xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 69a53589b8c3c82ae8bb5be56f1100c7d3468573) 
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 //------------------------------------------------------------------------------
20 // Setup Input/Output Fields
21 //------------------------------------------------------------------------------
22 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op,
23                                        bool inOrOut,
24                                        CeedVector *fullevecs, CeedVector *evecs,
25                                        CeedVector *qvecs, CeedInt starte,
26                                        CeedInt numfields, CeedInt Q) {
27   CeedInt dim, ierr, size, P;
28   Ceed ceed;
29   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
30   CeedBasis basis;
31   CeedElemRestriction Erestrict;
32   CeedOperatorField *opfields;
33   CeedQFunctionField *qffields;
34   if (inOrOut) {
35     ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
36     ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
37   } else {
38     ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
39     ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
40   }
41 
42   // Loop over fields
43   for (CeedInt i=0; i<numfields; i++) {
44     CeedEvalMode emode;
45     ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
46 
47     if (emode != CEED_EVAL_WEIGHT) {
48       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
49       CeedChk(ierr);
50       ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
51                                              &fullevecs[i+starte]);
52       CeedChk(ierr);
53     }
54 
55     switch(emode) {
56     case CEED_EVAL_NONE:
57       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
58       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
59       break;
60     case CEED_EVAL_INTERP:
61       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
62       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
63       CeedChk(ierr);
64       ierr = CeedVectorCreate(ceed, P*size, &evecs[i]); CeedChk(ierr);
65       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
66       break;
67     case CEED_EVAL_GRAD:
68       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
69       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
70       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
71       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
72       CeedChk(ierr);
73       ierr = CeedVectorCreate(ceed, P*size/dim, &evecs[i]); CeedChk(ierr);
74       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
75       break;
76     case CEED_EVAL_WEIGHT: // Only on input fields
77       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
78       ierr = CeedVectorCreate(ceed, Q, &qvecs[i]); CeedChk(ierr);
79       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
80                             CEED_VECTOR_NONE, qvecs[i]); CeedChk(ierr);
81       break;
82     case CEED_EVAL_DIV:
83       break; // Not implemented
84     case CEED_EVAL_CURL:
85       break; // Not implemented
86     }
87   }
88   return 0;
89 }
90 
91 //------------------------------------------------------------------------------
92 // Setup Operator
93 //------------------------------------------------------------------------------/*
94 static int CeedOperatorSetup_Ref(CeedOperator op) {
95   int ierr;
96   bool setupdone;
97   ierr = CeedOperatorGetSetupStatus(op, &setupdone); CeedChk(ierr);
98   if (setupdone) return 0;
99   Ceed ceed;
100   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
101   CeedOperator_Ref *impl;
102   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
103   CeedQFunction qf;
104   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
105   CeedInt Q, numinputfields, numoutputfields;
106   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
107   ierr = CeedQFunctionGetIdentityStatus(qf, &impl->identityqf); CeedChk(ierr);
108   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
109   CeedChk(ierr);
110   CeedOperatorField *opinputfields, *opoutputfields;
111   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
112   CeedChk(ierr);
113   CeedQFunctionField *qfinputfields, *qfoutputfields;
114   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
115   CeedChk(ierr);
116 
117   // Allocate
118   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
119   CeedChk(ierr);
120   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->edata);
121   CeedChk(ierr);
122 
123   ierr = CeedCalloc(16, &impl->inputstate); CeedChk(ierr);
124   ierr = CeedCalloc(16, &impl->evecsin); CeedChk(ierr);
125   ierr = CeedCalloc(16, &impl->evecsout); CeedChk(ierr);
126   ierr = CeedCalloc(16, &impl->qvecsin); CeedChk(ierr);
127   ierr = CeedCalloc(16, &impl->qvecsout); CeedChk(ierr);
128 
129   impl->numein = numinputfields; impl->numeout = numoutputfields;
130 
131   // Set up infield and outfield evecs and qvecs
132   // Infields
133   ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->evecs,
134                                      impl->evecsin, impl->qvecsin, 0,
135                                      numinputfields, Q);
136   CeedChk(ierr);
137   // Outfields
138   ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->evecs,
139                                      impl->evecsout, impl->qvecsout,
140                                      numinputfields, numoutputfields, Q);
141   CeedChk(ierr);
142 
143   // Identity QFunctions
144   if (impl->identityqf) {
145     CeedEvalMode inmode, outmode;
146     CeedQFunctionField *infields, *outfields;
147     ierr = CeedQFunctionGetFields(qf, &infields, &outfields); CeedChk(ierr);
148 
149     for (CeedInt i=0; i<numinputfields; i++) {
150       ierr = CeedQFunctionFieldGetEvalMode(infields[i], &inmode);
151       CeedChk(ierr);
152       ierr = CeedQFunctionFieldGetEvalMode(outfields[i], &outmode);
153       CeedChk(ierr);
154 
155       ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
156       impl->qvecsout[i] = impl->qvecsin[i];
157       ierr = CeedVectorAddReference(impl->qvecsin[i]); CeedChk(ierr);
158     }
159   }
160 
161   ierr = CeedOperatorSetSetupDone(op); CeedChk(ierr);
162 
163   return 0;
164 }
165 
166 //------------------------------------------------------------------------------
167 // Setup Operator Inputs
168 //------------------------------------------------------------------------------
169 static inline int CeedOperatorSetupInputs_Ref(CeedInt numinputfields,
170     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
171     CeedVector invec, const bool skipactive, CeedOperator_Ref *impl,
172     CeedRequest *request) {
173   CeedInt ierr;
174   CeedEvalMode emode;
175   CeedVector vec;
176   CeedElemRestriction Erestrict;
177   uint64_t state;
178 
179   for (CeedInt i=0; i<numinputfields; i++) {
180     // Get input vector
181     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
182     if (vec == CEED_VECTOR_ACTIVE) {
183       if (skipactive)
184         continue;
185       else
186         vec = invec;
187     }
188 
189     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
190     CeedChk(ierr);
191     // Restrict and Evec
192     if (emode == CEED_EVAL_WEIGHT) { // Skip
193     } else {
194       // Restrict
195       ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
196       // Skip restriction if input is unchanged
197       if (state != impl->inputstate[i] || vec == invec) {
198         ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
199         CeedChk(ierr);
200         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE, vec,
201                                         impl->evecs[i], request); CeedChk(ierr);
202         impl->inputstate[i] = state;
203       }
204       // Get evec
205       ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
206                                     (const CeedScalar **) &impl->edata[i]);
207       CeedChk(ierr);
208     }
209   }
210   return 0;
211 }
212 
213 //------------------------------------------------------------------------------
214 // Input Basis Action
215 //------------------------------------------------------------------------------
216 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
217     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
218     CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
219   CeedInt ierr;
220   CeedInt dim, elemsize, size;
221   CeedElemRestriction Erestrict;
222   CeedEvalMode emode;
223   CeedBasis basis;
224 
225   for (CeedInt i=0; i<numinputfields; i++) {
226     // Skip active input
227     if (skipactive) {
228       CeedVector vec;
229       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
230       if (vec == CEED_VECTOR_ACTIVE)
231         continue;
232     }
233     // Get elemsize, emode, size
234     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
235     CeedChk(ierr);
236     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
237     CeedChk(ierr);
238     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
239     CeedChk(ierr);
240     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
241     // Basis action
242     switch(emode) {
243     case CEED_EVAL_NONE:
244       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
245                                 CEED_USE_POINTER,
246                                 &impl->edata[i][e*Q*size]); CeedChk(ierr);
247       break;
248     case CEED_EVAL_INTERP:
249       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
250       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
251                                 CEED_USE_POINTER,
252                                 &impl->edata[i][e*elemsize*size]);
253       CeedChk(ierr);
254       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
255                             CEED_EVAL_INTERP, impl->evecsin[i],
256                             impl->qvecsin[i]); CeedChk(ierr);
257       break;
258     case CEED_EVAL_GRAD:
259       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
260       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
261       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
262                                 CEED_USE_POINTER,
263                                 &impl->edata[i][e*elemsize*size/dim]);
264       CeedChk(ierr);
265       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
266                             CEED_EVAL_GRAD, impl->evecsin[i],
267                             impl->qvecsin[i]); CeedChk(ierr);
268       break;
269     case CEED_EVAL_WEIGHT:
270       break;  // No action
271     case CEED_EVAL_DIV:
272     case CEED_EVAL_CURL: {
273       // LCOV_EXCL_START
274       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
275       CeedChk(ierr);
276       Ceed ceed;
277       ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
278       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
279       // LCOV_EXCL_STOP
280       break; // Not implemented
281     }
282     }
283   }
284   return 0;
285 }
286 
287 //------------------------------------------------------------------------------
288 // Output Basis Action
289 //------------------------------------------------------------------------------
290 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
291     CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
292     CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
293     CeedOperator_Ref *impl) {
294   CeedInt ierr;
295   CeedInt dim, elemsize, size;
296   CeedElemRestriction Erestrict;
297   CeedEvalMode emode;
298   CeedBasis basis;
299 
300   for (CeedInt i=0; i<numoutputfields; i++) {
301     // Get elemsize, emode, size
302     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
303     CeedChk(ierr);
304     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
305     CeedChk(ierr);
306     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
307     CeedChk(ierr);
308     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
309     // Basis action
310     switch(emode) {
311     case CEED_EVAL_NONE:
312       break; // No action
313     case CEED_EVAL_INTERP:
314       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
315       CeedChk(ierr);
316       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
317                                 CEED_USE_POINTER,
318                                 &impl->edata[i + numinputfields][e*elemsize*size]);
319       CeedChk(ierr);
320       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
321                             CEED_EVAL_INTERP, impl->qvecsout[i],
322                             impl->evecsout[i]); CeedChk(ierr);
323       break;
324     case CEED_EVAL_GRAD:
325       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
326       CeedChk(ierr);
327       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
328       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
329                                 CEED_USE_POINTER,
330                                 &impl->edata[i + numinputfields][e*elemsize*size/dim]);
331       CeedChk(ierr);
332       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
333                             CEED_EVAL_GRAD, impl->qvecsout[i],
334                             impl->evecsout[i]); CeedChk(ierr);
335       break;
336     case CEED_EVAL_WEIGHT: {
337       // LCOV_EXCL_START
338       Ceed ceed;
339       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
340       return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
341                        "evaluation mode");
342       // LCOV_EXCL_STOP
343       break; // Should not occur
344     }
345     case CEED_EVAL_DIV:
346     case CEED_EVAL_CURL: {
347       // LCOV_EXCL_START
348       Ceed ceed;
349       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
350       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
351       // LCOV_EXCL_STOP
352       break; // Not implemented
353     }
354     }
355   }
356   return 0;
357 }
358 
359 //------------------------------------------------------------------------------
360 // Restore Input Vectors
361 //------------------------------------------------------------------------------
362 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
363     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
364     const bool skipactive, CeedOperator_Ref *impl) {
365   CeedInt ierr;
366   CeedEvalMode emode;
367 
368   for (CeedInt i=0; i<numinputfields; i++) {
369     // Skip active inputs
370     if (skipactive) {
371       CeedVector vec;
372       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
373       if (vec == CEED_VECTOR_ACTIVE)
374         continue;
375     }
376     // Restore input
377     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
378     CeedChk(ierr);
379     if (emode == CEED_EVAL_WEIGHT) { // Skip
380     } else {
381       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
382                                         (const CeedScalar **) &impl->edata[i]);
383       CeedChk(ierr);
384     }
385   }
386   return 0;
387 }
388 
389 //------------------------------------------------------------------------------
390 // Operator Apply
391 //------------------------------------------------------------------------------
392 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
393                                  CeedVector outvec, CeedRequest *request) {
394   int ierr;
395   CeedOperator_Ref *impl;
396   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
397   CeedQFunction qf;
398   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
399   CeedInt Q, numelements, numinputfields, numoutputfields, size;
400   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
401   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
402   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
403   CeedChk(ierr);
404   CeedOperatorField *opinputfields, *opoutputfields;
405   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
406   CeedChk(ierr);
407   CeedQFunctionField *qfinputfields, *qfoutputfields;
408   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
409   CeedChk(ierr);
410   CeedEvalMode emode;
411   CeedVector vec;
412   CeedElemRestriction Erestrict;
413 
414   // Setup
415   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
416 
417   // Input Evecs and Restriction
418   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
419                                      opinputfields, invec, false, impl,
420                                      request); CeedChk(ierr);
421 
422   // Output Evecs
423   for (CeedInt i=0; i<numoutputfields; i++) {
424     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
425                               &impl->edata[i + numinputfields]); CeedChk(ierr);
426   }
427 
428   // Loop through elements
429   for (CeedInt e=0; e<numelements; e++) {
430     // Output pointers
431     for (CeedInt i=0; i<numoutputfields; i++) {
432       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
433       CeedChk(ierr);
434       if (emode == CEED_EVAL_NONE) {
435         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
436         CeedChk(ierr);
437         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
438                                   CEED_USE_POINTER,
439                                   &impl->edata[i + numinputfields][e*Q*size]);
440         CeedChk(ierr);
441       }
442     }
443 
444     // Input basis apply
445     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
446                                       numinputfields, false, impl);
447     CeedChk(ierr);
448 
449     // Q function
450     if (!impl->identityqf) {
451       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
452       CeedChk(ierr);
453     }
454 
455     // Output basis apply
456     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
457                                        numinputfields, numoutputfields, op, impl);
458     CeedChk(ierr);
459   }
460 
461   // Output restriction
462   for (CeedInt i=0; i<numoutputfields; i++) {
463     // Restore evec
464     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
465                                   &impl->edata[i + numinputfields]);
466     CeedChk(ierr);
467     // Get output vector
468     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
469     // Active
470     if (vec == CEED_VECTOR_ACTIVE)
471       vec = outvec;
472     // Restrict
473     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
474     CeedChk(ierr);
475     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
476                                     impl->evecs[i+impl->numein], vec, request);
477     CeedChk(ierr);
478   }
479 
480   // Restore input arrays
481   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
482                                        opinputfields, false, impl);
483   CeedChk(ierr);
484 
485   return 0;
486 }
487 
488 //------------------------------------------------------------------------------
489 // Assemble Linear QFunction
490 //------------------------------------------------------------------------------
491 static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
492     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
493   int ierr;
494   CeedOperator_Ref *impl;
495   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
496   CeedQFunction qf;
497   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
498   CeedInt Q, numelements, numinputfields, numoutputfields, size;
499   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
500   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
501   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
502   CeedChk(ierr);
503   CeedOperatorField *opinputfields, *opoutputfields;
504   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
505   CeedChk(ierr);
506   CeedQFunctionField *qfinputfields, *qfoutputfields;
507   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
508   CeedChk(ierr);
509   CeedVector vec;
510   CeedInt numactivein = 0, numactiveout = 0;
511   CeedVector *activein = NULL;
512   CeedScalar *a, *tmp;
513   Ceed ceed, ceedparent;
514   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
515   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
516   ceedparent = ceedparent ? ceedparent : ceed;
517 
518   // Setup
519   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
520 
521   // Check for identity
522   if (impl->identityqf)
523     // LCOV_EXCL_START
524     return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
525   // LCOV_EXCL_STOP
526 
527   // Input Evecs and Restriction
528   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
529                                      opinputfields, NULL, true, impl, request);
530   CeedChk(ierr);
531 
532   // Count number of active input fields
533   for (CeedInt i=0; i<numinputfields; i++) {
534     // Get input vector
535     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
536     // Check if active input
537     if (vec == CEED_VECTOR_ACTIVE) {
538       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
539       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
540       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
541       CeedChk(ierr);
542       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
543       for (CeedInt field=0; field<size; field++) {
544         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
545         CeedChk(ierr);
546         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
547                                   CEED_USE_POINTER, &tmp[field*Q]);
548         CeedChk(ierr);
549       }
550       numactivein += size;
551       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
552     }
553   }
554 
555   // Count number of active output fields
556   for (CeedInt i=0; i<numoutputfields; i++) {
557     // Get output vector
558     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
559     // Check if active output
560     if (vec == CEED_VECTOR_ACTIVE) {
561       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
562       numactiveout += size;
563     }
564   }
565 
566   // Check sizes
567   if (!numactivein || !numactiveout)
568     // LCOV_EXCL_START
569     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
570                      "and outputs");
571   // LCOV_EXCL_STOP
572 
573   // Create output restriction
574   CeedInt strides[3] = {1, Q, numactivein *numactiveout*Q};
575   ierr = CeedElemRestrictionCreateStrided(ceedparent, numelements, Q,
576                                           numelements*Q,
577                                           numactivein*numactiveout, strides,
578                                           rstr); CeedChk(ierr);
579   // Create assembled vector
580   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
581                           assembled); CeedChk(ierr);
582   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
583   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
584 
585   // Loop through elements
586   for (CeedInt e=0; e<numelements; e++) {
587     // Input basis apply
588     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
589                                       numinputfields, true, impl);
590     CeedChk(ierr);
591 
592     // Assemble QFunction
593     for (CeedInt in=0; in<numactivein; in++) {
594       // Set Inputs
595       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
596       if (numactivein > 1) {
597         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
598                                   0.0); CeedChk(ierr);
599       }
600       // Set Outputs
601       for (CeedInt out=0; out<numoutputfields; out++) {
602         // Get output vector
603         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
604         CeedChk(ierr);
605         // Check if active output
606         if (vec == CEED_VECTOR_ACTIVE) {
607           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
608                              CEED_USE_POINTER, a); CeedChk(ierr);
609           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
610           CeedChk(ierr);
611           a += size*Q; // Advance the pointer by the size of the output
612         }
613       }
614       // Apply QFunction
615       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
616       CeedChk(ierr);
617     }
618   }
619 
620   // Un-set output Qvecs to prevent accidental overwrite of Assembled
621   for (CeedInt out=0; out<numoutputfields; out++) {
622     // Get output vector
623     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
624     CeedChk(ierr);
625     // Check if active output
626     if (vec == CEED_VECTOR_ACTIVE) {
627       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
628                          NULL); CeedChk(ierr);
629     }
630   }
631 
632   // Restore input arrays
633   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
634                                        opinputfields, true, impl);
635   CeedChk(ierr);
636 
637   // Restore output
638   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
639 
640   // Cleanup
641   for (CeedInt i=0; i<numactivein; i++) {
642     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
643   }
644   ierr = CeedFree(&activein); CeedChk(ierr);
645 
646   return 0;
647 }
648 
649 //------------------------------------------------------------------------------
650 // Get Basis Emode Pointer
651 //------------------------------------------------------------------------------
652 static inline void CeedOperatorGetBasisPointer_Ref(CeedScalar **basisptr,
653     CeedEvalMode emode, CeedScalar *identity, CeedScalar *interp,
654     CeedScalar *grad) {
655   switch (emode) {
656   case CEED_EVAL_NONE:
657     *basisptr = identity;
658     break;
659   case CEED_EVAL_INTERP:
660     *basisptr = interp;
661     break;
662   case CEED_EVAL_GRAD:
663     *basisptr = grad;
664     break;
665   case CEED_EVAL_WEIGHT:
666   case CEED_EVAL_DIV:
667   case CEED_EVAL_CURL:
668     break; // Caught by QF Assembly
669   }
670 }
671 
672 //------------------------------------------------------------------------------
673 // Assemble Linear Diagonal
674 //------------------------------------------------------------------------------
675 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
676     CeedVector *assembled, CeedRequest *request) {
677   int ierr;
678 
679   // Assemble QFunction
680   CeedQFunction qf;
681   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
682   CeedInt numinputfields, numoutputfields;
683   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
684   CeedChk(ierr);
685   CeedVector assembledqf;
686   CeedElemRestriction rstr;
687   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
688   CeedChk(ierr);
689   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
690   CeedScalar maxnorm = 0;
691   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
692 
693   // Determine active input basis
694   CeedOperatorField *opfields;
695   CeedQFunctionField *qffields;
696   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
697   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
698   CeedInt numemodein = 0, ncomp, dim = 1;
699   CeedEvalMode *emodein = NULL;
700   CeedBasis basisin = NULL;
701   CeedElemRestriction rstrin = NULL;
702   for (CeedInt i=0; i<numinputfields; i++) {
703     CeedVector vec;
704     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
705     if (vec == CEED_VECTOR_ACTIVE) {
706       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
707       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
708       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
709       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
710       CeedChk(ierr);
711       CeedEvalMode emode;
712       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
713       CeedChk(ierr);
714       switch (emode) {
715       case CEED_EVAL_NONE:
716       case CEED_EVAL_INTERP:
717         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
718         emodein[numemodein] = emode;
719         numemodein += 1;
720         break;
721       case CEED_EVAL_GRAD:
722         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
723         for (CeedInt d=0; d<dim; d++)
724           emodein[numemodein+d] = emode;
725         numemodein += dim;
726         break;
727       case CEED_EVAL_WEIGHT:
728       case CEED_EVAL_DIV:
729       case CEED_EVAL_CURL:
730         break; // Caught by QF Assembly
731       }
732     }
733   }
734 
735   // Determine active output basis
736   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
737   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
738   CeedInt numemodeout = 0;
739   CeedEvalMode *emodeout = NULL;
740   CeedBasis basisout = NULL;
741   CeedElemRestriction rstrout = NULL;
742   for (CeedInt i=0; i<numoutputfields; i++) {
743     CeedVector vec;
744     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
745     if (vec == CEED_VECTOR_ACTIVE) {
746       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
747       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
748       CeedChk(ierr);
749       CeedEvalMode emode;
750       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
751       switch (emode) {
752       case CEED_EVAL_NONE:
753       case CEED_EVAL_INTERP:
754         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
755         emodeout[numemodeout] = emode;
756         numemodeout += 1;
757         break;
758       case CEED_EVAL_GRAD:
759         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
760         for (CeedInt d=0; d<dim; d++)
761           emodeout[numemodeout+d] = emode;
762         numemodeout += dim;
763         break;
764       case CEED_EVAL_WEIGHT:
765       case CEED_EVAL_DIV:
766       case CEED_EVAL_CURL:
767         break; // Caught by QF Assembly
768       }
769     }
770   }
771 
772   // Create diagonal vector
773   CeedVector elemdiag;
774   ierr = CeedElemRestrictionCreateVector(rstrin, assembled, &elemdiag);
775   CeedChk(ierr);
776 
777   // Assemble element operator diagonals
778   CeedScalar *elemdiagarray, *assembledqfarray;
779   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
780   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
781   CeedChk(ierr);
782   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
783   CeedChk(ierr);
784   CeedInt nelem, nnodes, nqpts;
785   ierr = CeedElemRestrictionGetNumElements(rstrin, &nelem); CeedChk(ierr);
786   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
787   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
788   // Basis matrices
789   CeedScalar *identity = NULL, *interpin, *interpout, *gradin, *gradout;
790   bool evalNone = false;
791   for (CeedInt i=0; i<numemodein; i++)
792     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
793   for (CeedInt i=0; i<numemodeout; i++)
794     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
795   if (evalNone) {
796     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
797     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
798       identity[i*nnodes+i] = 1.0;
799   }
800   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
801   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
802   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
803   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
804   // Compute the diagonal of B^T D B
805   // Each element
806   for (CeedInt e=0; e<nelem; e++) {
807     CeedInt dout = -1;
808     // Each basis eval mode pair
809     for (CeedInt eout=0; eout<numemodeout; eout++) {
810       CeedScalar *bt = NULL;
811       if (emodeout[eout] == CEED_EVAL_GRAD)
812         dout += 1;
813       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
814                                       &gradout[dout*nqpts*nnodes]);
815       CeedInt din = -1;
816       for (CeedInt ein=0; ein<numemodein; ein++) {
817         CeedScalar *b = NULL;
818         if (emodein[ein] == CEED_EVAL_GRAD)
819           din += 1;
820         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
821                                         &gradin[din*nqpts*nnodes]);
822         // Each component
823         for (CeedInt comp=0; comp<ncomp; comp++)
824           // Each qpoint/node pair
825           for (CeedInt q=0; q<nqpts; q++) {
826             const CeedScalar qfvalue =
827               assembledqfarray[((((e*numemodein+ein)*ncomp+comp)*
828                                  numemodeout+eout)*ncomp+comp)*nqpts+q];
829             if (fabs(qfvalue) > maxnorm*1e-12)
830               for (CeedInt n=0; n<nnodes; n++)
831                 elemdiagarray[(e*ncomp+comp)*nnodes+n] += bt[q*nnodes+n] *
832                     qfvalue * b[q*nnodes+n];
833             }
834       }
835     }
836   }
837   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
838   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
839 
840   // Assemble local operator diagonal
841   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
842   ierr = CeedElemRestrictionApply(rstrout, CEED_TRANSPOSE, elemdiag,
843                                   *assembled, request); CeedChk(ierr);
844 
845   // Cleanup
846   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
847   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
848   ierr = CeedFree(&emodein); CeedChk(ierr);
849   ierr = CeedFree(&emodeout); CeedChk(ierr);
850   ierr = CeedFree(&identity); CeedChk(ierr);
851 
852   return 0;
853 }
854 
855 //------------------------------------------------------------------------------
856 // Create FDM Element Inverse
857 //------------------------------------------------------------------------------
858 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
859     CeedOperator *fdminv,
860     CeedRequest *request) {
861   int ierr;
862   Ceed ceed, ceedparent;
863   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
864   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
865   ceedparent = ceedparent ? ceedparent : ceed;
866   CeedQFunction qf;
867   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
868 
869   // Determine active input basis
870   bool interp = false, grad = false;
871   CeedBasis basis = NULL;
872   CeedElemRestriction rstr = NULL;
873   CeedOperatorField *opfields;
874   CeedQFunctionField *qffields;
875   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
876   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
877   CeedInt numinputfields;
878   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
879   for (CeedInt i=0; i<numinputfields; i++) {
880     CeedVector vec;
881     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
882     if (vec == CEED_VECTOR_ACTIVE) {
883       CeedEvalMode emode;
884       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
885       interp = interp || emode == CEED_EVAL_INTERP;
886       grad = grad || emode == CEED_EVAL_GRAD;
887       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
888       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
889       CeedChk(ierr);
890     }
891   }
892   if (!basis)
893     // LCOV_EXCL_START
894     return CeedError(ceed, 1, "No active field set");
895   // LCOV_EXCL_STOP
896   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, nnodes = 1;
897   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
898   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
899   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
900   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
901   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
902   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
903   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
904   ierr = CeedElemRestrictionGetNumNodes(rstr, &nnodes); CeedChk(ierr);
905 
906   // Build and diagonalize 1D Mass and Laplacian
907   bool tensorbasis;
908   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
909   if (!tensorbasis)
910     // LCOV_EXCL_START
911     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
912                      "bases");
913   // LCOV_EXCL_STOP
914   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
915   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
916   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
917   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
918   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
919   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
920   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
921   // -- Mass
922   CeedScalar *interp1d, *grad1d, *qweight1d;
923   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
924   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
925   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
926   for (CeedInt i=0; i<Q1d; i++)
927     for (CeedInt j=0; j<P1d; j++)
928       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
929   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
930                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
931   CeedChk(ierr);
932   // -- Laplacian
933   for (CeedInt i=0; i<Q1d; i++)
934     for (CeedInt j=0; j<P1d; j++)
935       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
936   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
937                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
938   CeedChk(ierr);
939   // -- Diagonalize
940   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
941   CeedChk(ierr);
942   ierr = CeedFree(&work); CeedChk(ierr);
943   ierr = CeedFree(&mass); CeedChk(ierr);
944   ierr = CeedFree(&laplace); CeedChk(ierr);
945   for (CeedInt i=0; i<P1d; i++)
946     for (CeedInt j=0; j<P1d; j++)
947       x2[i+j*P1d] = x[j+i*P1d];
948   ierr = CeedFree(&x); CeedChk(ierr);
949 
950   // Assemble QFunction
951   CeedVector assembled;
952   CeedElemRestriction rstr_qf;
953   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
954           request); CeedChk(ierr);
955   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
956   CeedScalar maxnorm = 0;
957   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
958 
959   // Calculate element averages
960   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
961   CeedScalar *elemavg;
962   const CeedScalar *assembledarray, *qweightsarray;
963   CeedVector qweights;
964   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
965   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
966                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
967   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
968   CeedChk(ierr);
969   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
970   CeedChk(ierr);
971   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
972   for (CeedInt e=0; e<nelem; e++) {
973     CeedInt count = 0;
974     for (CeedInt q=0; q<nqpts; q++)
975       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
976         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
977                                                                   i*nqpts + q]) > maxnorm*1e-12) {
978           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
979                                        i*nqpts + q] / qweightsarray[q];
980           count++;
981         }
982     if (count)
983       elemavg[e] /= count;
984   }
985   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
986   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
987   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
988   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
989 
990   // Build FDM diagonal
991   CeedVector qdata;
992   CeedScalar *qdataarray;
993   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*nnodes, &qdata); CeedChk(ierr);
994   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
995   CeedChk(ierr);
996   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
997   for (CeedInt e=0; e<nelem; e++)
998     for (CeedInt c=0; c<ncomp; c++)
999       for (CeedInt n=0; n<nnodes; n++) {
1000         if (interp)
1001           qdataarray[(e*ncomp+c)*nnodes+n] = 1;
1002         if (grad)
1003           for (CeedInt d=0; d<dim; d++) {
1004             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1005             qdataarray[(e*ncomp+c)*nnodes+n] += lambda[i];
1006           }
1007         qdataarray[(e*ncomp+c)*nnodes+n] = 1 / (elemavg[e] *
1008                                                 qdataarray[(e*ncomp+c)*nnodes+n]);
1009       }
1010   ierr = CeedFree(&elemavg); CeedChk(ierr);
1011   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1012 
1013   // Setup FDM operator
1014   // -- Basis
1015   CeedBasis fdm_basis;
1016   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1017   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1018   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1019   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1020   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1021                                  graddummy, qrefdummy, qweightdummy,
1022                                  &fdm_basis); CeedChk(ierr);
1023   ierr = CeedFree(&graddummy); CeedChk(ierr);
1024   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1025   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1026   ierr = CeedFree(&x2); CeedChk(ierr);
1027   ierr = CeedFree(&lambda); CeedChk(ierr);
1028 
1029   // -- Restriction
1030   CeedElemRestriction rstr_i;
1031   CeedInt strides[3] = {1, nnodes, nnodes*ncomp};
1032   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, nnodes,
1033                                           nnodes*nelem, ncomp, strides, &rstr_i);
1034   CeedChk(ierr);
1035   // -- QFunction
1036   CeedQFunction mass_qf;
1037   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1038   CeedChk(ierr);
1039   // -- Operator
1040   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1041   CeedChk(ierr);
1042   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1043   CeedChk(ierr);
1044   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1045   CeedChk(ierr);
1046   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1047   CeedChk(ierr);
1048 
1049   // Cleanup
1050   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1051   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1052   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1053   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1054 
1055   return 0;
1056 }
1057 
1058 //------------------------------------------------------------------------------
1059 // Operator Destroy
1060 //------------------------------------------------------------------------------
1061 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1062   int ierr;
1063   CeedOperator_Ref *impl;
1064   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1065 
1066   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1067     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1068   }
1069   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1070   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1071   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1072 
1073   for (CeedInt i=0; i<impl->numein; i++) {
1074     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1075     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1076   }
1077   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1078   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1079 
1080   for (CeedInt i=0; i<impl->numeout; i++) {
1081     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1082     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1083   }
1084   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1085   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1086 
1087   ierr = CeedFree(&impl); CeedChk(ierr);
1088   return 0;
1089 }
1090 
1091 //------------------------------------------------------------------------------
1092 // Operator Create
1093 //------------------------------------------------------------------------------
1094 int CeedOperatorCreate_Ref(CeedOperator op) {
1095   int ierr;
1096   Ceed ceed;
1097   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1098   CeedOperator_Ref *impl;
1099 
1100   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1101   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1102 
1103   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1104                                 CeedOperatorAssembleLinearQFunction_Ref);
1105   CeedChk(ierr);
1106   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1107                                 CeedOperatorAssembleLinearDiagonal_Ref);
1108   CeedChk(ierr);
1109   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1110                                 CeedOperatorCreateFDMElementInverse_Ref);
1111   CeedChk(ierr);
1112   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1113                                 CeedOperatorApply_Ref); CeedChk(ierr);
1114   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1115                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1116   return 0;
1117 }
1118 //------------------------------------------------------------------------------
1119