xref: /libCEED/backends/ref/ceed-ref-operator.c (revision 5f67fade47e323fa44018f277580acfe24400ad4) 
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   int ierr;
713   Ceed ceed;
714   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
715 
716   // Assemble QFunction
717   CeedQFunction qf;
718   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
719   CeedInt numinputfields, numoutputfields;
720   ierr= CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
721   CeedChk(ierr);
722   CeedVector assembledqf;
723   CeedElemRestriction rstr;
724   ierr = CeedOperatorLinearAssembleQFunction(op,  &assembledqf, &rstr, request);
725   CeedChk(ierr);
726   ierr = CeedElemRestrictionDestroy(&rstr); CeedChk(ierr);
727   CeedScalar maxnorm = 0;
728   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
729 
730   // Determine active input basis
731   CeedOperatorField *opfields;
732   CeedQFunctionField *qffields;
733   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
734   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
735   CeedInt numemodein = 0, ncomp, dim = 1;
736   CeedEvalMode *emodein = NULL;
737   CeedBasis basisin = NULL;
738   CeedElemRestriction rstrin = NULL;
739   for (CeedInt i=0; i<numinputfields; i++) {
740     CeedVector vec;
741     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
742     if (vec == CEED_VECTOR_ACTIVE) {
743       CeedElemRestriction rstr;
744       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChk(ierr);
745       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChk(ierr);
746       ierr = CeedBasisGetDimension(basisin, &dim); CeedChk(ierr);
747       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
748       CeedChk(ierr);
749       if (rstrin && rstrin != rstr)
750         // LCOV_EXCL_START
751         return CeedError(ceed, 1,
752                          "Multi-field non-composite operator diagonal assembly not supported");
753       // LCOV_EXCL_STOP
754       rstrin = rstr;
755       CeedEvalMode emode;
756       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
757       CeedChk(ierr);
758       switch (emode) {
759       case CEED_EVAL_NONE:
760       case CEED_EVAL_INTERP:
761         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChk(ierr);
762         emodein[numemodein] = emode;
763         numemodein += 1;
764         break;
765       case CEED_EVAL_GRAD:
766         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChk(ierr);
767         for (CeedInt d=0; d<dim; d++)
768           emodein[numemodein+d] = emode;
769         numemodein += dim;
770         break;
771       case CEED_EVAL_WEIGHT:
772       case CEED_EVAL_DIV:
773       case CEED_EVAL_CURL:
774         break; // Caught by QF Assembly
775       }
776     }
777   }
778 
779   // Determine active output basis
780   ierr = CeedOperatorGetFields(op, NULL, &opfields); CeedChk(ierr);
781   ierr = CeedQFunctionGetFields(qf, NULL, &qffields); CeedChk(ierr);
782   CeedInt numemodeout = 0;
783   CeedEvalMode *emodeout = NULL;
784   CeedBasis basisout = NULL;
785   CeedElemRestriction rstrout = NULL;
786   for (CeedInt i=0; i<numoutputfields; i++) {
787     CeedVector vec;
788     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
789     if (vec == CEED_VECTOR_ACTIVE) {
790       CeedElemRestriction rstr;
791       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChk(ierr);
792       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
793       CeedChk(ierr);
794       if (rstrout && rstrout != rstr)
795         // LCOV_EXCL_START
796         return CeedError(ceed, 1,
797                          "Multi-field non-composite operator diagonal assembly not supported");
798       // LCOV_EXCL_STOP
799       rstrout = rstr;
800       CeedEvalMode emode;
801       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
802       switch (emode) {
803       case CEED_EVAL_NONE:
804       case CEED_EVAL_INTERP:
805         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChk(ierr);
806         emodeout[numemodeout] = emode;
807         numemodeout += 1;
808         break;
809       case CEED_EVAL_GRAD:
810         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChk(ierr);
811         for (CeedInt d=0; d<dim; d++)
812           emodeout[numemodeout+d] = emode;
813         numemodeout += dim;
814         break;
815       case CEED_EVAL_WEIGHT:
816       case CEED_EVAL_DIV:
817       case CEED_EVAL_CURL:
818         break; // Caught by QF Assembly
819       }
820     }
821   }
822 
823   // Assemble point-block diagonal restriction, if needed
824   CeedElemRestriction diagrstr = rstrout;
825   if (pointBlock) {
826     ierr = CreatePBRestriction(rstrout, &diagrstr); CeedChk(ierr);
827   }
828 
829   // Create diagonal vector
830   CeedVector elemdiag;
831   ierr = CeedElemRestrictionCreateVector(diagrstr, NULL, &elemdiag);
832   CeedChk(ierr);
833 
834   // Assemble element operator diagonals
835   CeedScalar *elemdiagarray, *assembledqfarray;
836   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChk(ierr);
837   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_HOST, &elemdiagarray);
838   CeedChk(ierr);
839   ierr = CeedVectorGetArray(assembledqf, CEED_MEM_HOST, &assembledqfarray);
840   CeedChk(ierr);
841   CeedInt nelem, nnodes, nqpts;
842   ierr = CeedElemRestrictionGetNumElements(diagrstr, &nelem); CeedChk(ierr);
843   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChk(ierr);
844   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChk(ierr);
845   // Basis matrices
846   const CeedScalar *interpin, *interpout, *gradin, *gradout;
847   CeedScalar *identity = NULL;
848   bool evalNone = false;
849   for (CeedInt i=0; i<numemodein; i++)
850     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
851   for (CeedInt i=0; i<numemodeout; i++)
852     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
853   if (evalNone) {
854     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChk(ierr);
855     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
856       identity[i*nnodes+i] = 1.0;
857   }
858   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChk(ierr);
859   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChk(ierr);
860   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChk(ierr);
861   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChk(ierr);
862   // Compute the diagonal of B^T D B
863   // Each element
864   for (CeedInt e=0; e<nelem; e++) {
865     CeedInt dout = -1;
866     // Each basis eval mode pair
867     for (CeedInt eout=0; eout<numemodeout; eout++) {
868       const CeedScalar *bt = NULL;
869       if (emodeout[eout] == CEED_EVAL_GRAD)
870         dout += 1;
871       CeedOperatorGetBasisPointer_Ref(&bt, emodeout[eout], identity, interpout,
872                                       &gradout[dout*nqpts*nnodes]);
873       CeedInt din = -1;
874       for (CeedInt ein=0; ein<numemodein; ein++) {
875         const CeedScalar *b = NULL;
876         if (emodein[ein] == CEED_EVAL_GRAD)
877           din += 1;
878         CeedOperatorGetBasisPointer_Ref(&b, emodein[ein], identity, interpin,
879                                         &gradin[din*nqpts*nnodes]);
880         // Each component
881         for (CeedInt compOut=0; compOut<ncomp; compOut++)
882           // Each qpoint/node pair
883           for (CeedInt q=0; q<nqpts; q++)
884             if (pointBlock) {
885               // Point Block Diagonal
886               for (CeedInt compIn=0; compIn<ncomp; compIn++) {
887                 const CeedScalar qfvalue =
888                   assembledqfarray[((((e*numemodein+ein)*ncomp+compIn)*
889                                      numemodeout+eout)*ncomp+compOut)*nqpts+q];
890                 if (fabs(qfvalue) > maxnorm*1e-12)
891                   for (CeedInt n=0; n<nnodes; n++)
892                     elemdiagarray[((e*ncomp+compOut)*ncomp+compIn)*nnodes+n] +=
893                       bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
894               }
895             } else {
896               // Diagonal Only
897               const CeedScalar qfvalue =
898                 assembledqfarray[((((e*numemodein+ein)*ncomp+compOut)*
899                                    numemodeout+eout)*ncomp+compOut)*nqpts+q];
900               if (fabs(qfvalue) > maxnorm*1e-12)
901                 for (CeedInt n=0; n<nnodes; n++)
902                   elemdiagarray[(e*ncomp+compOut)*nnodes+n] +=
903                     bt[q*nnodes+n] * qfvalue * b[q*nnodes+n];
904             }
905       }
906     }
907   }
908   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChk(ierr);
909   ierr = CeedVectorRestoreArray(assembledqf, &assembledqfarray); CeedChk(ierr);
910 
911   // Assemble local operator diagonal
912   ierr = CeedElemRestrictionApply(diagrstr, CEED_TRANSPOSE, elemdiag,
913                                   assembled, request); CeedChk(ierr);
914 
915   // Cleanup
916   if (pointBlock) {
917     ierr = CeedElemRestrictionDestroy(&diagrstr); CeedChk(ierr);
918   }
919   ierr = CeedVectorDestroy(&assembledqf); CeedChk(ierr);
920   ierr = CeedVectorDestroy(&elemdiag); CeedChk(ierr);
921   ierr = CeedFree(&emodein); CeedChk(ierr);
922   ierr = CeedFree(&emodeout); CeedChk(ierr);
923   ierr = CeedFree(&identity); CeedChk(ierr);
924 
925   return 0;
926 }
927 
928 //------------------------------------------------------------------------------
929 // Assemble composite diagonal common code
930 //------------------------------------------------------------------------------
931 static inline int CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(
932   CeedOperator op, CeedVector assembled, CeedRequest *request,
933   const bool pointBlock) {
934   int ierr;
935   CeedInt numSub;
936   CeedOperator *subOperators;
937   ierr = CeedOperatorGetNumSub(op, &numSub); CeedChk(ierr);
938   ierr = CeedOperatorGetSubList(op, &subOperators); CeedChk(ierr);
939   for (CeedInt i = 0; i < numSub; i++) {
940     ierr = CeedOperatorAssembleDiagonalCore_Ref(subOperators[i], assembled,
941            request, pointBlock); CeedChk(ierr);
942   }
943   return 0;
944 }
945 
946 //------------------------------------------------------------------------------
947 // Assemble Linear Diagonal
948 //------------------------------------------------------------------------------
949 static int CeedOperatorLinearAssembleDiagonal_Ref(CeedOperator op,
950     CeedVector assembled, CeedRequest *request) {
951   int ierr;
952   bool isComposite;
953   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChk(ierr);
954   if (isComposite) {
955     return CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(op, assembled,
956            request, false);
957   } else {
958     return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, false);
959   }
960 }
961 
962 //------------------------------------------------------------------------------
963 // Assemble Linear Point Block Diagonal
964 //------------------------------------------------------------------------------
965 static int CeedOperatorLinearAssemblePointBlockDiagonal_Ref(CeedOperator op,
966     CeedVector assembled, CeedRequest *request) {
967   int ierr;
968   bool isComposite;
969   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChk(ierr);
970   if (isComposite) {
971     return CeedOperatorLinearAssembleDiagonalCompositeCore_Ref(op, assembled,
972            request, true);
973   } else {
974     return CeedOperatorAssembleDiagonalCore_Ref(op, assembled, request, true);
975   }
976 }
977 
978 //------------------------------------------------------------------------------
979 // Create FDM Element Inverse
980 //------------------------------------------------------------------------------
981 int CeedOperatorCreateFDMElementInverse_Ref(CeedOperator op,
982     CeedOperator *fdminv, CeedRequest *request) {
983   int ierr;
984   Ceed ceed, ceedparent;
985   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
986   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent); CeedChk(ierr);
987   ceedparent = ceedparent ? ceedparent : ceed;
988   CeedQFunction qf;
989   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
990 
991   // Determine active input basis
992   bool interp = false, grad = false;
993   CeedBasis basis = NULL;
994   CeedElemRestriction rstr = NULL;
995   CeedOperatorField *opfields;
996   CeedQFunctionField *qffields;
997   ierr = CeedOperatorGetFields(op, &opfields, NULL); CeedChk(ierr);
998   ierr = CeedQFunctionGetFields(qf, &qffields, NULL); CeedChk(ierr);
999   CeedInt numinputfields;
1000   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, NULL); CeedChk(ierr);
1001   for (CeedInt i=0; i<numinputfields; i++) {
1002     CeedVector vec;
1003     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChk(ierr);
1004     if (vec == CEED_VECTOR_ACTIVE) {
1005       CeedEvalMode emode;
1006       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChk(ierr);
1007       interp = interp || emode == CEED_EVAL_INTERP;
1008       grad = grad || emode == CEED_EVAL_GRAD;
1009       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChk(ierr);
1010       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
1011       CeedChk(ierr);
1012     }
1013   }
1014   if (!basis)
1015     // LCOV_EXCL_START
1016     return CeedError(ceed, 1, "No active field set");
1017   // LCOV_EXCL_STOP
1018   CeedInt P1d, Q1d, elemsize, nqpts, dim, ncomp = 1, nelem = 1, lsize = 1;
1019   ierr = CeedBasisGetNumNodes1D(basis, &P1d); CeedChk(ierr);
1020   ierr = CeedBasisGetNumNodes(basis, &elemsize); CeedChk(ierr);
1021   ierr = CeedBasisGetNumQuadraturePoints1D(basis, &Q1d); CeedChk(ierr);
1022   ierr = CeedBasisGetNumQuadraturePoints(basis, &nqpts); CeedChk(ierr);
1023   ierr = CeedBasisGetDimension(basis, &dim); CeedChk(ierr);
1024   ierr = CeedBasisGetNumComponents(basis, &ncomp); CeedChk(ierr);
1025   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChk(ierr);
1026   ierr = CeedElemRestrictionGetLVectorSize(rstr, &lsize); CeedChk(ierr);
1027 
1028   // Build and diagonalize 1D Mass and Laplacian
1029   bool tensorbasis;
1030   ierr = CeedBasisIsTensor(basis, &tensorbasis); CeedChk(ierr);
1031   if (!tensorbasis)
1032     // LCOV_EXCL_START
1033     return CeedError(ceed, 1, "FDMElementInverse only supported for tensor "
1034                      "bases");
1035   // LCOV_EXCL_STOP
1036   CeedScalar *work, *mass, *laplace, *x, *x2, *lambda;
1037   ierr = CeedMalloc(Q1d*P1d, &work); CeedChk(ierr);
1038   ierr = CeedMalloc(P1d*P1d, &mass); CeedChk(ierr);
1039   ierr = CeedMalloc(P1d*P1d, &laplace); CeedChk(ierr);
1040   ierr = CeedMalloc(P1d*P1d, &x); CeedChk(ierr);
1041   ierr = CeedMalloc(P1d*P1d, &x2); CeedChk(ierr);
1042   ierr = CeedMalloc(P1d, &lambda); CeedChk(ierr);
1043   // -- Mass
1044   const CeedScalar *interp1d, *grad1d, *qweight1d;
1045   ierr = CeedBasisGetInterp1D(basis, &interp1d); CeedChk(ierr);
1046   ierr = CeedBasisGetGrad1D(basis, &grad1d); CeedChk(ierr);
1047   ierr = CeedBasisGetQWeights(basis, &qweight1d); CeedChk(ierr);
1048   for (CeedInt i=0; i<Q1d; i++)
1049     for (CeedInt j=0; j<P1d; j++)
1050       work[i+j*Q1d] = interp1d[i*P1d+j]*qweight1d[i];
1051   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1052                             (const CeedScalar *)interp1d, mass, P1d, P1d, Q1d);
1053   CeedChk(ierr);
1054   // -- Laplacian
1055   for (CeedInt i=0; i<Q1d; i++)
1056     for (CeedInt j=0; j<P1d; j++)
1057       work[i+j*Q1d] = grad1d[i*P1d+j]*qweight1d[i];
1058   ierr = CeedMatrixMultiply(ceed, (const CeedScalar *)work,
1059                             (const CeedScalar *)grad1d, laplace, P1d, P1d, Q1d);
1060   CeedChk(ierr);
1061   // -- Diagonalize
1062   ierr = CeedSimultaneousDiagonalization(ceed, laplace, mass, x, lambda, P1d);
1063   CeedChk(ierr);
1064   ierr = CeedFree(&work); CeedChk(ierr);
1065   ierr = CeedFree(&mass); CeedChk(ierr);
1066   ierr = CeedFree(&laplace); CeedChk(ierr);
1067   for (CeedInt i=0; i<P1d; i++)
1068     for (CeedInt j=0; j<P1d; j++)
1069       x2[i+j*P1d] = x[j+i*P1d];
1070   ierr = CeedFree(&x); CeedChk(ierr);
1071 
1072   // Assemble QFunction
1073   CeedVector assembled;
1074   CeedElemRestriction rstr_qf;
1075   ierr =  CeedOperatorLinearAssembleQFunction(op, &assembled, &rstr_qf,
1076           request); CeedChk(ierr);
1077   ierr = CeedElemRestrictionDestroy(&rstr_qf); CeedChk(ierr);
1078   CeedScalar maxnorm = 0;
1079   ierr = CeedVectorNorm(assembled, CEED_NORM_MAX, &maxnorm); CeedChk(ierr);
1080 
1081   // Calculate element averages
1082   CeedInt nfields = ((interp?1:0) + (grad?dim:0))*((interp?1:0) + (grad?dim:0));
1083   CeedScalar *elemavg;
1084   const CeedScalar *assembledarray, *qweightsarray;
1085   CeedVector qweights;
1086   ierr = CeedVectorCreate(ceedparent, nqpts, &qweights); CeedChk(ierr);
1087   ierr = CeedBasisApply(basis, 1, CEED_NOTRANSPOSE, CEED_EVAL_WEIGHT,
1088                         CEED_VECTOR_NONE, qweights); CeedChk(ierr);
1089   ierr = CeedVectorGetArrayRead(assembled, CEED_MEM_HOST, &assembledarray);
1090   CeedChk(ierr);
1091   ierr = CeedVectorGetArrayRead(qweights, CEED_MEM_HOST, &qweightsarray);
1092   CeedChk(ierr);
1093   ierr = CeedCalloc(nelem, &elemavg); CeedChk(ierr);
1094   for (CeedInt e=0; e<nelem; e++) {
1095     CeedInt count = 0;
1096     for (CeedInt q=0; q<nqpts; q++)
1097       for (CeedInt i=0; i<ncomp*ncomp*nfields; i++)
1098         if (fabs(assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1099                                                                   i*nqpts + q]) > maxnorm*1e-12) {
1100           elemavg[e] += assembledarray[e*nelem*nqpts*ncomp*ncomp*nfields +
1101                                        i*nqpts + q] / qweightsarray[q];
1102           count++;
1103         }
1104     if (count)
1105       elemavg[e] /= count;
1106   }
1107   ierr = CeedVectorRestoreArrayRead(assembled, &assembledarray); CeedChk(ierr);
1108   ierr = CeedVectorDestroy(&assembled); CeedChk(ierr);
1109   ierr = CeedVectorRestoreArrayRead(qweights, &qweightsarray); CeedChk(ierr);
1110   ierr = CeedVectorDestroy(&qweights); CeedChk(ierr);
1111 
1112   // Build FDM diagonal
1113   CeedVector qdata;
1114   CeedScalar *qdataarray;
1115   ierr = CeedVectorCreate(ceedparent, nelem*ncomp*lsize, &qdata); CeedChk(ierr);
1116   ierr = CeedVectorSetArray(qdata, CEED_MEM_HOST, CEED_COPY_VALUES, NULL);
1117   CeedChk(ierr);
1118   ierr = CeedVectorGetArray(qdata, CEED_MEM_HOST, &qdataarray); CeedChk(ierr);
1119   for (CeedInt e=0; e<nelem; e++)
1120     for (CeedInt c=0; c<ncomp; c++)
1121       for (CeedInt n=0; n<lsize; n++) {
1122         if (interp)
1123           qdataarray[(e*ncomp+c)*lsize+n] = 1;
1124         if (grad)
1125           for (CeedInt d=0; d<dim; d++) {
1126             CeedInt i = (n / CeedIntPow(P1d, d)) % P1d;
1127             qdataarray[(e*ncomp+c)*lsize+n] += lambda[i];
1128           }
1129         qdataarray[(e*ncomp+c)*lsize+n] = 1 / (elemavg[e] *
1130                                                qdataarray[(e*ncomp+c)*lsize+n]);
1131       }
1132   ierr = CeedFree(&elemavg); CeedChk(ierr);
1133   ierr = CeedVectorRestoreArray(qdata, &qdataarray); CeedChk(ierr);
1134 
1135   // Setup FDM operator
1136   // -- Basis
1137   CeedBasis fdm_basis;
1138   CeedScalar *graddummy, *qrefdummy, *qweightdummy;
1139   ierr = CeedCalloc(P1d*P1d, &graddummy); CeedChk(ierr);
1140   ierr = CeedCalloc(P1d, &qrefdummy); CeedChk(ierr);
1141   ierr = CeedCalloc(P1d, &qweightdummy); CeedChk(ierr);
1142   ierr = CeedBasisCreateTensorH1(ceedparent, dim, ncomp, P1d, P1d, x2,
1143                                  graddummy, qrefdummy, qweightdummy,
1144                                  &fdm_basis); CeedChk(ierr);
1145   ierr = CeedFree(&graddummy); CeedChk(ierr);
1146   ierr = CeedFree(&qrefdummy); CeedChk(ierr);
1147   ierr = CeedFree(&qweightdummy); CeedChk(ierr);
1148   ierr = CeedFree(&x2); CeedChk(ierr);
1149   ierr = CeedFree(&lambda); CeedChk(ierr);
1150 
1151   // -- Restriction
1152   CeedElemRestriction rstr_i;
1153   CeedInt strides[3] = {1, lsize, lsize*ncomp};
1154   ierr = CeedElemRestrictionCreateStrided(ceedparent, nelem, lsize, ncomp,
1155                                           lsize*nelem*ncomp, strides, &rstr_i);
1156   CeedChk(ierr);
1157   // -- QFunction
1158   CeedQFunction mass_qf;
1159   ierr = CeedQFunctionCreateInteriorByName(ceedparent, "MassApply", &mass_qf);
1160   CeedChk(ierr);
1161   // -- Operator
1162   ierr = CeedOperatorCreate(ceedparent, mass_qf, NULL, NULL, fdminv);
1163   CeedChk(ierr);
1164   CeedOperatorSetField(*fdminv, "u", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1165   CeedChk(ierr);
1166   CeedOperatorSetField(*fdminv, "qdata", rstr_i, CEED_BASIS_COLLOCATED, qdata);
1167   CeedChk(ierr);
1168   CeedOperatorSetField(*fdminv, "v", rstr_i, fdm_basis, CEED_VECTOR_ACTIVE);
1169   CeedChk(ierr);
1170 
1171   // Cleanup
1172   ierr = CeedVectorDestroy(&qdata); CeedChk(ierr);
1173   ierr = CeedBasisDestroy(&fdm_basis); CeedChk(ierr);
1174   ierr = CeedElemRestrictionDestroy(&rstr_i); CeedChk(ierr);
1175   ierr = CeedQFunctionDestroy(&mass_qf); CeedChk(ierr);
1176 
1177   return 0;
1178 }
1179 
1180 //------------------------------------------------------------------------------
1181 // Operator Destroy
1182 //------------------------------------------------------------------------------
1183 static int CeedOperatorDestroy_Ref(CeedOperator op) {
1184   int ierr;
1185   CeedOperator_Ref *impl;
1186   ierr = CeedOperatorGetData(op, (void *)&impl); CeedChk(ierr);
1187 
1188   for (CeedInt i=0; i<impl->numein+impl->numeout; i++) {
1189     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChk(ierr);
1190   }
1191   ierr = CeedFree(&impl->evecs); CeedChk(ierr);
1192   ierr = CeedFree(&impl->edata); CeedChk(ierr);
1193   ierr = CeedFree(&impl->inputstate); CeedChk(ierr);
1194 
1195   for (CeedInt i=0; i<impl->numein; i++) {
1196     ierr = CeedVectorDestroy(&impl->evecsin[i]); CeedChk(ierr);
1197     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChk(ierr);
1198   }
1199   ierr = CeedFree(&impl->evecsin); CeedChk(ierr);
1200   ierr = CeedFree(&impl->qvecsin); CeedChk(ierr);
1201 
1202   for (CeedInt i=0; i<impl->numeout; i++) {
1203     ierr = CeedVectorDestroy(&impl->evecsout[i]); CeedChk(ierr);
1204     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChk(ierr);
1205   }
1206   ierr = CeedFree(&impl->evecsout); CeedChk(ierr);
1207   ierr = CeedFree(&impl->qvecsout); CeedChk(ierr);
1208 
1209   ierr = CeedFree(&impl); CeedChk(ierr);
1210   return 0;
1211 }
1212 
1213 //------------------------------------------------------------------------------
1214 // Operator Create
1215 //------------------------------------------------------------------------------
1216 int CeedOperatorCreate_Ref(CeedOperator op) {
1217   int ierr;
1218   Ceed ceed;
1219   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1220   CeedOperator_Ref *impl;
1221 
1222   ierr = CeedCalloc(1, &impl); CeedChk(ierr);
1223   ierr = CeedOperatorSetData(op, (void *)&impl); CeedChk(ierr);
1224 
1225   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction",
1226                                 CeedOperatorLinearAssembleQFunction_Ref);
1227   CeedChk(ierr);
1228   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal",
1229                                 CeedOperatorLinearAssembleDiagonal_Ref);
1230   CeedChk(ierr);
1231   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1232                                 "LinearAssembleAddPointBlockDiagonal",
1233                                 CeedOperatorLinearAssemblePointBlockDiagonal_Ref);
1234   CeedChk(ierr);
1235   ierr = CeedSetBackendFunction(ceed, "Operator", op, "CreateFDMElementInverse",
1236                                 CeedOperatorCreateFDMElementInverse_Ref);
1237   CeedChk(ierr);
1238   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1239                                 CeedOperatorApply_Ref); CeedChk(ierr);
1240   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1241                                 CeedOperatorDestroy_Ref); CeedChk(ierr);
1242   return 0;
1243 }
1244 
1245 //------------------------------------------------------------------------------
1246 // Composite Operator Create
1247 //------------------------------------------------------------------------------
1248 int CeedCompositeOperatorCreate_Ref(CeedOperator op) {
1249   int ierr;
1250   Ceed ceed;
1251   ierr = CeedOperatorGetCeed(op, &ceed); CeedChk(ierr);
1252   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal",
1253                                 CeedOperatorLinearAssembleDiagonal_Ref);
1254   CeedChk(ierr);
1255   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1256                                 "LinearAssembleAddPointBlockDiagonal",
1257                                 CeedOperatorLinearAssemblePointBlockDiagonal_Ref);
1258   CeedChk(ierr);
1259   return 0;
1260 }
1261 //------------------------------------------------------------------------------
1262