xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 311baa061865f9a4db5f02dcb29af77abc64aec0) 
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 = CeedOperatorIsSetupDone(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 = CeedQFunctionIsIdentity(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       // LCOV_EXCL_STOP
280     }
281     }
282   }
283   return 0;
284 }
285 
286 //------------------------------------------------------------------------------
287 // Output Basis Action
288 //------------------------------------------------------------------------------
289 static inline int CeedOperatorOutputBasis_Ref(CeedInt e, CeedInt Q,
290     CeedQFunctionField *qfoutputfields, CeedOperatorField *opoutputfields,
291     CeedInt numinputfields, CeedInt numoutputfields, CeedOperator op,
292     CeedOperator_Ref *impl) {
293   CeedInt ierr;
294   CeedInt dim, elemsize, size;
295   CeedElemRestriction Erestrict;
296   CeedEvalMode emode;
297   CeedBasis basis;
298 
299   for (CeedInt i=0; i<numoutputfields; i++) {
300     // Get elemsize, emode, size
301     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
302     CeedChk(ierr);
303     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
304     CeedChk(ierr);
305     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
306     CeedChk(ierr);
307     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
308     // Basis action
309     switch(emode) {
310     case CEED_EVAL_NONE:
311       break; // No action
312     case CEED_EVAL_INTERP:
313       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
314       CeedChk(ierr);
315       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
316                                 CEED_USE_POINTER,
317                                 &impl->edata[i + numinputfields][e*elemsize*size]);
318       CeedChk(ierr);
319       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
320                             CEED_EVAL_INTERP, impl->qvecsout[i],
321                             impl->evecsout[i]); CeedChk(ierr);
322       break;
323     case CEED_EVAL_GRAD:
324       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
325       CeedChk(ierr);
326       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
327       ierr = CeedVectorSetArray(impl->evecsout[i], CEED_MEM_HOST,
328                                 CEED_USE_POINTER,
329                                 &impl->edata[i + numinputfields][e*elemsize*size/dim]);
330       CeedChk(ierr);
331       ierr = CeedBasisApply(basis, 1, CEED_TRANSPOSE,
332                             CEED_EVAL_GRAD, impl->qvecsout[i],
333                             impl->evecsout[i]); CeedChk(ierr);
334       break;
335     // LCOV_EXCL_START
336     case CEED_EVAL_WEIGHT: {
337       Ceed ceed;
338       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
339       return CeedError(ceed, 1, "CEED_EVAL_WEIGHT cannot be an output "
340                        "evaluation mode");
341     }
342     case CEED_EVAL_DIV:
343     case CEED_EVAL_CURL: {
344       Ceed ceed;
345       ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
346       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
347       // LCOV_EXCL_STOP
348     }
349     }
350   }
351   return 0;
352 }
353 
354 //------------------------------------------------------------------------------
355 // Restore Input Vectors
356 //------------------------------------------------------------------------------
357 static inline int CeedOperatorRestoreInputs_Ref(CeedInt numinputfields,
358     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
359     const bool skipactive, CeedOperator_Ref *impl) {
360   CeedInt ierr;
361   CeedEvalMode emode;
362 
363   for (CeedInt i=0; i<numinputfields; i++) {
364     // Skip active inputs
365     if (skipactive) {
366       CeedVector vec;
367       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
368       if (vec == CEED_VECTOR_ACTIVE)
369         continue;
370     }
371     // Restore input
372     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
373     CeedChk(ierr);
374     if (emode == CEED_EVAL_WEIGHT) { // Skip
375     } else {
376       ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
377                                         (const CeedScalar **) &impl->edata[i]);
378       CeedChk(ierr);
379     }
380   }
381   return 0;
382 }
383 
384 //------------------------------------------------------------------------------
385 // Operator Apply
386 //------------------------------------------------------------------------------
387 static int CeedOperatorApply_Ref(CeedOperator op, CeedVector invec,
388                                  CeedVector outvec, CeedRequest *request) {
389   int ierr;
390   CeedOperator_Ref *impl;
391   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
392   CeedQFunction qf;
393   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
394   CeedInt Q, numelements, numinputfields, numoutputfields, size;
395   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
396   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
397   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
398   CeedChk(ierr);
399   CeedOperatorField *opinputfields, *opoutputfields;
400   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
401   CeedChk(ierr);
402   CeedQFunctionField *qfinputfields, *qfoutputfields;
403   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
404   CeedChk(ierr);
405   CeedEvalMode emode;
406   CeedVector vec;
407   CeedElemRestriction Erestrict;
408 
409   // Setup
410   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
411 
412   // Input Evecs and Restriction
413   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
414                                      opinputfields, invec, false, impl,
415                                      request); CeedChk(ierr);
416 
417   // Output Evecs
418   for (CeedInt i=0; i<numoutputfields; i++) {
419     ierr = CeedVectorGetArray(impl->evecs[i+impl->numein], CEED_MEM_HOST,
420                               &impl->edata[i + numinputfields]); CeedChk(ierr);
421   }
422 
423   // Loop through elements
424   for (CeedInt e=0; e<numelements; e++) {
425     // Output pointers
426     for (CeedInt i=0; i<numoutputfields; i++) {
427       ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
428       CeedChk(ierr);
429       if (emode == CEED_EVAL_NONE) {
430         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
431         CeedChk(ierr);
432         ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_HOST,
433                                   CEED_USE_POINTER,
434                                   &impl->edata[i + numinputfields][e*Q*size]);
435         CeedChk(ierr);
436       }
437     }
438 
439     // Input basis apply
440     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
441                                       numinputfields, false, impl);
442     CeedChk(ierr);
443 
444     // Q function
445     if (!impl->identityqf) {
446       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
447       CeedChk(ierr);
448     }
449 
450     // Output basis apply
451     ierr = CeedOperatorOutputBasis_Ref(e, Q, qfoutputfields, opoutputfields,
452                                        numinputfields, numoutputfields, op, impl);
453     CeedChk(ierr);
454   }
455 
456   // Output restriction
457   for (CeedInt i=0; i<numoutputfields; i++) {
458     // Restore evec
459     ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
460                                   &impl->edata[i + numinputfields]);
461     CeedChk(ierr);
462     // Get output vector
463     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
464     // Active
465     if (vec == CEED_VECTOR_ACTIVE)
466       vec = outvec;
467     // Restrict
468     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
469     CeedChk(ierr);
470     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
471                                     impl->evecs[i+impl->numein], vec, request);
472     CeedChk(ierr);
473   }
474 
475   // Restore input arrays
476   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
477                                        opinputfields, false, impl);
478   CeedChk(ierr);
479 
480   return 0;
481 }
482 
483 //------------------------------------------------------------------------------
484 // Assemble Linear QFunction
485 //------------------------------------------------------------------------------
486 static int CeedOperatorLinearAssembleQFunction_Ref(CeedOperator op,
487     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
488   int ierr;
489   CeedOperator_Ref *impl;
490   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
491   CeedQFunction qf;
492   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
493   CeedInt Q, numelements, numinputfields, numoutputfields, size;
494   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
495   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChk(ierr);
496   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
497   CeedChk(ierr);
498   CeedOperatorField *opinputfields, *opoutputfields;
499   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
500   CeedChk(ierr);
501   CeedQFunctionField *qfinputfields, *qfoutputfields;
502   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
503   CeedChk(ierr);
504   CeedVector vec;
505   CeedInt numactivein = 0, numactiveout = 0;
506   CeedVector *activein = NULL;
507   CeedScalar *a, *tmp;
508   Ceed ceed, ceedparent;
509   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
510   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
511   ceedparent = ceedparent ? ceedparent : ceed;
512 
513   // Setup
514   ierr = CeedOperatorSetup_Ref(op); CeedChk(ierr);
515 
516   // Check for identity
517   if (impl->identityqf)
518     // LCOV_EXCL_START
519     return CeedError(ceed, 1, "Assembling identity QFunctions not supported");
520   // LCOV_EXCL_STOP
521 
522   // Input Evecs and Restriction
523   ierr = CeedOperatorSetupInputs_Ref(numinputfields, qfinputfields,
524                                      opinputfields, NULL, true, impl, request);
525   CeedChk(ierr);
526 
527   // Count number of active input fields
528   for (CeedInt i=0; i<numinputfields; i++) {
529     // Get input vector
530     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
531     // Check if active input
532     if (vec == CEED_VECTOR_ACTIVE) {
533       ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
534       ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChk(ierr);
535       ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_HOST, &tmp);
536       CeedChk(ierr);
537       ierr = CeedRealloc(numactivein + size, &activein); CeedChk(ierr);
538       for (CeedInt field=0; field<size; field++) {
539         ierr = CeedVectorCreate(ceed, Q, &activein[numactivein+field]);
540         CeedChk(ierr);
541         ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_HOST,
542                                   CEED_USE_POINTER, &tmp[field*Q]);
543         CeedChk(ierr);
544       }
545       numactivein += size;
546       ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChk(ierr);
547     }
548   }
549 
550   // Count number of active output fields
551   for (CeedInt i=0; i<numoutputfields; i++) {
552     // Get output vector
553     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec); CeedChk(ierr);
554     // Check if active output
555     if (vec == CEED_VECTOR_ACTIVE) {
556       ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size); CeedChk(ierr);
557       numactiveout += size;
558     }
559   }
560 
561   // Check sizes
562   if (!numactivein || !numactiveout)
563     // LCOV_EXCL_START
564     return CeedError(ceed, 1, "Cannot assemble QFunction without active inputs "
565                      "and outputs");
566   // LCOV_EXCL_STOP
567 
568   // Create output restriction
569   CeedInt strides[3] = {1, Q, numactivein*numactiveout*Q}; /* *NOPAD* */
570   ierr = CeedElemRestrictionCreateStrided(ceedparent, numelements, Q,
571                                           numactivein*numactiveout,
572                                           numactivein*numactiveout*numelements*Q,
573                                           strides, rstr); CeedChk(ierr);
574   // Create assembled vector
575   ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
576                           assembled); CeedChk(ierr);
577   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
578   ierr = CeedVectorGetArray(*assembled, CEED_MEM_HOST, &a); CeedChk(ierr);
579 
580   // Loop through elements
581   for (CeedInt e=0; e<numelements; e++) {
582     // Input basis apply
583     ierr = CeedOperatorInputBasis_Ref(e, Q, qfinputfields, opinputfields,
584                                       numinputfields, true, impl);
585     CeedChk(ierr);
586 
587     // Assemble QFunction
588     for (CeedInt in=0; in<numactivein; in++) {
589       // Set Inputs
590       ierr = CeedVectorSetValue(activein[in], 1.0); CeedChk(ierr);
591       if (numactivein > 1) {
592         ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
593                                   0.0); CeedChk(ierr);
594       }
595       // Set Outputs
596       for (CeedInt out=0; out<numoutputfields; out++) {
597         // Get output vector
598         ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
599         CeedChk(ierr);
600         // Check if active output
601         if (vec == CEED_VECTOR_ACTIVE) {
602           CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST,
603                              CEED_USE_POINTER, a); CeedChk(ierr);
604           ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
605           CeedChk(ierr);
606           a += size*Q; // Advance the pointer by the size of the output
607         }
608       }
609       // Apply QFunction
610       ierr = CeedQFunctionApply(qf, Q, impl->qvecsin, impl->qvecsout);
611       CeedChk(ierr);
612     }
613   }
614 
615   // Un-set output Qvecs to prevent accidental overwrite of Assembled
616   for (CeedInt out=0; out<numoutputfields; out++) {
617     // Get output vector
618     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
619     CeedChk(ierr);
620     // Check if active output
621     if (vec == CEED_VECTOR_ACTIVE) {
622       CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_HOST, CEED_COPY_VALUES,
623                          NULL); CeedChk(ierr);
624     }
625   }
626 
627   // Restore input arrays
628   ierr = CeedOperatorRestoreInputs_Ref(numinputfields, qfinputfields,
629                                        opinputfields, true, impl);
630   CeedChk(ierr);
631 
632   // Restore output
633   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChk(ierr);
634 
635   // Cleanup
636   for (CeedInt i=0; i<numactivein; i++) {
637     ierr = CeedVectorDestroy(&activein[i]); CeedChk(ierr);
638   }
639   ierr = CeedFree(&activein); CeedChk(ierr);
640 
641   return 0;
642 }
643 
644 //------------------------------------------------------------------------------
645 // Get Basis Emode Pointer
646 //------------------------------------------------------------------------------
647 static inline void CeedOperatorGetBasisPointer_Ref(const CeedScalar **basisptr,
648     CeedEvalMode emode, const CeedScalar *identity, const CeedScalar *interp,
649     const CeedScalar *grad) {
650   switch (emode) {
651   case CEED_EVAL_NONE:
652     *basisptr = identity;
653     break;
654   case CEED_EVAL_INTERP:
655     *basisptr = interp;
656     break;
657   case CEED_EVAL_GRAD:
658     *basisptr = grad;
659     break;
660   case CEED_EVAL_WEIGHT:
661   case CEED_EVAL_DIV:
662   case CEED_EVAL_CURL:
663     break; // Caught by QF Assembly
664   }
665 }
666 
667 //------------------------------------------------------------------------------
668 // Create point block restriction
669 //------------------------------------------------------------------------------
670 static int CreatePBRestriction(CeedElemRestriction rstr,
671                                CeedElemRestriction *pbRstr) {
672   int ierr;
673   Ceed ceed;
674   ierr = CeedElemRestrictionGetCeed(rstr, &ceed); CeedChk(ierr);
675   const CeedInt *offsets;
676   ierr = CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets);
677   CeedChk(ierr);
678 
679   // Expand offsets
680   CeedInt nelem, ncomp, elemsize, compstride, max = 1, *pbOffsets;
681   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
682   ierr = CeedElemRestrictionGetNumComponents(rstr, &ncomp); CeedChk(ierr);
683   ierr = CeedElemRestrictionGetElementSize(rstr, &elemsize); CeedChk(ierr);
684   ierr = CeedElemRestrictionGetCompStride(rstr, &compstride); CeedChk(ierr);
685   CeedInt shift = ncomp;
686   if (compstride != 1)
687     shift *= ncomp;
688   ierr = CeedCalloc(nelem*elemsize, &pbOffsets); CeedChk(ierr);
689   for (CeedInt i = 0; i < nelem*elemsize; i++) {
690     pbOffsets[i] = offsets[i]*shift;
691     if (pbOffsets[i] > max)
692       max = pbOffsets[i];
693   }
694 
695   // Create new restriction
696   ierr = CeedElemRestrictionCreate(ceed, nelem, elemsize, ncomp*ncomp, 1,
697                                    max + ncomp*ncomp, CEED_MEM_HOST,
698                                    CEED_OWN_POINTER, pbOffsets, pbRstr);
699   CeedChk(ierr);
700 
701   // Cleanup
702   ierr = CeedElemRestrictionRestoreOffsets(rstr, &offsets); CeedChk(ierr);
703 
704   return 0;
705 }
706 
707 //------------------------------------------------------------------------------
708 // Assemble diagonal common code
709 //------------------------------------------------------------------------------
710 static inline int CeedOperatorAssembleDiagonalCore_Ref(CeedOperator op,
711     CeedVector *assembled, CeedRequest *request, const bool pointBlock,
712     const bool createVector) {
713   int ierr;
714   Ceed ceed;
715   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
716 
717   // Assemble QFunction
718   CeedQFunction qf;
719   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
720   CeedInt numinputfields, numoutputfields;
721   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
722   CeedChk(ierr);
723   CeedVector assembledqf;
724   CeedElemRestriction rstr;
725   ierr = CeedOperatorLinearAssembleQFunction(op,  &assembledqf, &rstr, request);
726   CeedChk(ierr);
727   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
728   CeedScalar maxnorm = 0;
729   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
730 
731   // Determine active input basis
732   CeedOperatorField *opfields;
733   CeedQFunctionField *qffields;
734   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
735   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
736   CeedInt numemodein = 0, ncomp, dim = 1;
737   CeedEvalMode *emodein = NULL;
738   CeedBasis basisin = NULL;
739   CeedElemRestriction rstrin = NULL;
740   for (CeedInt i=0; i<numinputfields; i++) {
741     CeedVector vec;
742     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
743     if (vec == CEED_VECTOR_ACTIVE) {
744       CeedElemRestriction rstr;
745       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
746       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
747       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
748       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
749       CeedChk(ierr);
750       if (rstrin && rstrin != rstr)
751         // LCOV_EXCL_START
752         return CeedError(ceed, 1,
753                          "Multi-field non-composite operator diagonal assembly not supported");
754       // LCOV_EXCL_STOP
755       rstrin = rstr;
756       CeedEvalMode emode;
757       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
758       CeedChk(ierr);
759       switch (emode) {
760       case CEED_EVAL_NONE:
761       case CEED_EVAL_INTERP:
762         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
763         emodein[numemodein] = emode;
764         numemodein += 1;
765         break;
766       case CEED_EVAL_GRAD:
767         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
768         for (CeedInt d=0; d<dim; d++)
769           emodein[numemodein+d] = emode;
770         numemodein += dim;
771         break;
772       case CEED_EVAL_WEIGHT:
773       case CEED_EVAL_DIV:
774       case CEED_EVAL_CURL:
775         break; // Caught by QF Assembly
776       }
777     }
778   }
779 
780   // Determine active output basis
781   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
782   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
783   CeedInt numemodeout = 0;
784   CeedEvalMode *emodeout = NULL;
785   CeedBasis basisout = NULL;
786   CeedElemRestriction rstrout = NULL;
787   for (CeedInt i=0; i<numoutputfields; i++) {
788     CeedVector vec;
789     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
790     if (vec == CEED_VECTOR_ACTIVE) {
791       CeedElemRestriction rstr;
792       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
793       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
794       CeedChk(ierr);
795       if (rstrout && rstrout != rstr)
796         // LCOV_EXCL_START
797         return CeedError(ceed, 1,
798                          "Multi-field non-composite operator diagonal assembly not supported");
799       // LCOV_EXCL_STOP
800       rstrout = rstr;
801       CeedEvalMode emode;
802       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
803       switch (emode) {
804       case CEED_EVAL_NONE:
805       case CEED_EVAL_INTERP:
806         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
807         emodeout[numemodeout] = emode;
808         numemodeout += 1;
809         break;
810       case CEED_EVAL_GRAD:
811         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
812         for (CeedInt d=0; d<dim; d++)
813           emodeout[numemodeout+d] = emode;
814         numemodeout += dim;
815         break;
816       case CEED_EVAL_WEIGHT:
817       case CEED_EVAL_DIV:
818       case CEED_EVAL_CURL:
819         break; // Caught by QF Assembly
820       }
821     }
822   }
823 
824   // Assemble point-block diagonal restriction, if needed
825   CeedElemRestriction diagrstr = rstrout;
826   if (pointBlock) {
827     ierr = CreatePBRestriction(rstrout, &diagrstr); CeedChk(ierr);
828   }
829 
830   // Create diagonal vector
831   CeedVector elemdiag;
832   ierr = CeedElemRestrictionCreateVector(diagrstr, NULL, &elemdiag);
833   CeedChk(ierr);
834   if (createVector) {
835     ierr = CeedElemRestrictionCreateVector(diagrstr, assembled, NULL);
836     CeedChk(ierr);
837   }
838 
839   // Assemble element operator diagonals
840   CeedScalar *elemdiagarray, *assembledqfarray;
841   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
842   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
843   CeedChk(ierr);
844   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
845   CeedChk(ierr);
846   CeedInt nelem, nnodes, nqpts;
847   ierr = CeedElemRestrictionGetNumElements(diagrstr, &nelem); CeedChk(ierr);
848   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
849   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
850   // Basis matrices
851   const CeedScalar *interpin, *interpout, *gradin, *gradout;
852   CeedScalar *identity = NULL;
853   bool evalNone = false;
854   for (CeedInt i=0; i<numemodein; i++)
855     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
856   for (CeedInt i=0; i<numemodeout; i++)
857     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
858   if (evalNone) {
859     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
860     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
861       identity[i*nnodes+i] = 1.0;
862   }
863   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
864   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
865   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
866   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
867   // Compute the diagonal of B^T D B
868   // Each element
869   for (CeedInt e=0; e<nelem; e++) {
870     CeedInt dout = -1;
871     // Each basis eval mode pair
872     for (CeedInt eout=0; eout<numemodeout; eout++) {
873       const CeedScalar *bt = NULL;
874       if (emodeout[eout] == CEED_EVAL_GRAD)
875         dout += 1;
876       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
877                                       &gradout[dout*nqpts*nnodes]);
878       CeedInt din = -1;
879       for (CeedInt ein=0; ein<numemodein; ein++) {
880         const CeedScalar *b = NULL;
881         if (emodein[ein] == CEED_EVAL_GRAD)
882           din += 1;
883         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
884                                         &gradin[din*nqpts*nnodes]);
885         // Each component
886         for (CeedInt compOut=0; compOut<ncomp; compOut++)
887           // Each qpoint/node pair
888           for (CeedInt q=0; q<nqpts; q++)
889             if (pointBlock) {
890               // Point Block Diagonal
891               for (CeedInt compIn=0; compIn<ncomp; compIn++) {
892                 const CeedScalar qfvalue =
893                   assembledqfarray[((((e*numemodein+ein)*ncomp+compIn)*
894                                      numemodeout+eout)*ncomp+compOut)*nqpts+q];
895                 if (fabs(qfvalue) > maxnorm*1e-12)
896                   for (CeedInt n=0; n<nnodes; n++)
897                     elemdiagarray[((e*ncomp+compOut)*ncomp+compIn)*nnodes+n] +=
898                       bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
899               }
900             } else {
901               // Diagonal Only
902               const CeedScalar qfvalue =
903                 assembledqfarray[((((e*numemodein+ein)*ncomp+compOut)*
904                                    numemodeout+eout)*ncomp+compOut)*nqpts+q];
905               if (fabs(qfvalue) > maxnorm*1e-12)
906                 for (CeedInt n=0; n<nnodes; n++)
907                   elemdiagarray[(e*ncomp+compOut)*nnodes+n] +=
908                     bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
909             }
910       }
911     }
912   }
913   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
914   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
915 
916   // Assemble local operator diagonal
917   if (createVector) {
918     ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
919   }
920   ierr = CeedElemRestrictionApply(diagrstr, CEED_TRANSPOSE, elemdiag,
921                                   *assembled, request); CeedChk(ierr);
922 
923   // Cleanup
924   if (pointBlock) {
925     ierr = CeedElemRestrictionDestroy(&diagrstr); CeedChk(ierr);
926   }
927   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
928   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
929   ierr = CeedFree(&emodein); CeedChk(ierr);
930   ierr = CeedFree(&emodeout); CeedChk(ierr);
931   ierr = CeedFree(&identity); CeedChk(ierr);
932 
933   return 0;
934 }
935 
936 //------------------------------------------------------------------------------
937 // Assemble composite diagonal common code
938 //------------------------------------------------------------------------------
939 static inline int CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(
940   CeedOperator op, CeedVector *assembled, CeedRequest *request,
941   const bool pointBlock) {
942   int ierr;
943   CeedInt numSub;
944   CeedOperator *subOperators;
945   ierr = CeedOperatorGetNumSub(op, &numSub); CeedChk(ierr);
946   ierr = CeedOperatorGetSubList(op, &subOperators); CeedChk(ierr);
947   for (CeedInt i = 0; i < numSub; i++) {
948     ierr = CeedOperatorAssembleDiagonalCore_Ref(subOperators[i], assembled,
949            request, pointBlock, !i); CeedChk(ierr);
950   }
951   return 0;
952 }
953 
954 //------------------------------------------------------------------------------
955 // Assemble Linear Diagonal
956 //------------------------------------------------------------------------------
957 static int CeedOperatorLinearAssembleDiagonal_Ref(CeedOperator op,
958     CeedVector *assembled, CeedRequest *request) {
959   int ierr;
960   bool isComposite;
961   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChk(ierr);
962   if (isComposite) {
963     return CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(op, assembled,
964            request, false);
965   } else {
966     return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, false,
967            true);
968   }
969 }
970 
971 //------------------------------------------------------------------------------
972 // Assemble Linear Point Block Diagonal
973 //------------------------------------------------------------------------------
974 static int CeedOperatorLinearAssemblePointBlockDiagonal_Ref(CeedOperator op,
975     CeedVector *assembled, CeedRequest *request) {
976   int ierr;
977   bool isComposite;
978   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChk(ierr);
979   if (isComposite) {
980     return CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(op, assembled,
981            request, true);
982   } else {
983     return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, true,
984            true);
985   }
986 }
987 
988 //------------------------------------------------------------------------------
989 // Create FDM Element Inverse
990 //------------------------------------------------------------------------------
991 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
992     CeedOperator *fdminv, CeedRequest *request) {
993   int ierr;
994   Ceed ceed, ceedparent;
995   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
996   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
997   ceedparent = ceedparent ? ceedparent : ceed;
998   CeedQFunction qf;
999   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
1000 
1001   // Determine active input basis
1002   bool interp = false, grad = false;
1003   CeedBasis basis = NULL;
1004   CeedElemRestriction rstr = NULL;
1005   CeedOperatorField *opfields;
1006   CeedQFunctionField *qffields;
1007   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
1008   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
1009   CeedInt numinputfields;
1010   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
1011   for (CeedInt i=0; i<numinputfields; i++) {
1012     CeedVector vec;
1013     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
1014     if (vec == CEED_VECTOR_ACTIVE) {
1015       CeedEvalMode emode;
1016       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
1017       interp = interp || emode == CEED_EVAL_INTERP;
1018       grad = grad || emode == CEED_EVAL_GRAD;
1019       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
1020       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
1021       CeedChk(ierr);
1022     }
1023   }
1024   if (!basis)
1025     // LCOV_EXCL_START
1026     return CeedError(ceed, 1, "No active field set");
1027   // LCOV_EXCL_STOP
1028   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, lsize = 1;
1029   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
1030   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
1031   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
1032   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
1033   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
1034   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
1035   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
1036   ierr = CeedElemRestrictionGetLVectorSize(rstr, &lsize); CeedChk(ierr);
1037 
1038   // Build and diagonalize 1D Mass and Laplacian
1039   bool tensorbasis;
1040   ierr = CeedBasisIsTensor(basis, &tensorbasis); CeedChk(ierr);
1041   if (!tensorbasis)
1042     // LCOV_EXCL_START
1043     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
1044                      "bases");
1045   // LCOV_EXCL_STOP
1046   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
1047   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
1048   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
1049   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
1050   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
1051   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
1052   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
1053   // -- Mass
1054   const CeedScalar *interp1d, *grad1d, *qweight1d;
1055   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
1056   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
1057   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
1058   for (CeedInt i=0; i<Q1d; i++)
1059     for (CeedInt j=0; j<P1d; j++)
1060       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
1061   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1062                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
1063   CeedChk(ierr);
1064   // -- Laplacian
1065   for (CeedInt i=0; i<Q1d; i++)
1066     for (CeedInt j=0; j<P1d; j++)
1067       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
1068   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1069                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
1070   CeedChk(ierr);
1071   // -- Diagonalize
1072   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
1073   CeedChk(ierr);
1074   ierr = CeedFree(&work); CeedChk(ierr);
1075   ierr = CeedFree(&mass); CeedChk(ierr);
1076   ierr = CeedFree(&laplace); CeedChk(ierr);
1077   for (CeedInt i=0; i<P1d; i++)
1078     for (CeedInt j=0; j<P1d; j++)
1079       x2[i+j*P1d] = x[j+i*P1d];
1080   ierr = CeedFree(&x); CeedChk(ierr);
1081 
1082   // Assemble QFunction
1083   CeedVector assembled;
1084   CeedElemRestriction rstr_qf;
1085   ierr =  CeedOperatorLinearAssembleQFunction(op, &assembled, &rstr_qf,
1086           request); CeedChk(ierr);
1087   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
1088   CeedScalar maxnorm = 0;
1089   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
1090 
1091   // Calculate element averages
1092   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
1093   CeedScalar *elemavg;
1094   const CeedScalar *assembledarray, *qweightsarray;
1095   CeedVector qweights;
1096   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
1097   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
1098                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
1099   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
1100   CeedChk(ierr);
1101   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
1102   CeedChk(ierr);
1103   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
1104   for (CeedInt e=0; e<nelem; e++) {
1105     CeedInt count = 0;
1106     for (CeedInt q=0; q<nqpts; q++)
1107       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
1108         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1109                                                                   i*nqpts + q]) > maxnorm*1e-12) {
1110           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1111                                        i*nqpts + q] / qweightsarray[q];
1112           count++;
1113         }
1114     if (count)
1115       elemavg[e] /= count;
1116   }
1117   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
1118   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
1119   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
1120   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
1121 
1122   // Build FDM diagonal
1123   CeedVector qdata;
1124   CeedScalar *qdataarray;
1125   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*lsize, &qdata); CeedChk(ierr);
1126   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
1127   CeedChk(ierr);
1128   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
1129   for (CeedInt e=0; e<nelem; e++)
1130     for (CeedInt c=0; c<ncomp; c++)
1131       for (CeedInt n=0; n<lsize; n++) {
1132         if (interp)
1133           qdataarray[(e*ncomp+c)*lsize+n] = 1;
1134         if (grad)
1135           for (CeedInt d=0; d<dim; d++) {
1136             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1137             qdataarray[(e*ncomp+c)*lsize+n] += lambda[i];
1138           }
1139         qdataarray[(e*ncomp+c)*lsize+n] = 1 / (elemavg[e] *
1140                                                qdataarray[(e*ncomp+c)*lsize+n]);
1141       }
1142   ierr = CeedFree(&elemavg); CeedChk(ierr);
1143   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1144 
1145   // Setup FDM operator
1146   // -- Basis
1147   CeedBasis fdm_basis;
1148   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1149   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1150   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1151   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1152   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1153                                  graddummy, qrefdummy, qweightdummy,
1154                                  &fdm_basis); CeedChk(ierr);
1155   ierr = CeedFree(&graddummy); CeedChk(ierr);
1156   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1157   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1158   ierr = CeedFree(&x2); CeedChk(ierr);
1159   ierr = CeedFree(&lambda); CeedChk(ierr);
1160 
1161   // -- Restriction
1162   CeedElemRestriction rstr_i;
1163   CeedInt strides[3] = {1, lsize, lsize*ncomp};
1164   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, lsize, ncomp,
1165                                           lsize*nelem*ncomp, strides, &rstr_i);
1166   CeedChk(ierr);
1167   // -- QFunction
1168   CeedQFunction mass_qf;
1169   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1170   CeedChk(ierr);
1171   // -- Operator
1172   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1173   CeedChk(ierr);
1174   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1175   CeedChk(ierr);
1176   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1177   CeedChk(ierr);
1178   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1179   CeedChk(ierr);
1180 
1181   // Cleanup
1182   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1183   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1184   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1185   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1186 
1187   return 0;
1188 }
1189 
1190 //------------------------------------------------------------------------------
1191 // Operator Destroy
1192 //------------------------------------------------------------------------------
1193 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1194   int ierr;
1195   CeedOperator_Ref *impl;
1196   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1197 
1198   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1199     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1200   }
1201   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1202   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1203   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1204 
1205   for (CeedInt i=0; i<impl->numein; i++) {
1206     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1207     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1208   }
1209   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1210   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1211 
1212   for (CeedInt i=0; i<impl->numeout; i++) {
1213     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1214     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1215   }
1216   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1217   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1218 
1219   ierr = CeedFree(&impl); CeedChk(ierr);
1220   return 0;
1221 }
1222 
1223 //------------------------------------------------------------------------------
1224 // Operator Create
1225 //------------------------------------------------------------------------------
1226 int CeedOperatorCreate_Ref(CeedOperator op) {
1227   int ierr;
1228   Ceed ceed;
1229   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1230   CeedOperator_Ref *impl;
1231 
1232   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1233   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1234 
1235   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction",
1236                                 CeedOperatorLinearAssembleQFunction_Ref);
1237   CeedChk(ierr);
1238   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleDiagonal",
1239                                 CeedOperatorLinearAssembleDiagonal_Ref);
1240   CeedChk(ierr);
1241   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1242                                 "LinearAssemblePointBlockDiagonal",
1243                                 CeedOperatorLinearAssemblePointBlockDiagonal_Ref);
1244   CeedChk(ierr);
1245   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1246                                 CeedOperatorCreateFDMElementInverse_Ref);
1247   CeedChk(ierr);
1248   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1249                                 CeedOperatorApply_Ref); CeedChk(ierr);
1250   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1251                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1252   return 0;
1253 }
1254 
1255 //------------------------------------------------------------------------------
1256 // Composite Operator Create
1257 //------------------------------------------------------------------------------
1258 int CeedCompositeOperatorCreate_Ref(CeedOperator op) {
1259   int ierr;
1260   Ceed ceed;
1261   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1262   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleDiagonal",
1263                                 CeedOperatorLinearAssembleDiagonal_Ref);
1264   CeedChk(ierr);
1265   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1266                                 "LinearAssemblePointBlockDiagonal",
1267                                 CeedOperatorLinearAssemblePointBlockDiagonal_Ref);
1268   CeedChk(ierr);
1269   return 0;
1270 }
1271 //------------------------------------------------------------------------------
1272