk(ierr);
968   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
969 
970   // Calculate element averages
971   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
972   CeedScalar *elemavg;
973   const CeedScalar *assembledarray, *qweightsarray;
974   CeedVector qweights;
975   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
976   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
977                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
978   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
979   CeedChk(ierr);
980   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
981   CeedChk(ierr);
982   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
983   for (CeedInt e=0; e<nelem; e++) {
984     CeedInt count = 0;
985     for (CeedInt q=0; q<nqpts; q++)
986       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
987         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
988                                                                   i*nqpts + q]) > CEED_EPSILON) {
989           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
990                                        i*nqpts + q] / qweightsarray[q];
991           count++;
992         }
993     if (count)
994       elemavg[e] /= count;
995   }
996   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
997   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
998   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
999   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
1000 
1001   // Build FDM diagonal
1002   CeedVector qdata;
1003   CeedScalar *qdataarray;
1004   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*nnodes, &qdata); CeedChk(ierr);
1005   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
1006   CeedChk(ierr);
1007   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
1008   for (CeedInt e=0; e<nelem; e++)
1009     for (CeedInt c=0; c<ncomp; c++)
1010       for (CeedInt n=0; n<nnodes; n++) {
1011         if (interp)
1012           qdataarray[(e*ncomp+c)*nnodes+n] = 1;
1013         if (grad)
1014           for (CeedInt d=0; d<dim; d++) {
1015             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1016             qdataarray[(e*ncomp+c)*nnodes+n] += lambda[i];
1017           }
1018         qdataarray[(e*ncomp+c)*nnodes+n] = 1 / (elemavg[e] *
1019                                                 qdataarray[(e*ncomp+c)*nnodes+n]);
1020       }
1021   ierr = CeedFree(&elemavg); CeedChk(ierr);
1022   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1023 
1024   // Setup FDM operator
1025   // -- Basis
1026   CeedBasis fdm_basis;
1027   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1028   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1029   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1030   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1031   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1032                                  graddummy, qrefdummy, qweightdummy,
1033                                  &fdm_basis); CeedChk(ierr);
1034   ierr = CeedFree(&graddummy); CeedChk(ierr);
1035   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1036   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1037   ierr = CeedFree(&x2); CeedChk(ierr);
1038   ierr = CeedFree(&lambda); CeedChk(ierr);
1039 
1040   // -- Restriction
1041   CeedElemRestriction rstr_i;
1042   ierr = CeedElemRestrictionCreateIdentity(ceedparent, nelem, nnodes,
1043          nnodes*nelem, ncomp, &rstr_i); CeedChk(ierr);
1044   // -- QFunction
1045   CeedQFunction mass_qf;
1046   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1047   CeedChk(ierr);
1048   // -- Operator
1049   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1050   CeedChk(ierr);
1051   CeedOperatorSetField(*fdminv, "u", rstr_i, CEED_NOTRANSPOSE,
1052                        fdm_basis, CEED_VECTOR_ACTIVE); CeedChk(ierr);
1053   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_NOTRANSPOSE,
1054                        CEED_BASIS_COLLOCATED, qdata); CeedChk(ierr);
1055   CeedOperatorSetField(*fdminv, "v", rstr_i, CEED_NOTRANSPOSE,
1056                        fdm_basis, CEED_VECTOR_ACTIVE); CeedChk(ierr);
1057 
1058   // Cleanup
1059   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1060   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1061   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1062   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1063 
1064   return 0;
1065 }
1066 
1067 // Operator Create
1068 int CeedOperatorCreate_Ref(CeedOperator op) {
1069   int ierr;
1070   Ceed ceed;
1071   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1072   CeedOperator_Ref *impl;
1073 
1074   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1075   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1076 
1077   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1078                                 CeedOperatorAssembleLinearQFunction_Ref);
1079   CeedChk(ierr);
1080   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1081                                 CeedOperatorAssembleLinearDiagonal_Ref);
1082   CeedChk(ierr);
1083   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1084                                 CeedOperatorCreateFDMElementInverse_Ref);
1085   CeedChk(ierr);
1086   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1087                                 CeedOperatorApply_Ref); CeedChk(ierr);
1088   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1089                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1090   return 0;
1091 }
1092