xref: /libCEED/backends/ref/ceed-ref-operator.c (revision b1d741539a3b3c5bb086a98a1a97469f6c72b0e4) 
1 // Copyright (c) 2017-2018, Lawrence Livermore National Security, LLC.
2 // Produced at the Lawrence Livermore National Laboratory. LLNL-CODE-734707.
3 // All Rights reserved. See files LICENSE and NOTICE for details.
4 //
5 // This file is part of CEED, a collection of benchmarks, miniapps, software
6 // libraries and APIs for efficient high-order finite element and spectral
7 // element discretizations for exascale applications. For more information and
8 // source code availability see http://github.com/ceed.
9 //
10 // The CEED research is supported by the Exascale Computing Project 17-SC-20-SC,
11 // a collaborative effort of two U.S. Department of Energy organizations (Office
12 // of Science and the National Nuclear Security Administration) responsible for
13 // the planning and preparation of a capable exascale ecosystem, including
14 // software, applications, hardware, advanced system engineering and early
15 // testbed platforms, in support of the nation's exascale computing imperative.
16 
17 #include "ceed-ref.h"
18 
19 //------------------------------------------------------------------------------
20 // Setup Input/Output Fields
21 //------------------------------------------------------------------------------
22 static int CeedOperatorSetupFields_Ref(CeedQFunction qf, CeedOperator op,
23                                        bool inOrOut,
24                                        CeedVector *fullevecs, CeedVector *evecs,
25                                        CeedVector *qvecs, CeedInt starte,
26                                        CeedInt numfields, CeedInt Q) {
27   CeedInt dim, ierr, size, P;
28   Ceed ceed;
29   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
30   CeedBasis basis;
31   CeedElemRestriction Erestrict;
32   CeedOperatorField *opfields;
33   CeedQFunctionField *qffields;
34   if (inOrOut) {
35     ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
36     ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
37   } else {
38     ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
39     ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
40   }
41 
42   // Loop over fields
43   for (CeedInt i=0; i<numfields; i++) {
44     CeedEvalMode emode;
45     ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
46 
47     if (emode != CEED_EVAL_WEIGHT) {
48       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
49       CeedChk(ierr);
50       ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
51                                              &fullevecs[i+starte]);
52       CeedChk(ierr);
53     }
54 
55     switch(emode) {
56     case CEED_EVAL_NONE:
57       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
58       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
59       break;
60     case CEED_EVAL_INTERP:
61       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
62       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
63       CeedChk(ierr);
64       ierr = CeedVectorCreate(ceed, P*size, &evecs[i]); CeedChk(ierr);
65       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
66       break;
67     case CEED_EVAL_GRAD:
68       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
69       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChk(ierr);
70       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
71       ierr = CeedElemRestrictionGetElementSize(Erestrict, &P);
72       CeedChk(ierr);
73       ierr = CeedVectorCreate(ceed, P*size/dim, &evecs[i]); CeedChk(ierr);
74       ierr = CeedVectorCreate(ceed, Q*size, &qvecs[i]); CeedChk(ierr);
75       break;
76     case CEED_EVAL_WEIGHT: // Only on input fields
77       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
78       ierr = CeedVectorCreate(ceed, Q, &qvecs[i]); CeedChk(ierr);
79       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
80                             CEED_VECTOR_NONE, qvecs[i]); CeedChk(ierr);
81       break;
82     case CEED_EVAL_DIV:
83       break; // Not implemented
84     case CEED_EVAL_CURL:
85       break; // Not implemented
86     }
87   }
88   return 0;
89 }
90 
91 //------------------------------------------------------------------------------
92 // Setup Operator
93 //------------------------------------------------------------------------------/*
94 static int CeedOperatorSetup_Ref(CeedOperator op) {
95   int ierr;
96   bool setupdone;
97   ierr = CeedOperatorGetSetupStatus(op, &setupdone); CeedChk(ierr);
98   if (setupdone) return 0;
99   Ceed ceed;
100   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
101   CeedOperator_Ref *impl;
102   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
103   CeedQFunction qf;
104   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
105   CeedInt Q, numinputfields, numoutputfields;
106   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChk(ierr);
107   ierr = CeedQFunctionGetIdentityStatus(qf, &impl->identityqf); CeedChk(ierr);
108   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
109   CeedChk(ierr);
110   CeedOperatorField *opinputfields, *opoutputfields;
111   ierr = CeedOperatorGetFields(op, &opinputfields, &opoutputfields);
112   CeedChk(ierr);
113   CeedQFunctionField *qfinputfields, *qfoutputfields;
114   ierr = CeedQFunctionGetFields(qf, &qfinputfields, &qfoutputfields);
115   CeedChk(ierr);
116 
117   // Allocate
118   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
119   CeedChk(ierr);
120   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->edata);
121   CeedChk(ierr);
122 
123   ierr = CeedCalloc(16, &impl->inputstate); CeedChk(ierr);
124   ierr = CeedCalloc(16, &impl->evecsin); CeedChk(ierr);
125   ierr = CeedCalloc(16, &impl->evecsout); CeedChk(ierr);
126   ierr = CeedCalloc(16, &impl->qvecsin); CeedChk(ierr);
127   ierr = CeedCalloc(16, &impl->qvecsout); CeedChk(ierr);
128 
129   impl->numein = numinputfields; impl->numeout = numoutputfields;
130 
131   // Set up infield and outfield evecs and qvecs
132   // Infields
133   ierr = CeedOperatorSetupFields_Ref(qf, op, 0, impl->evecs,
134                                      impl->evecsin, impl->qvecsin, 0,
135                                      numinputfields, Q);
136   CeedChk(ierr);
137   // Outfields
138   ierr = CeedOperatorSetupFields_Ref(qf, op, 1, impl->evecs,
139                                      impl->evecsout, impl->qvecsout,
140                                      numinputfields, numoutputfields, Q);
141   CeedChk(ierr);
142 
143   // Identity QFunctions
144   if (impl->identityqf) {
145     CeedEvalMode inmode, outmode;
146     CeedQFunctionField *infields, *outfields;
147     ierr = CeedQFunctionGetFields(qf, &infields, &outfields); CeedChk(ierr);
148 
149     for (CeedInt i=0; i<numinputfields; i++) {
150       ierr = CeedQFunctionFieldGetEvalMode(infields[i], &inmode);
151       CeedChk(ierr);
152       ierr = CeedQFunctionFieldGetEvalMode(outfields[i], &outmode);
153       CeedChk(ierr);
154 
155       ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
156       impl->qvecsout[i] = impl->qvecsin[i];
157       ierr = CeedVectorAddReference(impl->qvecsin[i]); CeedChk(ierr);
158     }
159   }
160 
161   ierr = CeedOperatorSetSetupDone(op); CeedChk(ierr);
162 
163   return 0;
164 }
165 
166 //------------------------------------------------------------------------------
167 // Setup Operator Inputs
168 //------------------------------------------------------------------------------
169 static inline int CeedOperatorSetupInputs_Ref(CeedInt numinputfields,
170     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
171     CeedVector invec, const bool skipactive, CeedOperator_Ref *impl,
172     CeedRequest *request) {
173   CeedInt ierr;
174   CeedEvalMode emode;
175   CeedVector vec;
176   CeedElemRestriction Erestrict;
177   uint64_t state;
178 
179   for (CeedInt i=0; i<numinputfields; i++) {
180     // Get input vector
181     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
182     if (vec == CEED_VECTOR_ACTIVE) {
183       if (skipactive)
184         continue;
185       else
186         vec = invec;
187     }
188 
189     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
190     CeedChk(ierr);
191     // Restrict and Evec
192     if (emode == CEED_EVAL_WEIGHT) { // Skip
193     } else {
194       // Restrict
195       ierr = CeedVectorGetState(vec, &state); CeedChk(ierr);
196       // Skip restriction if input is unchanged
197       if (state != impl->inputstate[i] || vec == invec) {
198         ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
199         CeedChk(ierr);
200         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE, vec,
201                                         impl->evecs[i], request); CeedChk(ierr);
202         impl->inputstate[i] = state;
203       }
204       // Get evec
205       ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_HOST,
206                                     (const CeedScalar **) &impl->edata[i]);
207       CeedChk(ierr);
208     }
209   }
210   return 0;
211 }
212 
213 //------------------------------------------------------------------------------
214 // Input Basis Action
215 //------------------------------------------------------------------------------
216 static inline int CeedOperatorInputBasis_Ref(CeedInt e, CeedInt Q,
217     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
218     CeedInt numinputfields, const bool skipactive, CeedOperator_Ref *impl) {
219   CeedInt ierr;
220   CeedInt dim, elemsize, size;
221   CeedElemRestriction Erestrict;
222   CeedEvalMode emode;
223   CeedBasis basis;
224 
225   for (CeedInt i=0; i<numinputfields; i++) {
226     // Skip active input
227     if (skipactive) {
228       CeedVector vec;
229       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChk(ierr);
230       if (vec == CEED_VECTOR_ACTIVE)
231         continue;
232     }
233     // Get elemsize, emode, size
234     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
235     CeedChk(ierr);
236     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
237     CeedChk(ierr);
238     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
239     CeedChk(ierr);
240     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChk(ierr);
241     // Basis action
242     switch(emode) {
243     case CEED_EVAL_NONE:
244       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_HOST,
245                                 CEED_USE_POINTER,
246                                 &impl->edata[i][e*Q*size]); CeedChk(ierr);
247       break;
248     case CEED_EVAL_INTERP:
249       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
250       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
251                                 CEED_USE_POINTER,
252                                 &impl->edata[i][e*elemsize*size]);
253       CeedChk(ierr);
254       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
255                             CEED_EVAL_INTERP, impl->evecsin[i],
256                             impl->qvecsin[i]); CeedChk(ierr);
257       break;
258     case CEED_EVAL_GRAD:
259       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis); CeedChk(ierr);
260       ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
261       ierr = CeedVectorSetArray(impl->evecsin[i], CEED_MEM_HOST,
262                                 CEED_USE_POINTER,
263                                 &impl->edata[i][e*elemsize*size/dim]);
264       CeedChk(ierr);
265       ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE,
266                             CEED_EVAL_GRAD, impl->evecsin[i],
267                             impl->qvecsin[i]); CeedChk(ierr);
268       break;
269     case CEED_EVAL_WEIGHT:
270       break;  // No action
271     // LCOV_EXCL_START
272     case CEED_EVAL_DIV:
273     case CEED_EVAL_CURL: {
274       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
275       CeedChk(ierr);
276       Ceed ceed;
277       ierr = CeedBasisGetCeed(basis, &ceed); CeedChk(ierr);
278       return CeedError(ceed, 1, "Ceed evaluation mode not implemented");
279       // 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 CeedOperatorAssembleLinearQFunction_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 Linear Diagonal
709 //------------------------------------------------------------------------------
710 static int CeedOperatorAssembleDiagonalCore_Ref(CeedOperator op,
711     CeedVector *assembled, CeedRequest *request, const bool pointBlock) {
712   int ierr;
713 
714   // Assemble QFunction
715   CeedQFunction qf;
716   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
717   CeedInt numinputfields, numoutputfields;
718   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
719   CeedChk(ierr);
720   CeedVector assembledqf;
721   CeedElemRestriction rstr;
722   ierr = CeedOperatorAssembleLinearQFunction(op,  &assembledqf, &rstr, request);
723   CeedChk(ierr);
724   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
725   CeedScalar maxnorm = 0;
726   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
727 
728   // Determine active input basis
729   CeedOperatorField *opfields;
730   CeedQFunctionField *qffields;
731   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
732   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
733   CeedInt numemodein = 0, ncomp, dim = 1;
734   CeedEvalMode *emodein = NULL;
735   CeedBasis basisin = NULL;
736   CeedElemRestriction rstrin = NULL;
737   for (CeedInt i=0; i<numinputfields; i++) {
738     CeedVector vec;
739     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
740     if (vec == CEED_VECTOR_ACTIVE) {
741       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
742       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
743       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
744       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrin);
745       CeedChk(ierr);
746       CeedEvalMode emode;
747       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
748       CeedChk(ierr);
749       switch (emode) {
750       case CEED_EVAL_NONE:
751       case CEED_EVAL_INTERP:
752         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
753         emodein[numemodein] = emode;
754         numemodein += 1;
755         break;
756       case CEED_EVAL_GRAD:
757         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
758         for (CeedInt d=0; d<dim; d++)
759           emodein[numemodein+d] = emode;
760         numemodein += dim;
761         break;
762       case CEED_EVAL_WEIGHT:
763       case CEED_EVAL_DIV:
764       case CEED_EVAL_CURL:
765         break; // Caught by QF Assembly
766       }
767     }
768   }
769 
770   // Determine active output basis
771   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
772   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
773   CeedInt numemodeout = 0;
774   CeedEvalMode *emodeout = NULL;
775   CeedBasis basisout = NULL;
776   CeedElemRestriction rstrout = NULL;
777   for (CeedInt i=0; i<numoutputfields; i++) {
778     CeedVector vec;
779     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
780     if (vec == CEED_VECTOR_ACTIVE) {
781       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
782       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstrout);
783       CeedChk(ierr);
784       CeedEvalMode emode;
785       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
786       switch (emode) {
787       case CEED_EVAL_NONE:
788       case CEED_EVAL_INTERP:
789         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
790         emodeout[numemodeout] = emode;
791         numemodeout += 1;
792         break;
793       case CEED_EVAL_GRAD:
794         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
795         for (CeedInt d=0; d<dim; d++)
796           emodeout[numemodeout+d] = emode;
797         numemodeout += dim;
798         break;
799       case CEED_EVAL_WEIGHT:
800       case CEED_EVAL_DIV:
801       case CEED_EVAL_CURL:
802         break; // Caught by QF Assembly
803       }
804     }
805   }
806 
807   // Assemble point-block diagonal restriction, if needed
808   CeedElemRestriction diagrstr = rstrout;
809   if (pointBlock) {
810     ierr = CreatePBRestriction(rstrout, &diagrstr); CeedChk(ierr);
811   }
812 
813   // Create diagonal vector
814   CeedVector elemdiag;
815   ierr = CeedElemRestrictionCreateVector(diagrstr, assembled, &elemdiag);
816   CeedChk(ierr);
817 
818   // Assemble element operator diagonals
819   CeedScalar *elemdiagarray, *assembledqfarray;
820   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
821   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
822   CeedChk(ierr);
823   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
824   CeedChk(ierr);
825   CeedInt nelem, nnodes, nqpts;
826   ierr = CeedElemRestrictionGetNumElements(diagrstr, &nelem); CeedChk(ierr);
827   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
828   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
829   // Basis matrices
830   const CeedScalar *interpin, *interpout, *gradin, *gradout;
831   CeedScalar *identity = NULL;
832   bool evalNone = false;
833   for (CeedInt i=0; i<numemodein; i++)
834     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
835   for (CeedInt i=0; i<numemodeout; i++)
836     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
837   if (evalNone) {
838     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
839     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
840       identity[i*nnodes+i] = 1.0;
841   }
842   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
843   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
844   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
845   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
846   // Compute the diagonal of B^T D B
847   // Each element
848   for (CeedInt e=0; e<nelem; e++) {
849     CeedInt dout = -1;
850     // Each basis eval mode pair
851     for (CeedInt eout=0; eout<numemodeout; eout++) {
852       const CeedScalar *bt = NULL;
853       if (emodeout[eout] == CEED_EVAL_GRAD)
854         dout += 1;
855       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
856                                       &gradout[dout*nqpts*nnodes]);
857       CeedInt din = -1;
858       for (CeedInt ein=0; ein<numemodein; ein++) {
859         const CeedScalar *b = NULL;
860         if (emodein[ein] == CEED_EVAL_GRAD)
861           din += 1;
862         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
863                                         &gradin[din*nqpts*nnodes]);
864         // Each component
865         for (CeedInt compOut=0; compOut<ncomp; compOut++)
866           // Each qpoint/node pair
867           for (CeedInt q=0; q<nqpts; q++)
868             if (pointBlock) {
869               // Point Block Diagonal
870               for (CeedInt compIn=0; compIn<ncomp; compIn++) {
871                 const CeedScalar qfvalue =
872                   assembledqfarray[((((e*numemodein+ein)*ncomp+compIn)*
873                                      numemodeout+eout)*ncomp+compOut)*nqpts+q];
874                 if (fabs(qfvalue) > maxnorm*1e-12)
875                   for (CeedInt n=0; n<nnodes; n++)
876                     elemdiagarray[((e*ncomp+compOut)*ncomp+compIn)*nnodes+n] +=
877                       bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
878               }
879             } else {
880               // Diagonal Only
881               const CeedScalar qfvalue =
882                 assembledqfarray[((((e*numemodein+ein)*ncomp+compOut)*
883                                    numemodeout+eout)*ncomp+compOut)*nqpts+q];
884               if (fabs(qfvalue) > maxnorm*1e-12)
885                 for (CeedInt n=0; n<nnodes; n++)
886                   elemdiagarray[(e*ncomp+compOut)*nnodes+n] +=
887                     bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
888             }
889       }
890     }
891   }
892   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
893   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
894 
895   // Assemble local operator diagonal
896   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChk(ierr);
897   ierr = CeedElemRestrictionApply(diagrstr, CEED_TRANSPOSE, elemdiag,
898                                   *assembled, request); CeedChk(ierr);
899 
900   // Cleanup
901   if (pointBlock) {
902     ierr = CeedElemRestrictionDestroy(&diagrstr); CeedChk(ierr);
903   }
904   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
905   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
906   ierr = CeedFree(&emodein); CeedChk(ierr);
907   ierr = CeedFree(&emodeout); CeedChk(ierr);
908   ierr = CeedFree(&identity); CeedChk(ierr);
909 
910   return 0;
911 }
912 
913 //------------------------------------------------------------------------------
914 // Assemble Linear Diagonal
915 //------------------------------------------------------------------------------
916 static int CeedOperatorAssembleLinearDiagonal_Ref(CeedOperator op,
917     CeedVector *assembled, CeedRequest *request) {
918   return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, false);
919 }
920 
921 //------------------------------------------------------------------------------
922 // Assemble Linear Point Block Diagonal
923 //------------------------------------------------------------------------------
924 static int CeedOperatorAssembleLinearPointBlockDiagonal_Ref(CeedOperator op,
925     CeedVector *assembled, CeedRequest *request) {
926   return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, true);
927 }
928 
929 //------------------------------------------------------------------------------
930 // Create FDM Element Inverse
931 //------------------------------------------------------------------------------
932 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
933     CeedOperator *fdminv, CeedRequest *request) {
934   int ierr;
935   Ceed ceed, ceedparent;
936   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
937   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
938   ceedparent = ceedparent ? ceedparent : ceed;
939   CeedQFunction qf;
940   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
941 
942   // Determine active input basis
943   bool interp = false, grad = false;
944   CeedBasis basis = NULL;
945   CeedElemRestriction rstr = NULL;
946   CeedOperatorField *opfields;
947   CeedQFunctionField *qffields;
948   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
949   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
950   CeedInt numinputfields;
951   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
952   for (CeedInt i=0; i<numinputfields; i++) {
953     CeedVector vec;
954     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
955     if (vec == CEED_VECTOR_ACTIVE) {
956       CeedEvalMode emode;
957       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
958       interp = interp || emode == CEED_EVAL_INTERP;
959       grad = grad || emode == CEED_EVAL_GRAD;
960       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
961       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
962       CeedChk(ierr);
963     }
964   }
965   if (!basis)
966     // LCOV_EXCL_START
967     return CeedError(ceed, 1, "No active field set");
968   // LCOV_EXCL_STOP
969   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, lsize = 1;
970   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
971   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
972   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
973   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
974   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
975   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
976   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
977   ierr = CeedElemRestrictionGetLVectorSize(rstr, &lsize); CeedChk(ierr);
978 
979   // Build and diagonalize 1D Mass and Laplacian
980   bool tensorbasis;
981   ierr = CeedBasisGetTensorStatus(basis, &tensorbasis); CeedChk(ierr);
982   if (!tensorbasis)
983     // LCOV_EXCL_START
984     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
985                      "bases");
986   // LCOV_EXCL_STOP
987   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
988   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
989   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
990   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
991   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
992   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
993   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
994   // -- Mass
995   const CeedScalar *interp1d, *grad1d, *qweight1d;
996   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
997   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
998   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
999   for (CeedInt i=0; i<Q1d; i++)
1000     for (CeedInt j=0; j<P1d; j++)
1001       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
1002   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1003                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
1004   CeedChk(ierr);
1005   // -- Laplacian
1006   for (CeedInt i=0; i<Q1d; i++)
1007     for (CeedInt j=0; j<P1d; j++)
1008       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
1009   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1010                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
1011   CeedChk(ierr);
1012   // -- Diagonalize
1013   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
1014   CeedChk(ierr);
1015   ierr = CeedFree(&work); CeedChk(ierr);
1016   ierr = CeedFree(&mass); CeedChk(ierr);
1017   ierr = CeedFree(&laplace); CeedChk(ierr);
1018   for (CeedInt i=0; i<P1d; i++)
1019     for (CeedInt j=0; j<P1d; j++)
1020       x2[i+j*P1d] = x[j+i*P1d];
1021   ierr = CeedFree(&x); CeedChk(ierr);
1022 
1023   // Assemble QFunction
1024   CeedVector assembled;
1025   CeedElemRestriction rstr_qf;
1026   ierr =  CeedOperatorAssembleLinearQFunction(op, &assembled, &rstr_qf,
1027           request); CeedChk(ierr);
1028   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
1029   CeedScalar maxnorm = 0;
1030   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
1031 
1032   // Calculate element averages
1033   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
1034   CeedScalar *elemavg;
1035   const CeedScalar *assembledarray, *qweightsarray;
1036   CeedVector qweights;
1037   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
1038   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
1039                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
1040   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
1041   CeedChk(ierr);
1042   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
1043   CeedChk(ierr);
1044   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
1045   for (CeedInt e=0; e<nelem; e++) {
1046     CeedInt count = 0;
1047     for (CeedInt q=0; q<nqpts; q++)
1048       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
1049         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1050                                                                   i*nqpts + q]) > maxnorm*1e-12) {
1051           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1052                                        i*nqpts + q] / qweightsarray[q];
1053           count++;
1054         }
1055     if (count)
1056       elemavg[e] /= count;
1057   }
1058   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
1059   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
1060   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
1061   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
1062 
1063   // Build FDM diagonal
1064   CeedVector qdata;
1065   CeedScalar *qdataarray;
1066   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*lsize, &qdata); CeedChk(ierr);
1067   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
1068   CeedChk(ierr);
1069   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
1070   for (CeedInt e=0; e<nelem; e++)
1071     for (CeedInt c=0; c<ncomp; c++)
1072       for (CeedInt n=0; n<lsize; n++) {
1073         if (interp)
1074           qdataarray[(e*ncomp+c)*lsize+n] = 1;
1075         if (grad)
1076           for (CeedInt d=0; d<dim; d++) {
1077             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1078             qdataarray[(e*ncomp+c)*lsize+n] += lambda[i];
1079           }
1080         qdataarray[(e*ncomp+c)*lsize+n] = 1 / (elemavg[e] *
1081                                                qdataarray[(e*ncomp+c)*lsize+n]);
1082       }
1083   ierr = CeedFree(&elemavg); CeedChk(ierr);
1084   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1085 
1086   // Setup FDM operator
1087   // -- Basis
1088   CeedBasis fdm_basis;
1089   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1090   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1091   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1092   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1093   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1094                                  graddummy, qrefdummy, qweightdummy,
1095                                  &fdm_basis); CeedChk(ierr);
1096   ierr = CeedFree(&graddummy); CeedChk(ierr);
1097   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1098   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1099   ierr = CeedFree(&x2); CeedChk(ierr);
1100   ierr = CeedFree(&lambda); CeedChk(ierr);
1101 
1102   // -- Restriction
1103   CeedElemRestriction rstr_i;
1104   CeedInt strides[3] = {1, lsize, lsize*ncomp};
1105   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, lsize, ncomp,
1106                                           lsize*nelem*ncomp, strides, &rstr_i);
1107   CeedChk(ierr);
1108   // -- QFunction
1109   CeedQFunction mass_qf;
1110   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1111   CeedChk(ierr);
1112   // -- Operator
1113   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1114   CeedChk(ierr);
1115   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1116   CeedChk(ierr);
1117   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1118   CeedChk(ierr);
1119   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1120   CeedChk(ierr);
1121 
1122   // Cleanup
1123   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1124   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1125   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1126   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1127 
1128   return 0;
1129 }
1130 
1131 //------------------------------------------------------------------------------
1132 // Operator Destroy
1133 //------------------------------------------------------------------------------
1134 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1135   int ierr;
1136   CeedOperator_Ref *impl;
1137   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1138 
1139   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1140     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1141   }
1142   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1143   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1144   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1145 
1146   for (CeedInt i=0; i<impl->numein; i++) {
1147     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1148     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1149   }
1150   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1151   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1152 
1153   for (CeedInt i=0; i<impl->numeout; i++) {
1154     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1155     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1156   }
1157   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1158   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1159 
1160   ierr = CeedFree(&impl); CeedChk(ierr);
1161   return 0;
1162 }
1163 
1164 //------------------------------------------------------------------------------
1165 // Operator Create
1166 //------------------------------------------------------------------------------
1167 int CeedOperatorCreate_Ref(CeedOperator op) {
1168   int ierr;
1169   Ceed ceed;
1170   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1171   CeedOperator_Ref *impl;
1172 
1173   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1174   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1175 
1176   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearQFunction",
1177                                 CeedOperatorAssembleLinearQFunction_Ref);
1178   CeedChk(ierr);
1179   ierr = CeedSetBackendFunction(ceed, "Operator", op, "AssembleLinearDiagonal",
1180                                 CeedOperatorAssembleLinearDiagonal_Ref);
1181   CeedChk(ierr);
1182   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1183                                 "AssembleLinearPointBlockDiagonal",
1184                                 CeedOperatorAssembleLinearPointBlockDiagonal_Ref);
1185   CeedChk(ierr);
1186   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1187                                 CeedOperatorCreateFDMElementInverse_Ref);
1188   CeedChk(ierr);
1189   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1190                                 CeedOperatorApply_Ref); CeedChk(ierr);
1191   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1192                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1193   return 0;
1194 }
1195 //------------------------------------------------------------------------------
1196