xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 4f694d2f4054fe7ace9e8c0dd8f6d16830dbab04) 
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   CeedTransposeMode lmode;
178   uint64_t state;
179 
180   for (CeedInt i=0; i<numinputfields; i++) {
181     // Get input vector
182     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
183     if (vec == CEED_VECTOR_ACTIVE) {
184       if (skipactive)
185         continue;
186       else
187         vec = invec;
188     }
189 
190     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
191     CeedChk(ierr);
192     // Restrict and Evec
193     if (emode == CEED_EVAL_WEIGHT) { // Skip
194     } else {
195       // Restrict
196       ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
197       // Skip restriction if input is unchanged
198       if (state != impl->inputstate[i] || vec == invec) {
199         ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
200         CeedChk(ierr);
201         ierr = CeedOperatorFieldGetLMode(opinputfields[i], &lmode);
202         CeedChk(ierr);
203         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE,
204                                         lmode, vec, impl->evecs[i],
205                                         request); CeedChk(ierr);
206         impl->inputstate[i] = state;
207       }
208       // Get evec
209       ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
210                                     (const CeedScalar **) &impl->edata[i]);
211       CeedChk(ierr);
212     }
213   }
214   return 0;
215 }
216 
217 //------------------------------------------------------------------------------
218 // Input Basis Action
219 //------------------------------------------------------------------------------
220 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
221     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
222     CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
223   CeedInt ierr;
224   CeedInt dim, elemsize, size;
225   CeedElemRestriction Erestrict;
226   CeedEvalMode emode;
227   CeedBasis basis;
228 
229   for (CeedInt i=0; i<numinputfields; i++) {
230     // Skip active input
231     if (skipactive) {
232       CeedVector vec;
233       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
234       if (vec == CEED_VECTOR_ACTIVE)
235         continue;
236     }
237     // Get elemsize, emode, size
238     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
239     CeedChk(ierr);
240     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
241     CeedChk(ierr);
242     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
243     CeedChk(ierr);
244     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
245     // Basis action
246     switch(emode) {
247     case CEED_EVAL_NONE:
248       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
249                                 CEED_USE_POINTER,
250                                 &impl->edata[i][e*Q*size]); CeedChk(ierr);
251       break;
252     case CEED_EVAL_INTERP:
253       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
254       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
255                                 CEED_USE_POINTER,
256                                 &impl->edata[i][e*elemsize*size]);
257       CeedChk(ierr);
258       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
259                             CEED_EVAL_INTERP, impl->evecsin[i],
260                             impl->qvecsin[i]); CeedChk(ierr);
261       break;
262     case CEED_EVAL_GRAD:
263       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
264       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
265       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
266                                 CEED_USE_POINTER,
267                                 &impl->edata[i][e*elemsize*size/dim]);
268       CeedChk(ierr);
269       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
270                             CEED_EVAL_GRAD, impl->evecsin[i],
271                             impl->qvecsin[i]); CeedChk(ierr);
272       break;
273     case CEED_EVAL_WEIGHT:
274       break;  // No action
275     case CEED_EVAL_DIV:
276     case CEED_EVAL_CURL: {
277       // LCOV_EXCL_START
278       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
279       CeedChk(ierr);
280       Ceed ceed;
281       ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
282       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
283       // LCOV_EXCL_STOP
284       break; // Not implemented
285     }
286     }
287   }
288   return 0;
289 }
290 
291 //------------------------------------------------------------------------------
292 // Output Basis Action
293 //------------------------------------------------------------------------------
294 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
295     CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
296     CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
297     CeedOperator_Ref *impl) {
298   CeedInt ierr;
299   CeedInt dim, elemsize, size;
300   CeedElemRestriction Erestrict;
301   CeedEvalMode emode;
302   CeedBasis basis;
303 
304   for (CeedInt i=0; i<numoutputfields; i++) {
305     // Get elemsize, emode, size
306     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
307     CeedChk(ierr);
308     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
309     CeedChk(ierr);
310     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
311     CeedChk(ierr);
312     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
313     // Basis action
314     switch(emode) {
315     case CEED_EVAL_NONE:
316       break; // No action
317     case CEED_EVAL_INTERP:
318       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
319       CeedChk(ierr);
320       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
321                                 CEED_USE_POINTER,
322                                 &impl->edata[i + numinputfields][e*elemsize*size]);
323       CeedChk(ierr);
324       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
325                             CEED_EVAL_INTERP, impl->qvecsout[i],
326                             impl->evecsout[i]); CeedChk(ierr);
327       break;
328     case CEED_EVAL_GRAD:
329       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
330       CeedChk(ierr);
331       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
332       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
333                                 CEED_USE_POINTER,
334                                 &impl->edata[i + numinputfields][e*elemsize*size/dim]);
335       CeedChk(ierr);
336       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
337                             CEED_EVAL_GRAD, impl->qvecsout[i],
338                             impl->evecsout[i]); CeedChk(ierr);
339       break;
340     case CEED_EVAL_WEIGHT: {
341       // LCOV_EXCL_START
342       Ceed ceed;
343       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
344       return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
345                        "evaluation mode");
346       // LCOV_EXCL_STOP
347       break; // Should not occur
348     }
349     case CEED_EVAL_DIV:
350     case CEED_EVAL_CURL: {
351       // LCOV_EXCL_START
352       Ceed ceed;
353       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
354       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
355       // LCOV_EXCL_STOP
356       break; // Not implemented
357     }
358     }
359   }
360   return 0;
361 }
362 
363 //------------------------------------------------------------------------------
364 // Restore Input Vectors
365 //------------------------------------------------------------------------------
366 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
367     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
368     const bool skipactive, CeedOperator_Ref *impl) {
369   CeedInt ierr;
370   CeedEvalMode emode;
371 
372   for (CeedInt i=0; i<numinputfields; i++) {
373     // Skip active inputs
374     if (skipactive) {
375       CeedVector vec;
376       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
377       if (vec == CEED_VECTOR_ACTIVE)
378         continue;
379     }
380     // Restore input
381     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
382     CeedChk(ierr);
383     if (emode == CEED_EVAL_WEIGHT) { // Skip
384     } else {
385       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
386                                         (const CeedScalar **) &impl->edata[i]);
387       CeedChk(ierr);
388     }
389   }
390   return 0;
391 }
392 
393 //------------------------------------------------------------------------------
394 // Operator Apply
395 //------------------------------------------------------------------------------
396 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
397                                  CeedVector outvec, CeedRequest *request) {
398   int ierr;
399   CeedOperator_Ref *impl;
400   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
401   CeedQFunction qf;
402   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
403   CeedInt Q, numelements, numinputfields, numoutputfields, size;
404   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
405   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
406   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
407   CeedChk(ierr);
408   CeedTransposeMode lmode;
409   CeedOperatorField *opinputfields, *opoutputfields;
410   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
411   CeedChk(ierr);
412   CeedQFunctionField *qfinputfields, *qfoutputfields;
413   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
414   CeedChk(ierr);
415   CeedEvalMode emode;
416   CeedVector vec;
417   CeedElemRestriction Erestrict;
418 
419   // Setup
420   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
421 
422   // Input Evecs and Restriction
423   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
424                                      opinputfields, invec, false, impl,
425                                      request); CeedChk(ierr);
426 
427   // Output Evecs
428   for (CeedInt i=0; i<numoutputfields; i++) {
429     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
430                               &impl->edata[i + numinputfields]); CeedChk(ierr);
431   }
432 
433   // Loop through elements
434   for (CeedInt e=0; e<numelements; e++) {
435     // Output pointers
436     for (CeedInt i=0; i<numoutputfields; i++) {
437       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
438       CeedChk(ierr);
439       if (emode == CEED_EVAL_NONE) {
440         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
441         CeedChk(ierr);
442         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
443                                   CEED_USE_POINTER,
444                                   &impl->edata[i + numinputfields][e*Q*size]);
445         CeedChk(ierr);
446       }
447     }
448 
449     // Input basis apply
450     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
451                                       numinputfields, false, impl);
452     CeedChk(ierr);
453 
454     // Q function
455     if (!impl->identityqf) {
456       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
457       CeedChk(ierr);
458     }
459 
460     // Output basis apply
461     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
462                                        numinputfields, numoutputfields, op, impl);
463     CeedChk(ierr);
464   }
465 
466   // Output restriction
467   for (CeedInt i=0; i<numoutputfields; i++) {
468     // Restore evec
469     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
470                                   &impl->edata[i + numinputfields]);
471     CeedChk(ierr);
472     // Get output vector
473     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
474     // Active
475     if (vec == CEED_VECTOR_ACTIVE)
476       vec = outvec;
477     // Restrict
478     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
479     CeedChk(ierr);
480     ierr = CeedOperatorFieldGetLMode(opoutputfields[i], &lmode); CeedChk(ierr);
481     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
482                                     lmode, impl->evecs[i+impl->numein], vec,
483                                     request); CeedChk(ierr);
484   }
485 
486   // Restore input arrays
487   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
488                                        opinputfields, false, impl);
489   CeedChk(ierr);
490 
491   return 0;
492 }
493 
494 //------------------------------------------------------------------------------
495 // Assemble Linear QFunction
496 //------------------------------------------------------------------------------
497 static int CeedOperatorAssembleLinearQFunction_Ref(CeedOperator op,
498     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
499   int ierr;
500   CeedOperator_Ref *impl;
501   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
502   CeedQFunction qf;
503   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
504   CeedInt Q, numelements, numinputfields, numoutputfields, size;
505   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
506   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
507   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
508   CeedChk(ierr);
509   CeedOperatorField *opinputfields, *opoutputfields;
510   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
511   CeedChk(ierr);
512   CeedQFunctionField *qfinputfields, *qfoutputfields;
513   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
514   CeedChk(ierr);
515   CeedVector vec;
516   CeedInt numactivein = 0, numactiveout = 0;
517   CeedVector *activein = NULL;
518   CeedScalar *a, *tmp;
519   Ceed ceed, ceedparent;
520   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
521   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
522   ceedparent = ceedparent ? ceedparent : ceed;
523 
524   // Setup
525   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
526 
527   // Check for identity
528   if (impl->identityqf)
529     // LCOV_EXCL_START
530     return CeedError(ceed, 1, "Assembling identity qfunctions not supported");
531   // LCOV_EXCL_STOP
532 
533   // Input Evecs and Restriction
534   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
535                                      opinputfields, NULL, true, impl, request);
536   CeedChk(ierr);
537 
538   // Count number of active input fields
539   for (CeedInt i=0; i<numinputfields; i++) {
540     // Get input vector
541     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
542     // Check if active input
543     if (vec == CEED_VECTOR_ACTIVE) {
544       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
545       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
546       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
547       CeedChk(ierr);
548       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
549       for (CeedInt field=0; field<size; field++) {
550         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
551         CeedChk(ierr);
552         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
553                                   CEED_USE_POINTER, &tmp[field*Q]);
554         CeedChk(ierr);
555       }
556       numactivein += size;
557       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
558     }
559   }
560 
561   // Count number of active output fields
562   for (CeedInt i=0; i<numoutputfields; i++) {
563     // Get output vector
564     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
565     // Check if active output
566     if (vec == CEED_VECTOR_ACTIVE) {
567       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
568       numactiveout += size;
569     }
570   }
571 
572   // Check sizes
573   if (!numactivein || !numactiveout)
574     // LCOV_EXCL_START
575     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
576                      "and outputs");
577   // LCOV_EXCL_STOP
578 
579   // Create output restriction
580   ierr = CeedElemRestrictionCreateIdentity(ceedparent, numelements, Q,
581          numelements*Q, numactivein*numactiveout, rstr); CeedChk(ierr);
582   // Create assembled vector
583   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
584                           assembled); CeedChk(ierr);
585   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
586   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
587 
588   // Loop through elements
589   for (CeedInt e=0; e<numelements; e++) {
590     // Input basis apply
591     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
592                                       numinputfields, true, impl);
593     CeedChk(ierr);
594 
595     // Assemble QFunction
596     for (CeedInt in=0; in<numactivein; in++) {
597       // Set Inputs
598       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
599       if (numactivein > 1) {
600         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
601                                   0.0); CeedChk(ierr);
602       }
603       // Set Outputs
604       for (CeedInt out=0; out<numoutputfields; out++) {
605         // Get output vector
606         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
607         CeedChk(ierr);
608         // Check if active output
609         if (vec == CEED_VECTOR_ACTIVE) {
610           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
611                              CEED_USE_POINTER, a); CeedChk(ierr);
612           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
613           CeedChk(ierr);
614           a += size*Q; // Advance the pointer by the size of the output
615         }
616       }
617       // Apply QFunction
618       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
619       CeedChk(ierr);
620     }
621   }
622 
623   // Un-set output Qvecs to prevent accidental overwrite of Assembled
624   for (CeedInt out=0; out<numoutputfields; out++) {
625     // Get output vector
626     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
627     CeedChk(ierr);
628     // Check if active output
629     if (vec == CEED_VECTOR_ACTIVE) {
630       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
631                          NULL); CeedChk(ierr);
632     }
633   }
634 
635   // Restore input arrays
636   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
637                                        opinputfields, true, impl);
638   CeedChk(ierr);
639 
640   // Restore output
641   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
642 
643   // Cleanup
644   for (CeedInt i=0; i<numactivein; i++) {
645     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
646   }
647   ierr = CeedFree(&activein); CeedChk(ierr);
648 
649   return 0;
650 }
651 
652 //------------------------------------------------------------------------------
653 // Get Basis Emode Pointer
654 //------------------------------------------------------------------------------
655 static inline void CeedOperatorGetBasisPointer_Ref(CeedScalar **basisptr,
656     CeedEvalMode emode, CeedScalar *identity, CeedScalar *interp,
657     CeedScalar *grad) {
658   switch (emode) {
659   case CEED_EVAL_NONE:
660     *basisptr = identity;
661     break;
662   case CEED_EVAL_INTERP:
663     *basisptr = interp;
664     break;
665   case CEED_EVAL_GRAD:
666     *basisptr = grad;
667     break;
668   case CEED_EVAL_WEIGHT:
669   case CEED_EVAL_DIV:
670   case CEED_EVAL_CURL:
671     break; // Caught by QF Assembly
672   }
673 }
674 
675 //------------------------------------------------------------------------------
676 // Assemble Linear Diagonal
677 //------------------------------------------------------------------------------
678 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
679     CeedVector *assembled, CeedRequest *request) {
680   int ierr;
681 
682   // Assemble QFunction
683   CeedQFunction qf;
684   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
685   CeedInt numinputfields, numoutputfields;
686   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
687   CeedChk(ierr);
688   CeedVector assembledqf;
689   CeedElemRestriction rstr;
690   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
691   CeedChk(ierr);
692   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
693   CeedScalar maxnorm = 0;
694   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
695 
696   // Determine active input basis
697   CeedOperatorField *opfields;
698   CeedQFunctionField *qffields;
699   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
700   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
701   CeedInt numemodein = 0, ncomp, dim = 1;
702   CeedEvalMode *emodein = NULL;
703   CeedBasis basisin = NULL;
704   CeedElemRestriction rstrin = NULL;
705   for (CeedInt i=0; i<numinputfields; i++) {
706     CeedVector vec;
707     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
708     if (vec == CEED_VECTOR_ACTIVE) {
709       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
710       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
711       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
712       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
713       CeedChk(ierr);
714       CeedEvalMode emode;
715       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
716       CeedChk(ierr);
717       switch (emode) {
718       case CEED_EVAL_NONE:
719       case CEED_EVAL_INTERP:
720         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
721         emodein[numemodein] = emode;
722         numemodein += 1;
723         break;
724       case CEED_EVAL_GRAD:
725         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
726         for (CeedInt d=0; d<dim; d++)
727           emodein[numemodein+d] = emode;
728         numemodein += dim;
729         break;
730       case CEED_EVAL_WEIGHT:
731       case CEED_EVAL_DIV:
732       case CEED_EVAL_CURL:
733         break; // Caught by QF Assembly
734       }
735     }
736   }
737 
738   // Determine active output basis
739   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
740   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
741   CeedInt numemodeout = 0;
742   CeedEvalMode *emodeout = NULL;
743   CeedBasis basisout = NULL;
744   CeedElemRestriction rstrout = NULL;
745   CeedTransposeMode lmodeout = CEED_NOTRANSPOSE;
746   for (CeedInt i=0; i<numoutputfields; i++) {
747     CeedVector vec;
748     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
749     if (vec == CEED_VECTOR_ACTIVE) {
750       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
751       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
752       CeedChk(ierr);
753       ierr = CeedOperatorFieldGetLMode(opfields[i], &lmodeout); CeedChk(ierr);
754       CeedEvalMode emode;
755       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
756       switch (emode) {
757       case CEED_EVAL_NONE:
758       case CEED_EVAL_INTERP:
759         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
760         emodeout[numemodeout] = emode;
761         numemodeout += 1;
762         break;
763       case CEED_EVAL_GRAD:
764         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
765         for (CeedInt d=0; d<dim; d++)
766           emodeout[numemodeout+d] = emode;
767         numemodeout += dim;
768         break;
769       case CEED_EVAL_WEIGHT:
770       case CEED_EVAL_DIV:
771       case CEED_EVAL_CURL:
772         break; // Caught by QF Assembly
773       }
774     }
775   }
776 
777   // Create diagonal vector
778   CeedVector elemdiag;
779   ierr = CeedElemRestrictionCreateVector(rstrin, assembled, &elemdiag);
780   CeedChk(ierr);
781 
782   // Assemble element operator diagonals
783   CeedScalar *elemdiagarray, *assembledqfarray;
784   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
785   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
786   CeedChk(ierr);
787   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
788   CeedChk(ierr);
789   CeedInt nelem, nnodes, nqpts;
790   ierr = CeedElemRestrictionGetNumElements(rstrin, &nelem); CeedChk(ierr);
791   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
792   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
793   // Basis matrices
794   CeedScalar *identity = NULL, *interpin, *interpout, *gradin, *gradout;
795   bool evalNone = false;
796   for (CeedInt i=0; i<numemodein; i++)
797     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
798   for (CeedInt i=0; i<numemodeout; i++)
799     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
800   if (evalNone) {
801     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
802     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
803       identity[i*nnodes+i] = 1.0;
804   }
805   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
806   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
807   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
808   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
809   // Compute the diagonal of B^T D B
810   // Each element
811   for (CeedInt e=0; e<nelem; e++) {
812     CeedInt dout = -1;
813     // Each basis eval mode pair
814     for (CeedInt eout=0; eout<numemodeout; eout++) {
815       CeedScalar *bt = NULL;
816       if (emodeout[eout] == CEED_EVAL_GRAD)
817         dout += 1;
818       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
819                                       &gradout[dout*nqpts*nnodes]);
820       CeedInt din = -1;
821       for (CeedInt ein=0; ein<numemodein; ein++) {
822         CeedScalar *b = NULL;
823         if (emodein[ein] == CEED_EVAL_GRAD)
824           din += 1;
825         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
826                                         &gradin[din*nqpts*nnodes]);
827         // Each component pair
828         for (CeedInt cout=0; cout<ncomp; cout++)
829           for (CeedInt cin=0; cin<ncomp; cin++)
830             // Each qpoint/node pair
831             for (CeedInt q=0; q<nqpts; q++) {
832               const CeedScalar qfvalue =
833                 assembledqfarray[((((e*numemodein+ein)*ncomp+cin)*
834                                    numemodeout+eout)*ncomp+cout)*nqpts+q];
835               if (fabs(qfvalue) > maxnorm*1e-12)
836                 for (CeedInt n=0; n<nnodes; n++)
837                   elemdiagarray[(e*ncomp+cout)*nnodes+n] += bt[q*nnodes+n] *
838                       qfvalue * b[q*nnodes+n];
839             }
840       }
841     }
842   }
843   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
844   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
845 
846   // Assemble local operator diagonal
847   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
848   ierr = CeedElemRestrictionApply(rstrout, CEED_TRANSPOSE, lmodeout, elemdiag,
849                                   *assembled, request); CeedChk(ierr);
850 
851   // Cleanup
852   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
853   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
854   ierr = CeedFree(&emodein); CeedChk(ierr);
855   ierr = CeedFree(&emodeout); CeedChk(ierr);
856   ierr = CeedFree(&identity); CeedChk(ierr);
857 
858   return 0;
859 }
860 
861 //------------------------------------------------------------------------------
862 // Create FDM Element Inverse
863 //------------------------------------------------------------------------------
864 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
865     CeedOperator *fdminv,
866     CeedRequest *request) {
867   int ierr;
868   Ceed ceed, ceedparent;
869   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
870   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
871   ceedparent = ceedparent ? ceedparent : ceed;
872   CeedQFunction qf;
873   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
874 
875   // Determine active input basis
876   bool interp = false, grad = false;
877   CeedBasis basis = NULL;
878   CeedElemRestriction rstr = NULL;
879   CeedOperatorField *opfields;
880   CeedQFunctionField *qffields;
881   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
882   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
883   CeedInt numinputfields;
884   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
885   for (CeedInt i=0; i<numinputfields; i++) {
886     CeedVector vec;
887     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
888     if (vec == CEED_VECTOR_ACTIVE) {
889       CeedEvalMode emode;
890       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
891       interp = interp || emode == CEED_EVAL_INTERP;
892       grad = grad || emode == CEED_EVAL_GRAD;
893       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
894       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
895       CeedChk(ierr);
896     }
897   }
898   if (!basis)
899     // LCOV_EXCL_START
900     return CeedError(ceed, 1, "No active field set");
901   // LCOV_EXCL_STOP
902   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, nnodes = 1;
903   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
904   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
905   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
906   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
907   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
908   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
909   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
910   ierr = CeedElemRestrictionGetNumNodes(rstr, &nnodes); CeedChk(ierr);
911 
912   // Build and diagonalize 1D Mass and Laplacian
913   bool tensorbasis;
914   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
915   if (!tensorbasis)
916     // LCOV_EXCL_START
917     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
918                      "bases");
919   // LCOV_EXCL_STOP
920   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
921   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
922   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
923   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
924   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
925   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
926   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
927   // -- Mass
928   CeedScalar *interp1d, *grad1d, *qweight1d;
929   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
930   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
931   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
932   for (CeedInt i=0; i<Q1d; i++)
933     for (CeedInt j=0; j<P1d; j++)
934       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
935   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
936                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
937   CeedChk(ierr);
938   // -- Laplacian
939   for (CeedInt i=0; i<Q1d; i++)
940     for (CeedInt j=0; j<P1d; j++)
941       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
942   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
943                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
944   CeedChk(ierr);
945   // -- Diagonalize
946   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
947   CeedChk(ierr);
948   ierr = CeedFree(&work); CeedChk(ierr);
949   ierr = CeedFree(&mass); CeedChk(ierr);
950   ierr = CeedFree(&laplace); CeedChk(ierr);
951   for (CeedInt i=0; i<P1d; i++)
952     for (CeedInt j=0; j<P1d; j++)
953       x2[i+j*P1d] = x[j+i*P1d];
954   ierr = CeedFree(&x); CeedChk(ierr);
955 
956   // Assemble QFunction
957   CeedVector assembled;
958   CeedElemRestriction rstr_qf;
959   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
960           request); CeedChk(ierr);
961   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
962   CeedScalar maxnorm = 0;
963   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
964 
965   // Calculate element averages
966   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
967   CeedScalar *elemavg;
968   const CeedScalar *assembledarray, *qweightsarray;
969   CeedVector qweights;
970   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
971   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
972                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
973   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
974   CeedChk(ierr);
975   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
976   CeedChk(ierr);
977   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
978   for (CeedInt e=0; e<nelem; e++) {
979     CeedInt count = 0;
980     for (CeedInt q=0; q<nqpts; q++)
981       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
982         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
983                                                                   i*nqpts + q]) > maxnorm*1e-12) {
984           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
985                                        i*nqpts + q] / qweightsarray[q];
986           count++;
987         }
988     if (count)
989       elemavg[e] /= count;
990   }
991   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
992   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
993   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
994   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
995 
996   // Build FDM diagonal
997   CeedVector qdata;
998   CeedScalar *qdataarray;
999   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*nnodes, &qdata); CeedChk(ierr);
1000   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
1001   CeedChk(ierr);
1002   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
1003   for (CeedInt e=0; e<nelem; e++)
1004     for (CeedInt c=0; c<ncomp; c++)
1005       for (CeedInt n=0; n<nnodes; n++) {
1006         if (interp)
1007           qdataarray[(e*ncomp+c)*nnodes+n] = 1;
1008         if (grad)
1009           for (CeedInt d=0; d<dim; d++) {
1010             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1011             qdataarray[(e*ncomp+c)*nnodes+n] += lambda[i];
1012           }
1013         qdataarray[(e*ncomp+c)*nnodes+n] = 1 / (elemavg[e] *
1014                                                 qdataarray[(e*ncomp+c)*nnodes+n]);
1015       }
1016   ierr = CeedFree(&elemavg); CeedChk(ierr);
1017   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1018 
1019   // Setup FDM operator
1020   // -- Basis
1021   CeedBasis fdm_basis;
1022   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1023   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1024   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1025   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1026   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1027                                  graddummy, qrefdummy, qweightdummy,
1028                                  &fdm_basis); CeedChk(ierr);
1029   ierr = CeedFree(&graddummy); CeedChk(ierr);
1030   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1031   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1032   ierr = CeedFree(&x2); CeedChk(ierr);
1033   ierr = CeedFree(&lambda); CeedChk(ierr);
1034 
1035   // -- Restriction
1036   CeedElemRestriction rstr_i;
1037   ierr = CeedElemRestrictionCreateIdentity(ceedparent, nelem, nnodes,
1038          nnodes*nelem, ncomp, &rstr_i); CeedChk(ierr);
1039   // -- QFunction
1040   CeedQFunction mass_qf;
1041   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1042   CeedChk(ierr);
1043   // -- Operator
1044   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1045   CeedChk(ierr);
1046   CeedOperatorSetField(*fdminv, "u", rstr_i, CEED_NOTRANSPOSE,
1047                        fdm_basis, CEED_VECTOR_ACTIVE); CeedChk(ierr);
1048   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_NOTRANSPOSE,
1049                        CEED_BASIS_COLLOCATED, qdata); CeedChk(ierr);
1050   CeedOperatorSetField(*fdminv, "v", rstr_i, CEED_NOTRANSPOSE,
1051                        fdm_basis, CEED_VECTOR_ACTIVE); CeedChk(ierr);
1052 
1053   // Cleanup
1054   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1055   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1056   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1057   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1058 
1059   return 0;
1060 }
1061 
1062 //------------------------------------------------------------------------------
1063 // Operator Destroy
1064 //------------------------------------------------------------------------------
1065 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1066   int ierr;
1067   CeedOperator_Ref *impl;
1068   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1069 
1070   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1071     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1072   }
1073   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1074   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1075   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1076 
1077   for (CeedInt i=0; i<impl->numein; i++) {
1078     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1079     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1080   }
1081   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1082   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1083 
1084   for (CeedInt i=0; i<impl->numeout; i++) {
1085     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1086     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1087   }
1088   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1089   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1090 
1091   ierr = CeedFree(&impl); CeedChk(ierr);
1092   return 0;
1093 }
1094 
1095 //------------------------------------------------------------------------------
1096 // Operator Create
1097 //------------------------------------------------------------------------------
1098 int CeedOperatorCreate_Ref(CeedOperator op) {
1099   int ierr;
1100   Ceed ceed;
1101   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1102   CeedOperator_Ref *impl;
1103 
1104   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1105   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1106 
1107   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1108                                 CeedOperatorAssembleLinearQFunction_Ref);
1109   CeedChk(ierr);
1110   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1111                                 CeedOperatorAssembleLinearDiagonal_Ref);
1112   CeedChk(ierr);
1113   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1114                                 CeedOperatorCreateFDMElementInverse_Ref);
1115   CeedChk(ierr);
1116   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1117                                 CeedOperatorApply_Ref); CeedChk(ierr);
1118   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1119                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1120   return 0;
1121 }
1122 //------------------------------------------------------------------------------
1123