xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 523b8ea09bebe65e72854bf0f9327b4f4d8bccdb) ! 
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     // LCOV_EXCL_START
272     case CEED_EVAL_DIV:
273     case CEED_EVAL_CURL: {
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       break; // Not implemented
280       // LCOV_EXCL_STOP
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     // LCOV_EXCL_START
337     case CEED_EVAL_WEIGHT: {
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       break; // Should not occur
343     }
344     case CEED_EVAL_DIV:
345     case CEED_EVAL_CURL: {
346       Ceed ceed;
347       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
348       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
349       // LCOV_EXCL_STOP
350       break; // Not implemented
351     }
352     }
353   }
354   return 0;
355 }
356 
357 //------------------------------------------------------------------------------
358 // Restore Input Vectors
359 //------------------------------------------------------------------------------
360 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
361     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
362     const bool skipactive, CeedOperator_Ref *impl) {
363   CeedInt ierr;
364   CeedEvalMode emode;
365 
366   for (CeedInt i=0; i<numinputfields; i++) {
367     // Skip active inputs
368     if (skipactive) {
369       CeedVector vec;
370       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
371       if (vec == CEED_VECTOR_ACTIVE)
372         continue;
373     }
374     // Restore input
375     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
376     CeedChk(ierr);
377     if (emode == CEED_EVAL_WEIGHT) { // Skip
378     } else {
379       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
380                                         (const CeedScalar **) &impl->edata[i]);
381       CeedChk(ierr);
382     }
383   }
384   return 0;
385 }
386 
387 //------------------------------------------------------------------------------
388 // Operator Apply
389 //------------------------------------------------------------------------------
390 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
391                                  CeedVector outvec, CeedRequest *request) {
392   int ierr;
393   CeedOperator_Ref *impl;
394   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
395   CeedQFunction qf;
396   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
397   CeedInt Q, numelements, numinputfields, numoutputfields, size;
398   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
399   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
400   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
401   CeedChk(ierr);
402   CeedOperatorField *opinputfields, *opoutputfields;
403   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
404   CeedChk(ierr);
405   CeedQFunctionField *qfinputfields, *qfoutputfields;
406   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
407   CeedChk(ierr);
408   CeedEvalMode emode;
409   CeedVector vec;
410   CeedElemRestriction Erestrict;
411 
412   // Setup
413   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
414 
415   // Input Evecs and Restriction
416   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
417                                      opinputfields, invec, false, impl,
418                                      request); CeedChk(ierr);
419 
420   // Output Evecs
421   for (CeedInt i=0; i<numoutputfields; i++) {
422     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
423                               &impl->edata[i + numinputfields]); CeedChk(ierr);
424   }
425 
426   // Loop through elements
427   for (CeedInt e=0; e<numelements; e++) {
428     // Output pointers
429     for (CeedInt i=0; i<numoutputfields; i++) {
430       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
431       CeedChk(ierr);
432       if (emode == CEED_EVAL_NONE) {
433         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
434         CeedChk(ierr);
435         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
436                                   CEED_USE_POINTER,
437                                   &impl->edata[i + numinputfields][e*Q*size]);
438         CeedChk(ierr);
439       }
440     }
441 
442     // Input basis apply
443     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
444                                       numinputfields, false, impl);
445     CeedChk(ierr);
446 
447     // Q function
448     if (!impl->identityqf) {
449       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
450       CeedChk(ierr);
451     }
452 
453     // Output basis apply
454     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
455                                        numinputfields, numoutputfields, op, impl);
456     CeedChk(ierr);
457   }
458 
459   // Output restriction
460   for (CeedInt i=0; i<numoutputfields; i++) {
461     // Restore evec
462     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
463                                   &impl->edata[i + numinputfields]);
464     CeedChk(ierr);
465     // Get output vector
466     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
467     // Active
468     if (vec == CEED_VECTOR_ACTIVE)
469       vec = outvec;
470     // Restrict
471     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
472     CeedChk(ierr);
473     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
474                                     impl->evecs[i+impl->numein], vec, request);
475     CeedChk(ierr);
476   }
477 
478   // Restore input arrays
479   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
480                                        opinputfields, false, impl);
481   CeedChk(ierr);
482 
483   return 0;
484 }
485 
486 //------------------------------------------------------------------------------
487 // Assemble Linear QFunction
488 //------------------------------------------------------------------------------
489 static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
490     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
491   int ierr;
492   CeedOperator_Ref *impl;
493   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
494   CeedQFunction qf;
495   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
496   CeedInt Q, numelements, numinputfields, numoutputfields, size;
497   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
498   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
499   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
500   CeedChk(ierr);
501   CeedOperatorField *opinputfields, *opoutputfields;
502   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
503   CeedChk(ierr);
504   CeedQFunctionField *qfinputfields, *qfoutputfields;
505   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
506   CeedChk(ierr);
507   CeedVector vec;
508   CeedInt numactivein = 0, numactiveout = 0;
509   CeedVector *activein = NULL;
510   CeedScalar *a, *tmp;
511   Ceed ceed, ceedparent;
512   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
513   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
514   ceedparent = ceedparent ? ceedparent : ceed;
515 
516   // Setup
517   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
518 
519   // Check for identity
520   if (impl->identityqf)
521     // LCOV_EXCL_START
522     return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
523   // LCOV_EXCL_STOP
524 
525   // Input Evecs and Restriction
526   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
527                                      opinputfields, NULL, true, impl, request);
528   CeedChk(ierr);
529 
530   // Count number of active input fields
531   for (CeedInt i=0; i<numinputfields; i++) {
532     // Get input vector
533     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
534     // Check if active input
535     if (vec == CEED_VECTOR_ACTIVE) {
536       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
537       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
538       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
539       CeedChk(ierr);
540       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
541       for (CeedInt field=0; field<size; field++) {
542         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
543         CeedChk(ierr);
544         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
545                                   CEED_USE_POINTER, &tmp[field*Q]);
546         CeedChk(ierr);
547       }
548       numactivein += size;
549       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
550     }
551   }
552 
553   // Count number of active output fields
554   for (CeedInt i=0; i<numoutputfields; i++) {
555     // Get output vector
556     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
557     // Check if active output
558     if (vec == CEED_VECTOR_ACTIVE) {
559       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
560       numactiveout += size;
561     }
562   }
563 
564   // Check sizes
565   if (!numactivein || !numactiveout)
566     // LCOV_EXCL_START
567     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
568                      "and outputs");
569   // LCOV_EXCL_STOP
570 
571   // Create output restriction
572   CeedInt strides[3] = {1, Q, numactivein *numactiveout*Q};
573   ierr = CeedElemRestrictionCreateStrided(ceedparent, numelements, Q,
574                                           numelements*Q,
575                                           numactivein*numactiveout, strides,
576                                           rstr); CeedChk(ierr);
577   // Create assembled vector
578   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
579                           assembled); CeedChk(ierr);
580   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
581   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
582 
583   // Loop through elements
584   for (CeedInt e=0; e<numelements; e++) {
585     // Input basis apply
586     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
587                                       numinputfields, true, impl);
588     CeedChk(ierr);
589 
590     // Assemble QFunction
591     for (CeedInt in=0; in<numactivein; in++) {
592       // Set Inputs
593       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
594       if (numactivein > 1) {
595         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
596                                   0.0); CeedChk(ierr);
597       }
598       // Set Outputs
599       for (CeedInt out=0; out<numoutputfields; out++) {
600         // Get output vector
601         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
602         CeedChk(ierr);
603         // Check if active output
604         if (vec == CEED_VECTOR_ACTIVE) {
605           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
606                              CEED_USE_POINTER, a); CeedChk(ierr);
607           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
608           CeedChk(ierr);
609           a += size*Q; // Advance the pointer by the size of the output
610         }
611       }
612       // Apply QFunction
613       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
614       CeedChk(ierr);
615     }
616   }
617 
618   // Un-set output Qvecs to prevent accidental overwrite of Assembled
619   for (CeedInt out=0; out<numoutputfields; out++) {
620     // Get output vector
621     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
622     CeedChk(ierr);
623     // Check if active output
624     if (vec == CEED_VECTOR_ACTIVE) {
625       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
626                          NULL); CeedChk(ierr);
627     }
628   }
629 
630   // Restore input arrays
631   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
632                                        opinputfields, true, impl);
633   CeedChk(ierr);
634 
635   // Restore output
636   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
637 
638   // Cleanup
639   for (CeedInt i=0; i<numactivein; i++) {
640     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
641   }
642   ierr = CeedFree(&activein); CeedChk(ierr);
643 
644   return 0;
645 }
646 
647 //------------------------------------------------------------------------------
648 // Get Basis Emode Pointer
649 //------------------------------------------------------------------------------
650 static inline void CeedOperatorGetBasisPointer_Ref(CeedScalar **basisptr,
651     CeedEvalMode emode, CeedScalar *identity, CeedScalar *interp,
652     CeedScalar *grad) {
653   switch (emode) {
654   case CEED_EVAL_NONE:
655     *basisptr = identity;
656     break;
657   case CEED_EVAL_INTERP:
658     *basisptr = interp;
659     break;
660   case CEED_EVAL_GRAD:
661     *basisptr = grad;
662     break;
663   case CEED_EVAL_WEIGHT:
664   case CEED_EVAL_DIV:
665   case CEED_EVAL_CURL:
666     break; // Caught by QF Assembly
667   }
668 }
669 
670 //------------------------------------------------------------------------------
671 // Assemble Linear Diagonal
672 //------------------------------------------------------------------------------
673 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
674     CeedVector *assembled, CeedRequest *request) {
675   int ierr;
676 
677   // Assemble QFunction
678   CeedQFunction qf;
679   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
680   CeedInt numinputfields, numoutputfields;
681   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
682   CeedChk(ierr);
683   CeedVector assembledqf;
684   CeedElemRestriction rstr;
685   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
686   CeedChk(ierr);
687   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
688   CeedScalar maxnorm = 0;
689   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
690 
691   // Determine active input basis
692   CeedOperatorField *opfields;
693   CeedQFunctionField *qffields;
694   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
695   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
696   CeedInt numemodein = 0, ncomp, dim = 1;
697   CeedEvalMode *emodein = NULL;
698   CeedBasis basisin = NULL;
699   CeedElemRestriction rstrin = NULL;
700   for (CeedInt i=0; i<numinputfields; i++) {
701     CeedVector vec;
702     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
703     if (vec == CEED_VECTOR_ACTIVE) {
704       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
705       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
706       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
707       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
708       CeedChk(ierr);
709       CeedEvalMode emode;
710       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
711       CeedChk(ierr);
712       switch (emode) {
713       case CEED_EVAL_NONE:
714       case CEED_EVAL_INTERP:
715         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
716         emodein[numemodein] = emode;
717         numemodein += 1;
718         break;
719       case CEED_EVAL_GRAD:
720         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
721         for (CeedInt d=0; d<dim; d++)
722           emodein[numemodein+d] = emode;
723         numemodein += dim;
724         break;
725       case CEED_EVAL_WEIGHT:
726       case CEED_EVAL_DIV:
727       case CEED_EVAL_CURL:
728         break; // Caught by QF Assembly
729       }
730     }
731   }
732 
733   // Determine active output basis
734   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
735   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
736   CeedInt numemodeout = 0;
737   CeedEvalMode *emodeout = NULL;
738   CeedBasis basisout = NULL;
739   CeedElemRestriction rstrout = NULL;
740   for (CeedInt i=0; i<numoutputfields; i++) {
741     CeedVector vec;
742     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
743     if (vec == CEED_VECTOR_ACTIVE) {
744       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
745       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
746       CeedChk(ierr);
747       CeedEvalMode emode;
748       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
749       switch (emode) {
750       case CEED_EVAL_NONE:
751       case CEED_EVAL_INTERP:
752         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
753         emodeout[numemodeout] = emode;
754         numemodeout += 1;
755         break;
756       case CEED_EVAL_GRAD:
757         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
758         for (CeedInt d=0; d<dim; d++)
759           emodeout[numemodeout+d] = emode;
760         numemodeout += dim;
761         break;
762       case CEED_EVAL_WEIGHT:
763       case CEED_EVAL_DIV:
764       case CEED_EVAL_CURL:
765         break; // Caught by QF Assembly
766       }
767     }
768   }
769 
770   // Create diagonal vector
771   CeedVector elemdiag;
772   ierr = CeedElemRestrictionCreateVector(rstrin, assembled, &elemdiag);
773   CeedChk(ierr);
774 
775   // Assemble element operator diagonals
776   CeedScalar *elemdiagarray, *assembledqfarray;
777   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
778   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
779   CeedChk(ierr);
780   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
781   CeedChk(ierr);
782   CeedInt nelem, nnodes, nqpts;
783   ierr = CeedElemRestrictionGetNumElements(rstrin, &nelem); CeedChk(ierr);
784   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
785   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
786   // Basis matrices
787   CeedScalar *identity = NULL, *interpin, *interpout, *gradin, *gradout;
788   bool evalNone = false;
789   for (CeedInt i=0; i<numemodein; i++)
790     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
791   for (CeedInt i=0; i<numemodeout; i++)
792     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
793   if (evalNone) {
794     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
795     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
796       identity[i*nnodes+i] = 1.0;
797   }
798   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
799   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
800   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
801   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
802   // Compute the diagonal of B^T D B
803   // Each element
804   for (CeedInt e=0; e<nelem; e++) {
805     CeedInt dout = -1;
806     // Each basis eval mode pair
807     for (CeedInt eout=0; eout<numemodeout; eout++) {
808       CeedScalar *bt = NULL;
809       if (emodeout[eout] == CEED_EVAL_GRAD)
810         dout += 1;
811       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
812                                       &gradout[dout*nqpts*nnodes]);
813       CeedInt din = -1;
814       for (CeedInt ein=0; ein<numemodein; ein++) {
815         CeedScalar *b = NULL;
816         if (emodein[ein] == CEED_EVAL_GRAD)
817           din += 1;
818         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
819                                         &gradin[din*nqpts*nnodes]);
820         // Each component
821         for (CeedInt comp=0; comp<ncomp; comp++)
822           // Each qpoint/node pair
823           for (CeedInt q=0; q<nqpts; q++) {
824             const CeedScalar qfvalue =
825               assembledqfarray[((((e*numemodein+ein)*ncomp+comp)*
826                                  numemodeout+eout)*ncomp+comp)*nqpts+q];
827             if (fabs(qfvalue) > maxnorm*1e-12)
828               for (CeedInt n=0; n<nnodes; n++)
829                 elemdiagarray[(e*ncomp+comp)*nnodes+n] += bt[q*nnodes+n] *
830                     qfvalue * b[q*nnodes+n];
831             }
832       }
833     }
834   }
835   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
836   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
837 
838   // Assemble local operator diagonal
839   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
840   ierr = CeedElemRestrictionApply(rstrout, CEED_TRANSPOSE, elemdiag,
841                                   *assembled, request); CeedChk(ierr);
842 
843   // Cleanup
844   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
845   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
846   ierr = CeedFree(&emodein); CeedChk(ierr);
847   ierr = CeedFree(&emodeout); CeedChk(ierr);
848   ierr = CeedFree(&identity); CeedChk(ierr);
849 
850   return 0;
851 }
852 
853 //------------------------------------------------------------------------------
854 // Create FDM Element Inverse
855 //------------------------------------------------------------------------------
856 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
857     CeedOperator *fdminv,
858     CeedRequest *request) {
859   int ierr;
860   Ceed ceed, ceedparent;
861   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
862   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
863   ceedparent = ceedparent ? ceedparent : ceed;
864   CeedQFunction qf;
865   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
866 
867   // Determine active input basis
868   bool interp = false, grad = false;
869   CeedBasis basis = NULL;
870   CeedElemRestriction rstr = NULL;
871   CeedOperatorField *opfields;
872   CeedQFunctionField *qffields;
873   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
874   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
875   CeedInt numinputfields;
876   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
877   for (CeedInt i=0; i<numinputfields; i++) {
878     CeedVector vec;
879     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
880     if (vec == CEED_VECTOR_ACTIVE) {
881       CeedEvalMode emode;
882       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
883       interp = interp || emode == CEED_EVAL_INTERP;
884       grad = grad || emode == CEED_EVAL_GRAD;
885       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
886       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
887       CeedChk(ierr);
888     }
889   }
890   if (!basis)
891     // LCOV_EXCL_START
892     return CeedError(ceed, 1, "No active field set");
893   // LCOV_EXCL_STOP
894   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, nnodes = 1;
895   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
896   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
897   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
898   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
899   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
900   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
901   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
902   ierr = CeedElemRestrictionGetNumNodes(rstr, &nnodes); CeedChk(ierr);
903 
904   // Build and diagonalize 1D Mass and Laplacian
905   bool tensorbasis;
906   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
907   if (!tensorbasis)
908     // LCOV_EXCL_START
909     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
910                      "bases");
911   // LCOV_EXCL_STOP
912   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
913   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
914   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
915   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
916   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
917   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
918   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
919   // -- Mass
920   CeedScalar *interp1d, *grad1d, *qweight1d;
921   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
922   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
923   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
924   for (CeedInt i=0; i<Q1d; i++)
925     for (CeedInt j=0; j<P1d; j++)
926       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
927   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
928                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
929   CeedChk(ierr);
930   // -- Laplacian
931   for (CeedInt i=0; i<Q1d; i++)
932     for (CeedInt j=0; j<P1d; j++)
933       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
934   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
935                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
936   CeedChk(ierr);
937   // -- Diagonalize
938   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
939   CeedChk(ierr);
940   ierr = CeedFree(&work); CeedChk(ierr);
941   ierr = CeedFree(&mass); CeedChk(ierr);
942   ierr = CeedFree(&laplace); CeedChk(ierr);
943   for (CeedInt i=0; i<P1d; i++)
944     for (CeedInt j=0; j<P1d; j++)
945       x2[i+j*P1d] = x[j+i*P1d];
946   ierr = CeedFree(&x); CeedChk(ierr);
947 
948   // Assemble QFunction
949   CeedVector assembled;
950   CeedElemRestriction rstr_qf;
951   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
952           request); CeedChk(ierr);
953   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
954   CeedScalar maxnorm = 0;
955   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
956 
957   // Calculate element averages
958   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
959   CeedScalar *elemavg;
960   const CeedScalar *assembledarray, *qweightsarray;
961   CeedVector qweights;
962   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
963   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
964                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
965   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
966   CeedChk(ierr);
967   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
968   CeedChk(ierr);
969   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
970   for (CeedInt e=0; e<nelem; e++) {
971     CeedInt count = 0;
972     for (CeedInt q=0; q<nqpts; q++)
973       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
974         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
975                                                                   i*nqpts + q]) > maxnorm*1e-12) {
976           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
977                                        i*nqpts + q] / qweightsarray[q];
978           count++;
979         }
980     if (count)
981       elemavg[e] /= count;
982   }
983   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
984   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
985   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
986   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
987 
988   // Build FDM diagonal
989   CeedVector qdata;
990   CeedScalar *qdataarray;
991   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*nnodes, &qdata); CeedChk(ierr);
992   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
993   CeedChk(ierr);
994   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
995   for (CeedInt e=0; e<nelem; e++)
996     for (CeedInt c=0; c<ncomp; c++)
997       for (CeedInt n=0; n<nnodes; n++) {
998         if (interp)
999           qdataarray[(e*ncomp+c)*nnodes+n] = 1;
1000         if (grad)
1001           for (CeedInt d=0; d<dim; d++) {
1002             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1003             qdataarray[(e*ncomp+c)*nnodes+n] += lambda[i];
1004           }
1005         qdataarray[(e*ncomp+c)*nnodes+n] = 1 / (elemavg[e] *
1006                                                 qdataarray[(e*ncomp+c)*nnodes+n]);
1007       }
1008   ierr = CeedFree(&elemavg); CeedChk(ierr);
1009   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1010 
1011   // Setup FDM operator
1012   // -- Basis
1013   CeedBasis fdm_basis;
1014   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1015   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1016   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1017   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1018   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1019                                  graddummy, qrefdummy, qweightdummy,
1020                                  &fdm_basis); CeedChk(ierr);
1021   ierr = CeedFree(&graddummy); CeedChk(ierr);
1022   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1023   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1024   ierr = CeedFree(&x2); CeedChk(ierr);
1025   ierr = CeedFree(&lambda); CeedChk(ierr);
1026 
1027   // -- Restriction
1028   CeedElemRestriction rstr_i;
1029   CeedInt strides[3] = {1, nnodes, nnodes*ncomp};
1030   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, nnodes,
1031                                           nnodes*nelem, ncomp, strides, &rstr_i);
1032   CeedChk(ierr);
1033   // -- QFunction
1034   CeedQFunction mass_qf;
1035   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1036   CeedChk(ierr);
1037   // -- Operator
1038   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1039   CeedChk(ierr);
1040   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1041   CeedChk(ierr);
1042   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1043   CeedChk(ierr);
1044   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1045   CeedChk(ierr);
1046 
1047   // Cleanup
1048   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1049   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1050   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1051   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1052 
1053   return 0;
1054 }
1055 
1056 //------------------------------------------------------------------------------
1057 // Operator Destroy
1058 //------------------------------------------------------------------------------
1059 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1060   int ierr;
1061   CeedOperator_Ref *impl;
1062   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1063 
1064   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1065     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1066   }
1067   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1068   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1069   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1070 
1071   for (CeedInt i=0; i<impl->numein; i++) {
1072     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1073     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1074   }
1075   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1076   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1077 
1078   for (CeedInt i=0; i<impl->numeout; i++) {
1079     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1080     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1081   }
1082   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1083   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1084 
1085   ierr = CeedFree(&impl); CeedChk(ierr);
1086   return 0;
1087 }
1088 
1089 //------------------------------------------------------------------------------
1090 // Operator Create
1091 //------------------------------------------------------------------------------
1092 int CeedOperatorCreate_Ref(CeedOperator op) {
1093   int ierr;
1094   Ceed ceed;
1095   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1096   CeedOperator_Ref *impl;
1097 
1098   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1099   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1100 
1101   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1102                                 CeedOperatorAssembleLinearQFunction_Ref);
1103   CeedChk(ierr);
1104   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1105                                 CeedOperatorAssembleLinearDiagonal_Ref);
1106   CeedChk(ierr);
1107   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1108                                 CeedOperatorCreateFDMElementInverse_Ref);
1109   CeedChk(ierr);
1110   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1111                                 CeedOperatorApply_Ref); CeedChk(ierr);
1112   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1113                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1114   return 0;
1115 }
1116 //------------------------------------------------------------------------------
1117