xref: /libCEED/backends/cuda-ref/ceed-cuda-ref-operator.c (revision cc132f9a20f00d9393835714dbcdd5760a8efede)
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/ceed.h>
18 #include <ceed/backend.h>
19 #include <assert.h>
20 #include <cuda.h>
21 #include <cuda_runtime.h>
22 #include <stdbool.h>
23 #include <string.h>
24 #include "ceed-cuda-ref.h"
25 #include "../cuda/ceed-cuda-compile.h"
26 
27 //------------------------------------------------------------------------------
28 // Destroy operator
29 //------------------------------------------------------------------------------
30 static int CeedOperatorDestroy_Cuda(CeedOperator op) {
31   int ierr;
32   CeedOperator_Cuda *impl;
33   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
34 
35   // Apply data
36   for (CeedInt i = 0; i < impl->numein + impl->numeout; i++) {
37     ierr = CeedVectorDestroy(&impl->evecs[i]); CeedChkBackend(ierr);
38   }
39   ierr = CeedFree(&impl->evecs); CeedChkBackend(ierr);
40 
41   for (CeedInt i = 0; i < impl->numein; i++) {
42     ierr = CeedVectorDestroy(&impl->qvecsin[i]); CeedChkBackend(ierr);
43   }
44   ierr = CeedFree(&impl->qvecsin); CeedChkBackend(ierr);
45 
46   for (CeedInt i = 0; i < impl->numeout; i++) {
47     ierr = CeedVectorDestroy(&impl->qvecsout[i]); CeedChkBackend(ierr);
48   }
49   ierr = CeedFree(&impl->qvecsout); CeedChkBackend(ierr);
50 
51   // QFunction assembly data
52   for (CeedInt i=0; i<impl->qfnumactivein; i++) {
53     ierr = CeedVectorDestroy(&impl->qfactivein[i]); CeedChkBackend(ierr);
54   }
55   ierr = CeedFree(&impl->qfactivein); CeedChkBackend(ierr);
56 
57   // Diag data
58   if (impl->diag) {
59     Ceed ceed;
60     ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
61     CeedChk_Cu(ceed, cuModuleUnload(impl->diag->module));
62     ierr = CeedFree(&impl->diag->h_emodein); CeedChkBackend(ierr);
63     ierr = CeedFree(&impl->diag->h_emodeout); CeedChkBackend(ierr);
64     ierr = cudaFree(impl->diag->d_emodein); CeedChk_Cu(ceed, ierr);
65     ierr = cudaFree(impl->diag->d_emodeout); CeedChk_Cu(ceed, ierr);
66     ierr = cudaFree(impl->diag->d_identity); CeedChk_Cu(ceed, ierr);
67     ierr = cudaFree(impl->diag->d_interpin); CeedChk_Cu(ceed, ierr);
68     ierr = cudaFree(impl->diag->d_interpout); CeedChk_Cu(ceed, ierr);
69     ierr = cudaFree(impl->diag->d_gradin); CeedChk_Cu(ceed, ierr);
70     ierr = cudaFree(impl->diag->d_gradout); CeedChk_Cu(ceed, ierr);
71     ierr = CeedElemRestrictionDestroy(&impl->diag->pbdiagrstr);
72     CeedChkBackend(ierr);
73     ierr = CeedVectorDestroy(&impl->diag->elemdiag); CeedChkBackend(ierr);
74     ierr = CeedVectorDestroy(&impl->diag->pbelemdiag); CeedChkBackend(ierr);
75   }
76   ierr = CeedFree(&impl->diag); CeedChkBackend(ierr);
77 
78   if (impl->asmb) {
79     Ceed ceed;
80     ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
81     CeedChk_Cu(ceed, cuModuleUnload(impl->asmb->module));
82     ierr = cudaFree(impl->asmb->d_B_in); CeedChk_Cu(ceed, ierr);
83     ierr = cudaFree(impl->asmb->d_B_out); CeedChk_Cu(ceed, ierr);
84   }
85   ierr = CeedFree(&impl->asmb); CeedChkBackend(ierr);
86 
87   ierr = CeedFree(&impl); CeedChkBackend(ierr);
88   return CEED_ERROR_SUCCESS;
89 }
90 
91 //------------------------------------------------------------------------------
92 // Setup infields or outfields
93 //------------------------------------------------------------------------------
94 static int CeedOperatorSetupFields_Cuda(CeedQFunction qf, CeedOperator op,
95                                         bool isinput, CeedVector *evecs,
96                                         CeedVector *qvecs, CeedInt starte,
97                                         CeedInt numfields, CeedInt Q,
98                                         CeedInt numelements) {
99   CeedInt dim, ierr, size;
100   Ceed ceed;
101   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
102   CeedBasis basis;
103   CeedElemRestriction Erestrict;
104   CeedOperatorField *opfields;
105   CeedQFunctionField *qffields;
106   CeedVector fieldvec;
107   bool strided;
108   bool skiprestrict;
109 
110   if (isinput) {
111     ierr = CeedOperatorGetFields(op, NULL, &opfields, NULL, NULL);
112     CeedChkBackend(ierr);
113     ierr = CeedQFunctionGetFields(qf, NULL, &qffields, NULL, NULL);
114     CeedChkBackend(ierr);
115   } else {
116     ierr = CeedOperatorGetFields(op, NULL, NULL, NULL, &opfields);
117     CeedChkBackend(ierr);
118     ierr = CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qffields);
119     CeedChkBackend(ierr);
120   }
121 
122   // Loop over fields
123   for (CeedInt i = 0; i < numfields; i++) {
124     CeedEvalMode emode;
125     ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChkBackend(ierr);
126 
127     strided = false;
128     skiprestrict = false;
129     if (emode != CEED_EVAL_WEIGHT) {
130       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &Erestrict);
131       CeedChkBackend(ierr);
132 
133       // Check whether this field can skip the element restriction:
134       // must be passive input, with emode NONE, and have a strided restriction with
135       // CEED_STRIDES_BACKEND.
136 
137       // First, check whether the field is input or output:
138       if (isinput) {
139         // Check for passive input:
140         ierr = CeedOperatorFieldGetVector(opfields[i], &fieldvec); CeedChkBackend(ierr);
141         if (fieldvec != CEED_VECTOR_ACTIVE) {
142           // Check emode
143           if (emode == CEED_EVAL_NONE) {
144             // Check for strided restriction
145             ierr = CeedElemRestrictionIsStrided(Erestrict, &strided);
146             CeedChkBackend(ierr);
147             if (strided) {
148               // Check if vector is already in preferred backend ordering
149               ierr = CeedElemRestrictionHasBackendStrides(Erestrict,
150                      &skiprestrict); CeedChkBackend(ierr);
151             }
152           }
153         }
154       }
155       if (skiprestrict) {
156         // We do not need an E-Vector, but will use the input field vector's data
157         // directly in the operator application.
158         evecs[i + starte] = NULL;
159       } else {
160         ierr = CeedElemRestrictionCreateVector(Erestrict, NULL,
161                                                &evecs[i + starte]);
162         CeedChkBackend(ierr);
163       }
164     }
165 
166     switch (emode) {
167     case CEED_EVAL_NONE:
168       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChkBackend(ierr);
169       ierr = CeedVectorCreate(ceed, numelements * Q * size, &qvecs[i]);
170       CeedChkBackend(ierr);
171       break;
172     case CEED_EVAL_INTERP:
173       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChkBackend(ierr);
174       ierr = CeedVectorCreate(ceed, numelements * Q * size, &qvecs[i]);
175       CeedChkBackend(ierr);
176       break;
177     case CEED_EVAL_GRAD:
178       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChkBackend(ierr);
179       ierr = CeedQFunctionFieldGetSize(qffields[i], &size); CeedChkBackend(ierr);
180       ierr = CeedBasisGetDimension(basis, &dim); CeedChkBackend(ierr);
181       ierr = CeedVectorCreate(ceed, numelements * Q * size, &qvecs[i]);
182       CeedChkBackend(ierr);
183       break;
184     case CEED_EVAL_WEIGHT: // Only on input fields
185       ierr = CeedOperatorFieldGetBasis(opfields[i], &basis); CeedChkBackend(ierr);
186       ierr = CeedVectorCreate(ceed, numelements * Q, &qvecs[i]); CeedChkBackend(ierr);
187       ierr = CeedBasisApply(basis, numelements, CEED_NOTRANSPOSE,
188                             CEED_EVAL_WEIGHT, NULL, qvecs[i]); CeedChkBackend(ierr);
189       break;
190     case CEED_EVAL_DIV:
191       break; // TODO: Not implemented
192     case CEED_EVAL_CURL:
193       break; // TODO: Not implemented
194     }
195   }
196   return CEED_ERROR_SUCCESS;
197 }
198 
199 //------------------------------------------------------------------------------
200 // CeedOperator needs to connect all the named fields (be they active or passive)
201 //   to the named inputs and outputs of its CeedQFunction.
202 //------------------------------------------------------------------------------
203 static int CeedOperatorSetup_Cuda(CeedOperator op) {
204   int ierr;
205   bool setupdone;
206   ierr = CeedOperatorIsSetupDone(op, &setupdone); CeedChkBackend(ierr);
207   if (setupdone)
208     return CEED_ERROR_SUCCESS;
209   Ceed ceed;
210   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
211   CeedOperator_Cuda *impl;
212   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
213   CeedQFunction qf;
214   ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
215   CeedInt Q, numelements, numinputfields, numoutputfields;
216   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
217   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChkBackend(ierr);
218   CeedChkBackend(ierr);
219   CeedOperatorField *opinputfields, *opoutputfields;
220   ierr = CeedOperatorGetFields(op, &numinputfields, &opinputfields,
221                                &numoutputfields, &opoutputfields);
222   CeedChkBackend(ierr);
223   CeedQFunctionField *qfinputfields, *qfoutputfields;
224   ierr = CeedQFunctionGetFields(qf, NULL, &qfinputfields, NULL, &qfoutputfields);
225   CeedChkBackend(ierr);
226 
227   // Allocate
228   ierr = CeedCalloc(numinputfields + numoutputfields, &impl->evecs);
229   CeedChkBackend(ierr);
230 
231   ierr = CeedCalloc(CEED_FIELD_MAX, &impl->qvecsin); CeedChkBackend(ierr);
232   ierr = CeedCalloc(CEED_FIELD_MAX, &impl->qvecsout); CeedChkBackend(ierr);
233 
234   impl->numein = numinputfields; impl->numeout = numoutputfields;
235 
236   // Set up infield and outfield evecs and qvecs
237   // Infields
238   ierr = CeedOperatorSetupFields_Cuda(qf, op, true,
239                                       impl->evecs, impl->qvecsin, 0,
240                                       numinputfields, Q, numelements);
241   CeedChkBackend(ierr);
242 
243   // Outfields
244   ierr = CeedOperatorSetupFields_Cuda(qf, op, false,
245                                       impl->evecs, impl->qvecsout,
246                                       numinputfields, numoutputfields, Q,
247                                       numelements); CeedChkBackend(ierr);
248 
249   ierr = CeedOperatorSetSetupDone(op); CeedChkBackend(ierr);
250   return CEED_ERROR_SUCCESS;
251 }
252 
253 //------------------------------------------------------------------------------
254 // Setup Operator Inputs
255 //------------------------------------------------------------------------------
256 static inline int CeedOperatorSetupInputs_Cuda(CeedInt numinputfields,
257     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
258     CeedVector invec, const bool skipactive, CeedScalar *edata[2*CEED_FIELD_MAX],
259     CeedOperator_Cuda *impl, CeedRequest *request) {
260   CeedInt ierr;
261   CeedEvalMode emode;
262   CeedVector vec;
263   CeedElemRestriction Erestrict;
264 
265   for (CeedInt i = 0; i < numinputfields; i++) {
266     // Get input vector
267     ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
268     if (vec == CEED_VECTOR_ACTIVE) {
269       if (skipactive)
270         continue;
271       else
272         vec = invec;
273     }
274 
275     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
276     CeedChkBackend(ierr);
277     if (emode == CEED_EVAL_WEIGHT) { // Skip
278     } else {
279       // Get input vector
280       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
281       // Get input element restriction
282       ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
283       CeedChkBackend(ierr);
284       if (vec == CEED_VECTOR_ACTIVE)
285         vec = invec;
286       // Restrict, if necessary
287       if (!impl->evecs[i]) {
288         // No restriction for this field; read data directly from vec.
289         ierr = CeedVectorGetArrayRead(vec, CEED_MEM_DEVICE,
290                                       (const CeedScalar **) &edata[i]);
291         CeedChkBackend(ierr);
292       } else {
293         ierr = CeedElemRestrictionApply(Erestrict, CEED_NOTRANSPOSE, vec,
294                                         impl->evecs[i], request); CeedChkBackend(ierr);
295         // Get evec
296         ierr = CeedVectorGetArrayRead(impl->evecs[i], CEED_MEM_DEVICE,
297                                       (const CeedScalar **) &edata[i]);
298         CeedChkBackend(ierr);
299       }
300     }
301   }
302   return CEED_ERROR_SUCCESS;
303 }
304 
305 //------------------------------------------------------------------------------
306 // Input Basis Action
307 //------------------------------------------------------------------------------
308 static inline int CeedOperatorInputBasis_Cuda(CeedInt numelements,
309     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
310     CeedInt numinputfields, const bool skipactive,
311     CeedScalar *edata[2*CEED_FIELD_MAX],CeedOperator_Cuda *impl) {
312   CeedInt ierr;
313   CeedInt elemsize, size;
314   CeedElemRestriction Erestrict;
315   CeedEvalMode emode;
316   CeedBasis basis;
317 
318   for (CeedInt i=0; i<numinputfields; i++) {
319     // Skip active input
320     if (skipactive) {
321       CeedVector vec;
322       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
323       if (vec == CEED_VECTOR_ACTIVE)
324         continue;
325     }
326     // Get elemsize, emode, size
327     ierr = CeedOperatorFieldGetElemRestriction(opinputfields[i], &Erestrict);
328     CeedChkBackend(ierr);
329     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
330     CeedChkBackend(ierr);
331     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
332     CeedChkBackend(ierr);
333     ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChkBackend(ierr);
334     // Basis action
335     switch (emode) {
336     case CEED_EVAL_NONE:
337       ierr = CeedVectorSetArray(impl->qvecsin[i], CEED_MEM_DEVICE,
338                                 CEED_USE_POINTER, edata[i]); CeedChkBackend(ierr);
339       break;
340     case CEED_EVAL_INTERP:
341       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
342       CeedChkBackend(ierr);
343       ierr = CeedBasisApply(basis, numelements, CEED_NOTRANSPOSE,
344                             CEED_EVAL_INTERP, impl->evecs[i],
345                             impl->qvecsin[i]); CeedChkBackend(ierr);
346       break;
347     case CEED_EVAL_GRAD:
348       ierr = CeedOperatorFieldGetBasis(opinputfields[i], &basis);
349       CeedChkBackend(ierr);
350       ierr = CeedBasisApply(basis, numelements, CEED_NOTRANSPOSE,
351                             CEED_EVAL_GRAD, impl->evecs[i],
352                             impl->qvecsin[i]); CeedChkBackend(ierr);
353       break;
354     case CEED_EVAL_WEIGHT:
355       break; // No action
356     case CEED_EVAL_DIV:
357       break; // TODO: Not implemented
358     case CEED_EVAL_CURL:
359       break; // TODO: Not implemented
360     }
361   }
362   return CEED_ERROR_SUCCESS;
363 }
364 
365 //------------------------------------------------------------------------------
366 // Restore Input Vectors
367 //------------------------------------------------------------------------------
368 static inline int CeedOperatorRestoreInputs_Cuda(CeedInt numinputfields,
369     CeedQFunctionField *qfinputfields, CeedOperatorField *opinputfields,
370     const bool skipactive, CeedScalar *edata[2*CEED_FIELD_MAX],
371     CeedOperator_Cuda *impl) {
372   CeedInt ierr;
373   CeedEvalMode emode;
374   CeedVector vec;
375 
376   for (CeedInt i = 0; i < numinputfields; i++) {
377     // Skip active input
378     if (skipactive) {
379       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
380       if (vec == CEED_VECTOR_ACTIVE)
381         continue;
382     }
383     ierr = CeedQFunctionFieldGetEvalMode(qfinputfields[i], &emode);
384     CeedChkBackend(ierr);
385     if (emode == CEED_EVAL_WEIGHT) { // Skip
386     } else {
387       if (!impl->evecs[i]) {  // This was a skiprestrict case
388         ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
389         ierr = CeedVectorRestoreArrayRead(vec,
390                                           (const CeedScalar **)&edata[i]);
391         CeedChkBackend(ierr);
392       } else {
393         ierr = CeedVectorRestoreArrayRead(impl->evecs[i],
394                                           (const CeedScalar **) &edata[i]);
395         CeedChkBackend(ierr);
396       }
397     }
398   }
399   return CEED_ERROR_SUCCESS;
400 }
401 
402 //------------------------------------------------------------------------------
403 // Apply and add to output
404 //------------------------------------------------------------------------------
405 static int CeedOperatorApplyAdd_Cuda(CeedOperator op, CeedVector invec,
406                                      CeedVector outvec, CeedRequest *request) {
407   int ierr;
408   CeedOperator_Cuda *impl;
409   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
410   CeedQFunction qf;
411   ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
412   CeedInt Q, numelements, elemsize, numinputfields, numoutputfields, size;
413   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
414   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChkBackend(ierr);
415   CeedChkBackend(ierr);
416   CeedOperatorField *opinputfields, *opoutputfields;
417   ierr = CeedOperatorGetFields(op, &numinputfields, &opinputfields,
418                                &numoutputfields, &opoutputfields);
419   CeedChkBackend(ierr);
420   CeedQFunctionField *qfinputfields, *qfoutputfields;
421   ierr = CeedQFunctionGetFields(qf, NULL, &qfinputfields, NULL, &qfoutputfields);
422   CeedChkBackend(ierr);
423   CeedEvalMode emode;
424   CeedVector vec;
425   CeedBasis basis;
426   CeedElemRestriction Erestrict;
427   CeedScalar *edata[2*CEED_FIELD_MAX] = {0};
428 
429   // Setup
430   ierr = CeedOperatorSetup_Cuda(op); CeedChkBackend(ierr);
431 
432   // Input Evecs and Restriction
433   ierr = CeedOperatorSetupInputs_Cuda(numinputfields, qfinputfields,
434                                       opinputfields, invec, false, edata,
435                                       impl, request); CeedChkBackend(ierr);
436 
437   // Input basis apply if needed
438   ierr = CeedOperatorInputBasis_Cuda(numelements, qfinputfields, opinputfields,
439                                      numinputfields, false, edata, impl);
440   CeedChkBackend(ierr);
441 
442   // Output pointers, as necessary
443   for (CeedInt i = 0; i < numoutputfields; i++) {
444     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
445     CeedChkBackend(ierr);
446     if (emode == CEED_EVAL_NONE) {
447       // Set the output Q-Vector to use the E-Vector data directly.
448       ierr = CeedVectorGetArrayWrite(impl->evecs[i + impl->numein], CEED_MEM_DEVICE,
449                                      &edata[i + numinputfields]); CeedChkBackend(ierr);
450       ierr = CeedVectorSetArray(impl->qvecsout[i], CEED_MEM_DEVICE,
451                                 CEED_USE_POINTER, edata[i + numinputfields]);
452       CeedChkBackend(ierr);
453     }
454   }
455 
456   // Q function
457   ierr = CeedQFunctionApply(qf, numelements * Q, impl->qvecsin, impl->qvecsout);
458   CeedChkBackend(ierr);
459 
460   // Output basis apply if needed
461   for (CeedInt i = 0; i < numoutputfields; i++) {
462     // Get elemsize, emode, size
463     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
464     CeedChkBackend(ierr);
465     ierr = CeedElemRestrictionGetElementSize(Erestrict, &elemsize);
466     CeedChkBackend(ierr);
467     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
468     CeedChkBackend(ierr);
469     ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
470     CeedChkBackend(ierr);
471     // Basis action
472     switch (emode) {
473     case CEED_EVAL_NONE:
474       break;
475     case CEED_EVAL_INTERP:
476       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
477       CeedChkBackend(ierr);
478       ierr = CeedBasisApply(basis, numelements, CEED_TRANSPOSE,
479                             CEED_EVAL_INTERP, impl->qvecsout[i],
480                             impl->evecs[i + impl->numein]); CeedChkBackend(ierr);
481       break;
482     case CEED_EVAL_GRAD:
483       ierr = CeedOperatorFieldGetBasis(opoutputfields[i], &basis);
484       CeedChkBackend(ierr);
485       ierr = CeedBasisApply(basis, numelements, CEED_TRANSPOSE,
486                             CEED_EVAL_GRAD, impl->qvecsout[i],
487                             impl->evecs[i + impl->numein]); CeedChkBackend(ierr);
488       break;
489     // LCOV_EXCL_START
490     case CEED_EVAL_WEIGHT: {
491       Ceed ceed;
492       ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
493       return CeedError(ceed, CEED_ERROR_BACKEND,
494                        "CEED_EVAL_WEIGHT cannot be an output evaluation mode");
495       break; // Should not occur
496     }
497     case CEED_EVAL_DIV:
498       break; // TODO: Not implemented
499     case CEED_EVAL_CURL:
500       break; // TODO: Not implemented
501       // LCOV_EXCL_STOP
502     }
503   }
504 
505   // Output restriction
506   for (CeedInt i = 0; i < numoutputfields; i++) {
507     // Restore evec
508     ierr = CeedQFunctionFieldGetEvalMode(qfoutputfields[i], &emode);
509     CeedChkBackend(ierr);
510     if (emode == CEED_EVAL_NONE) {
511       ierr = CeedVectorRestoreArray(impl->evecs[i+impl->numein],
512                                     &edata[i + numinputfields]);
513       CeedChkBackend(ierr);
514     }
515     // Get output vector
516     ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec);
517     CeedChkBackend(ierr);
518     // Restrict
519     ierr = CeedOperatorFieldGetElemRestriction(opoutputfields[i], &Erestrict);
520     CeedChkBackend(ierr);
521     // Active
522     if (vec == CEED_VECTOR_ACTIVE)
523       vec = outvec;
524 
525     ierr = CeedElemRestrictionApply(Erestrict, CEED_TRANSPOSE,
526                                     impl->evecs[i + impl->numein], vec,
527                                     request); CeedChkBackend(ierr);
528   }
529 
530   // Restore input arrays
531   ierr = CeedOperatorRestoreInputs_Cuda(numinputfields, qfinputfields,
532                                         opinputfields, false, edata, impl);
533   CeedChkBackend(ierr);
534   return CEED_ERROR_SUCCESS;
535 }
536 
537 //------------------------------------------------------------------------------
538 // Core code for assembling linear QFunction
539 //------------------------------------------------------------------------------
540 static inline int CeedOperatorLinearAssembleQFunctionCore_Cuda(CeedOperator op,
541     bool build_objects, CeedVector *assembled, CeedElemRestriction *rstr,
542     CeedRequest *request) {
543   int ierr;
544   CeedOperator_Cuda *impl;
545   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
546   CeedQFunction qf;
547   ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
548   CeedInt Q, numelements, numinputfields, numoutputfields, size;
549   ierr = CeedOperatorGetNumQuadraturePoints(op, &Q); CeedChkBackend(ierr);
550   ierr = CeedOperatorGetNumElements(op, &numelements); CeedChkBackend(ierr);
551   CeedChkBackend(ierr);
552   CeedOperatorField *opinputfields, *opoutputfields;
553   ierr = CeedOperatorGetFields(op, &numinputfields, &opinputfields,
554                                &numoutputfields, &opoutputfields);
555   CeedChkBackend(ierr);
556   CeedQFunctionField *qfinputfields, *qfoutputfields;
557   ierr = CeedQFunctionGetFields(qf, NULL, &qfinputfields, NULL, &qfoutputfields);
558   CeedChkBackend(ierr);
559   CeedVector vec;
560   CeedInt numactivein = impl->qfnumactivein, numactiveout = impl->qfnumactiveout;
561   CeedVector *activein = impl->qfactivein;
562   CeedScalar *a, *tmp;
563   Ceed ceed, ceedparent;
564   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
565   ierr = CeedGetOperatorFallbackParentCeed(ceed, &ceedparent);
566   CeedChkBackend(ierr);
567   ceedparent = ceedparent ? ceedparent : ceed;
568   CeedScalar *edata[2*CEED_FIELD_MAX];
569 
570   // Setup
571   ierr = CeedOperatorSetup_Cuda(op); CeedChkBackend(ierr);
572 
573   // Check for identity
574   bool identityqf;
575   ierr = CeedQFunctionIsIdentity(qf, &identityqf); CeedChkBackend(ierr);
576   if (identityqf)
577     // LCOV_EXCL_START
578     return CeedError(ceed, CEED_ERROR_BACKEND,
579                      "Assembling identity QFunctions not supported");
580   // LCOV_EXCL_STOP
581 
582   // Input Evecs and Restriction
583   ierr = CeedOperatorSetupInputs_Cuda(numinputfields, qfinputfields,
584                                       opinputfields, NULL, true, edata,
585                                       impl, request); CeedChkBackend(ierr);
586 
587   // Count number of active input fields
588   if (!numactivein) {
589     for (CeedInt i=0; i<numinputfields; i++) {
590       // Get input vector
591       ierr = CeedOperatorFieldGetVector(opinputfields[i], &vec); CeedChkBackend(ierr);
592       // Check if active input
593       if (vec == CEED_VECTOR_ACTIVE) {
594         ierr = CeedQFunctionFieldGetSize(qfinputfields[i], &size); CeedChkBackend(ierr);
595         ierr = CeedVectorSetValue(impl->qvecsin[i], 0.0); CeedChkBackend(ierr);
596         ierr = CeedVectorGetArray(impl->qvecsin[i], CEED_MEM_DEVICE, &tmp);
597         CeedChkBackend(ierr);
598         ierr = CeedRealloc(numactivein + size, &activein); CeedChkBackend(ierr);
599         for (CeedInt field = 0; field < size; field++) {
600           ierr = CeedVectorCreate(ceed, Q*numelements,
601                                   &activein[numactivein+field]); CeedChkBackend(ierr);
602           ierr = CeedVectorSetArray(activein[numactivein+field], CEED_MEM_DEVICE,
603                                     CEED_USE_POINTER, &tmp[field*Q*numelements]);
604           CeedChkBackend(ierr);
605         }
606         numactivein += size;
607         ierr = CeedVectorRestoreArray(impl->qvecsin[i], &tmp); CeedChkBackend(ierr);
608       }
609     }
610     impl->qfnumactivein = numactivein;
611     impl->qfactivein = activein;
612   }
613 
614   // Count number of active output fields
615   if (!numactiveout) {
616     for (CeedInt i=0; i<numoutputfields; i++) {
617       // Get output vector
618       ierr = CeedOperatorFieldGetVector(opoutputfields[i], &vec);
619       CeedChkBackend(ierr);
620       // Check if active output
621       if (vec == CEED_VECTOR_ACTIVE) {
622         ierr = CeedQFunctionFieldGetSize(qfoutputfields[i], &size);
623         CeedChkBackend(ierr);
624         numactiveout += size;
625       }
626     }
627     impl->qfnumactiveout = numactiveout;
628   }
629 
630   // Check sizes
631   if (!numactivein || !numactiveout)
632     // LCOV_EXCL_START
633     return CeedError(ceed, CEED_ERROR_BACKEND,
634                      "Cannot assemble QFunction without active inputs "
635                      "and outputs");
636   // LCOV_EXCL_STOP
637 
638   // Build objects if needed
639   if (build_objects) {
640     // Create output restriction
641     CeedInt strides[3] = {1, numelements*Q, Q}; /* *NOPAD* */
642     ierr = CeedElemRestrictionCreateStrided(ceedparent, numelements, Q,
643                                             numactivein*numactiveout,
644                                             numactivein*numactiveout*numelements*Q,
645                                             strides, rstr); CeedChkBackend(ierr);
646     // Create assembled vector
647     ierr = CeedVectorCreate(ceedparent, numelements*Q*numactivein*numactiveout,
648                             assembled); CeedChkBackend(ierr);
649   }
650   ierr = CeedVectorSetValue(*assembled, 0.0); CeedChkBackend(ierr);
651   ierr = CeedVectorGetArray(*assembled, CEED_MEM_DEVICE, &a);
652   CeedChkBackend(ierr);
653 
654   // Input basis apply
655   ierr = CeedOperatorInputBasis_Cuda(numelements, qfinputfields, opinputfields,
656                                      numinputfields, true, edata, impl);
657   CeedChkBackend(ierr);
658 
659   // Assemble QFunction
660   for (CeedInt in=0; in<numactivein; in++) {
661     // Set Inputs
662     ierr = CeedVectorSetValue(activein[in], 1.0); CeedChkBackend(ierr);
663     if (numactivein > 1) {
664       ierr = CeedVectorSetValue(activein[(in+numactivein-1)%numactivein],
665                                 0.0); CeedChkBackend(ierr);
666     }
667     // Set Outputs
668     for (CeedInt out=0; out<numoutputfields; out++) {
669       // Get output vector
670       ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
671       CeedChkBackend(ierr);
672       // Check if active output
673       if (vec == CEED_VECTOR_ACTIVE) {
674         CeedVectorSetArray(impl->qvecsout[out], CEED_MEM_DEVICE,
675                            CEED_USE_POINTER, a); CeedChkBackend(ierr);
676         ierr = CeedQFunctionFieldGetSize(qfoutputfields[out], &size);
677         CeedChkBackend(ierr);
678         a += size*Q*numelements; // Advance the pointer by the size of the output
679       }
680     }
681     // Apply QFunction
682     ierr = CeedQFunctionApply(qf, Q*numelements, impl->qvecsin, impl->qvecsout);
683     CeedChkBackend(ierr);
684   }
685 
686   // Un-set output Qvecs to prevent accidental overwrite of Assembled
687   for (CeedInt out=0; out<numoutputfields; out++) {
688     // Get output vector
689     ierr = CeedOperatorFieldGetVector(opoutputfields[out], &vec);
690     CeedChkBackend(ierr);
691     // Check if active output
692     if (vec == CEED_VECTOR_ACTIVE) {
693       ierr = CeedVectorTakeArray(impl->qvecsout[out], CEED_MEM_DEVICE, NULL);
694       CeedChkBackend(ierr);
695     }
696   }
697 
698   // Restore input arrays
699   ierr = CeedOperatorRestoreInputs_Cuda(numinputfields, qfinputfields,
700                                         opinputfields, true, edata, impl);
701   CeedChkBackend(ierr);
702 
703   // Restore output
704   ierr = CeedVectorRestoreArray(*assembled, &a); CeedChkBackend(ierr);
705 
706   return CEED_ERROR_SUCCESS;
707 }
708 
709 //------------------------------------------------------------------------------
710 // Assemble Linear QFunction
711 //------------------------------------------------------------------------------
712 static int CeedOperatorLinearAssembleQFunction_Cuda(CeedOperator op,
713     CeedVector *assembled, CeedElemRestriction *rstr, CeedRequest *request) {
714   return CeedOperatorLinearAssembleQFunctionCore_Cuda(op, true, assembled, rstr,
715          request);
716 }
717 
718 //------------------------------------------------------------------------------
719 // Update Assembled Linear QFunction
720 //------------------------------------------------------------------------------
721 static int CeedOperatorLinearAssembleQFunctionUpdate_Cuda(CeedOperator op,
722     CeedVector assembled, CeedElemRestriction rstr, CeedRequest *request) {
723   return CeedOperatorLinearAssembleQFunctionCore_Cuda(op, false, &assembled,
724          &rstr, request);
725 }
726 
727 //------------------------------------------------------------------------------
728 // Diagonal assembly kernels
729 //------------------------------------------------------------------------------
730 // *INDENT-OFF*
731 static const char *diagonalkernels = QUOTE(
732 
733 typedef enum {
734   /// Perform no evaluation (either because there is no data or it is already at
735   /// quadrature points)
736   CEED_EVAL_NONE   = 0,
737   /// Interpolate from nodes to quadrature points
738   CEED_EVAL_INTERP = 1,
739   /// Evaluate gradients at quadrature points from input in a nodal basis
740   CEED_EVAL_GRAD   = 2,
741   /// Evaluate divergence at quadrature points from input in a nodal basis
742   CEED_EVAL_DIV    = 4,
743   /// Evaluate curl at quadrature points from input in a nodal basis
744   CEED_EVAL_CURL   = 8,
745   /// Using no input, evaluate quadrature weights on the reference element
746   CEED_EVAL_WEIGHT = 16,
747 } CeedEvalMode;
748 
749 //------------------------------------------------------------------------------
750 // Get Basis Emode Pointer
751 //------------------------------------------------------------------------------
752 extern "C" __device__ void CeedOperatorGetBasisPointer_Cuda(const CeedScalar **basisptr,
753     CeedEvalMode emode, const CeedScalar *identity, const CeedScalar *interp,
754     const CeedScalar *grad) {
755   switch (emode) {
756   case CEED_EVAL_NONE:
757     *basisptr = identity;
758     break;
759   case CEED_EVAL_INTERP:
760     *basisptr = interp;
761     break;
762   case CEED_EVAL_GRAD:
763     *basisptr = grad;
764     break;
765   case CEED_EVAL_WEIGHT:
766   case CEED_EVAL_DIV:
767   case CEED_EVAL_CURL:
768     break; // Caught by QF Assembly
769   }
770 }
771 
772 //------------------------------------------------------------------------------
773 // Core code for diagonal assembly
774 //------------------------------------------------------------------------------
775 __device__ void diagonalCore(const CeedInt nelem,
776     const CeedScalar maxnorm, const bool pointBlock,
777     const CeedScalar *identity,
778     const CeedScalar *interpin, const CeedScalar *gradin,
779     const CeedScalar *interpout, const CeedScalar *gradout,
780     const CeedEvalMode *emodein, const CeedEvalMode *emodeout,
781     const CeedScalar *__restrict__ assembledqfarray,
782     CeedScalar *__restrict__ elemdiagarray) {
783   const int tid = threadIdx.x; // running with P threads, tid is evec node
784   const CeedScalar qfvaluebound = maxnorm*1e-12;
785 
786   // Compute the diagonal of B^T D B
787   // Each element
788   for (CeedInt e = blockIdx.x*blockDim.z + threadIdx.z; e < nelem;
789        e += gridDim.x*blockDim.z) {
790     CeedInt dout = -1;
791     // Each basis eval mode pair
792     for (CeedInt eout = 0; eout < NUMEMODEOUT; eout++) {
793       const CeedScalar *bt = NULL;
794       if (emodeout[eout] == CEED_EVAL_GRAD)
795         dout += 1;
796       CeedOperatorGetBasisPointer_Cuda(&bt, emodeout[eout], identity, interpout,
797                                       &gradout[dout*NQPTS*NNODES]);
798       CeedInt din = -1;
799       for (CeedInt ein = 0; ein < NUMEMODEIN; ein++) {
800         const CeedScalar *b = NULL;
801         if (emodein[ein] == CEED_EVAL_GRAD)
802           din += 1;
803         CeedOperatorGetBasisPointer_Cuda(&b, emodein[ein], identity, interpin,
804                                         &gradin[din*NQPTS*NNODES]);
805         // Each component
806         for (CeedInt compOut = 0; compOut < NCOMP; compOut++) {
807           // Each qpoint/node pair
808           if (pointBlock) {
809             // Point Block Diagonal
810             for (CeedInt compIn = 0; compIn < NCOMP; compIn++) {
811               CeedScalar evalue = 0.;
812               for (CeedInt q = 0; q < NQPTS; q++) {
813                 const CeedScalar qfvalue =
814                   assembledqfarray[((((ein*NCOMP+compIn)*NUMEMODEOUT+eout)*
815                                      NCOMP+compOut)*nelem+e)*NQPTS+q];
816                 if (abs(qfvalue) > qfvaluebound)
817                   evalue += bt[q*NNODES+tid] * qfvalue * b[q*NNODES+tid];
818               }
819               elemdiagarray[((compOut*NCOMP+compIn)*nelem+e)*NNODES+tid] += evalue;
820             }
821           } else {
822             // Diagonal Only
823             CeedScalar evalue = 0.;
824             for (CeedInt q = 0; q < NQPTS; q++) {
825               const CeedScalar qfvalue =
826                 assembledqfarray[((((ein*NCOMP+compOut)*NUMEMODEOUT+eout)*
827                                    NCOMP+compOut)*nelem+e)*NQPTS+q];
828               if (abs(qfvalue) > qfvaluebound)
829                 evalue += bt[q*NNODES+tid] * qfvalue * b[q*NNODES+tid];
830             }
831             elemdiagarray[(compOut*nelem+e)*NNODES+tid] += evalue;
832           }
833         }
834       }
835     }
836   }
837 }
838 
839 //------------------------------------------------------------------------------
840 // Linear diagonal
841 //------------------------------------------------------------------------------
842 extern "C" __global__ void linearDiagonal(const CeedInt nelem,
843     const CeedScalar maxnorm, const CeedScalar *identity,
844     const CeedScalar *interpin, const CeedScalar *gradin,
845     const CeedScalar *interpout, const CeedScalar *gradout,
846     const CeedEvalMode *emodein, const CeedEvalMode *emodeout,
847     const CeedScalar *__restrict__ assembledqfarray,
848     CeedScalar *__restrict__ elemdiagarray) {
849   diagonalCore(nelem, maxnorm, false, identity, interpin, gradin, interpout,
850                gradout, emodein, emodeout, assembledqfarray, elemdiagarray);
851 }
852 
853 //------------------------------------------------------------------------------
854 // Linear point block diagonal
855 //------------------------------------------------------------------------------
856 extern "C" __global__ void linearPointBlockDiagonal(const CeedInt nelem,
857     const CeedScalar maxnorm, const CeedScalar *identity,
858     const CeedScalar *interpin, const CeedScalar *gradin,
859     const CeedScalar *interpout, const CeedScalar *gradout,
860     const CeedEvalMode *emodein, const CeedEvalMode *emodeout,
861     const CeedScalar *__restrict__ assembledqfarray,
862     CeedScalar *__restrict__ elemdiagarray) {
863   diagonalCore(nelem, maxnorm, true, identity, interpin, gradin, interpout,
864                gradout, emodein, emodeout, assembledqfarray, elemdiagarray);
865 }
866 
867 );
868 // *INDENT-ON*
869 
870 //------------------------------------------------------------------------------
871 // Create point block restriction
872 //------------------------------------------------------------------------------
873 static int CreatePBRestriction(CeedElemRestriction rstr,
874                                CeedElemRestriction *pbRstr) {
875   int ierr;
876   Ceed ceed;
877   ierr = CeedElemRestrictionGetCeed(rstr, &ceed); CeedChkBackend(ierr);
878   const CeedInt *offsets;
879   ierr = CeedElemRestrictionGetOffsets(rstr, CEED_MEM_HOST, &offsets);
880   CeedChkBackend(ierr);
881 
882   // Expand offsets
883   CeedInt nelem, ncomp, elemsize, compstride, max = 1, *pbOffsets;
884   ierr = CeedElemRestrictionGetNumElements(rstr, &nelem); CeedChkBackend(ierr);
885   ierr = CeedElemRestrictionGetNumComponents(rstr, &ncomp); CeedChkBackend(ierr);
886   ierr = CeedElemRestrictionGetElementSize(rstr, &elemsize); CeedChkBackend(ierr);
887   ierr = CeedElemRestrictionGetCompStride(rstr, &compstride);
888   CeedChkBackend(ierr);
889   CeedInt shift = ncomp;
890   if (compstride != 1)
891     shift *= ncomp;
892   ierr = CeedCalloc(nelem*elemsize, &pbOffsets); CeedChkBackend(ierr);
893   for (CeedInt i = 0; i < nelem*elemsize; i++) {
894     pbOffsets[i] = offsets[i]*shift;
895     if (pbOffsets[i] > max)
896       max = pbOffsets[i];
897   }
898 
899   // Create new restriction
900   ierr = CeedElemRestrictionCreate(ceed, nelem, elemsize, ncomp*ncomp, 1,
901                                    max + ncomp*ncomp, CEED_MEM_HOST,
902                                    CEED_OWN_POINTER, pbOffsets, pbRstr);
903   CeedChkBackend(ierr);
904 
905   // Cleanup
906   ierr = CeedElemRestrictionRestoreOffsets(rstr, &offsets); CeedChkBackend(ierr);
907 
908   return CEED_ERROR_SUCCESS;
909 }
910 
911 //------------------------------------------------------------------------------
912 // Assemble diagonal setup
913 //------------------------------------------------------------------------------
914 static inline int CeedOperatorAssembleDiagonalSetup_Cuda(CeedOperator op,
915     const bool pointBlock) {
916   int ierr;
917   Ceed ceed;
918   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
919   CeedQFunction qf;
920   ierr = CeedOperatorGetQFunction(op, &qf); CeedChkBackend(ierr);
921   CeedInt numinputfields, numoutputfields;
922   ierr = CeedQFunctionGetNumArgs(qf, &numinputfields, &numoutputfields);
923   CeedChkBackend(ierr);
924 
925   // Determine active input basis
926   CeedOperatorField *opfields;
927   CeedQFunctionField *qffields;
928   ierr = CeedOperatorGetFields(op, NULL, &opfields, NULL, NULL);
929   CeedChkBackend(ierr);
930   ierr = CeedQFunctionGetFields(qf, NULL, &qffields, NULL, NULL);
931   CeedChkBackend(ierr);
932   CeedInt numemodein = 0, ncomp = 0, dim = 1;
933   CeedEvalMode *emodein = NULL;
934   CeedBasis basisin = NULL;
935   CeedElemRestriction rstrin = NULL;
936   for (CeedInt i = 0; i < numinputfields; i++) {
937     CeedVector vec;
938     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChkBackend(ierr);
939     if (vec == CEED_VECTOR_ACTIVE) {
940       CeedElemRestriction rstr;
941       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisin); CeedChkBackend(ierr);
942       ierr = CeedBasisGetNumComponents(basisin, &ncomp); CeedChkBackend(ierr);
943       ierr = CeedBasisGetDimension(basisin, &dim); CeedChkBackend(ierr);
944       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
945       CeedChkBackend(ierr);
946       if (rstrin && rstrin != rstr)
947         // LCOV_EXCL_START
948         return CeedError(ceed, CEED_ERROR_BACKEND,
949                          "Multi-field non-composite operator diagonal assembly not supported");
950       // LCOV_EXCL_STOP
951       rstrin = rstr;
952       CeedEvalMode emode;
953       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode);
954       CeedChkBackend(ierr);
955       switch (emode) {
956       case CEED_EVAL_NONE:
957       case CEED_EVAL_INTERP:
958         ierr = CeedRealloc(numemodein + 1, &emodein); CeedChkBackend(ierr);
959         emodein[numemodein] = emode;
960         numemodein += 1;
961         break;
962       case CEED_EVAL_GRAD:
963         ierr = CeedRealloc(numemodein + dim, &emodein); CeedChkBackend(ierr);
964         for (CeedInt d = 0; d < dim; d++)
965           emodein[numemodein+d] = emode;
966         numemodein += dim;
967         break;
968       case CEED_EVAL_WEIGHT:
969       case CEED_EVAL_DIV:
970       case CEED_EVAL_CURL:
971         break; // Caught by QF Assembly
972       }
973     }
974   }
975 
976   // Determine active output basis
977   ierr = CeedOperatorGetFields(op, NULL, NULL, NULL, &opfields);
978   CeedChkBackend(ierr);
979   ierr = CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qffields);
980   CeedChkBackend(ierr);
981   CeedInt numemodeout = 0;
982   CeedEvalMode *emodeout = NULL;
983   CeedBasis basisout = NULL;
984   CeedElemRestriction rstrout = NULL;
985   for (CeedInt i = 0; i < numoutputfields; i++) {
986     CeedVector vec;
987     ierr = CeedOperatorFieldGetVector(opfields[i], &vec); CeedChkBackend(ierr);
988     if (vec == CEED_VECTOR_ACTIVE) {
989       CeedElemRestriction rstr;
990       ierr = CeedOperatorFieldGetBasis(opfields[i], &basisout); CeedChkBackend(ierr);
991       ierr = CeedOperatorFieldGetElemRestriction(opfields[i], &rstr);
992       CeedChkBackend(ierr);
993       if (rstrout && rstrout != rstr)
994         // LCOV_EXCL_START
995         return CeedError(ceed, CEED_ERROR_BACKEND,
996                          "Multi-field non-composite operator diagonal assembly not supported");
997       // LCOV_EXCL_STOP
998       rstrout = rstr;
999       CeedEvalMode emode;
1000       ierr = CeedQFunctionFieldGetEvalMode(qffields[i], &emode); CeedChkBackend(ierr);
1001       switch (emode) {
1002       case CEED_EVAL_NONE:
1003       case CEED_EVAL_INTERP:
1004         ierr = CeedRealloc(numemodeout + 1, &emodeout); CeedChkBackend(ierr);
1005         emodeout[numemodeout] = emode;
1006         numemodeout += 1;
1007         break;
1008       case CEED_EVAL_GRAD:
1009         ierr = CeedRealloc(numemodeout + dim, &emodeout); CeedChkBackend(ierr);
1010         for (CeedInt d = 0; d < dim; d++)
1011           emodeout[numemodeout+d] = emode;
1012         numemodeout += dim;
1013         break;
1014       case CEED_EVAL_WEIGHT:
1015       case CEED_EVAL_DIV:
1016       case CEED_EVAL_CURL:
1017         break; // Caught by QF Assembly
1018       }
1019     }
1020   }
1021 
1022   // Operator data struct
1023   CeedOperator_Cuda *impl;
1024   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
1025   ierr = CeedCalloc(1, &impl->diag); CeedChkBackend(ierr);
1026   CeedOperatorDiag_Cuda *diag = impl->diag;
1027   diag->basisin = basisin;
1028   diag->basisout = basisout;
1029   diag->h_emodein = emodein;
1030   diag->h_emodeout = emodeout;
1031   diag->numemodein = numemodein;
1032   diag->numemodeout = numemodeout;
1033 
1034   // Assemble kernel
1035   CeedInt nnodes, nqpts;
1036   ierr = CeedBasisGetNumNodes(basisin, &nnodes); CeedChkBackend(ierr);
1037   ierr = CeedBasisGetNumQuadraturePoints(basisin, &nqpts); CeedChkBackend(ierr);
1038   diag->nnodes = nnodes;
1039   ierr = CeedCompileCuda(ceed, diagonalkernels, &diag->module, 5,
1040                          "NUMEMODEIN", numemodein,
1041                          "NUMEMODEOUT", numemodeout,
1042                          "NNODES", nnodes,
1043                          "NQPTS", nqpts,
1044                          "NCOMP", ncomp
1045                         ); CeedChk_Cu(ceed, ierr);
1046   ierr = CeedGetKernelCuda(ceed, diag->module, "linearDiagonal",
1047                            &diag->linearDiagonal); CeedChk_Cu(ceed, ierr);
1048   ierr = CeedGetKernelCuda(ceed, diag->module, "linearPointBlockDiagonal",
1049                            &diag->linearPointBlock);
1050   CeedChk_Cu(ceed, ierr);
1051 
1052   // Basis matrices
1053   const CeedInt qBytes = nqpts * sizeof(CeedScalar);
1054   const CeedInt iBytes = qBytes * nnodes;
1055   const CeedInt gBytes = qBytes * nnodes * dim;
1056   const CeedInt eBytes = sizeof(CeedEvalMode);
1057   const CeedScalar *interpin, *interpout, *gradin, *gradout;
1058 
1059   // CEED_EVAL_NONE
1060   CeedScalar *identity = NULL;
1061   bool evalNone = false;
1062   for (CeedInt i=0; i<numemodein; i++)
1063     evalNone = evalNone || (emodein[i] == CEED_EVAL_NONE);
1064   for (CeedInt i=0; i<numemodeout; i++)
1065     evalNone = evalNone || (emodeout[i] == CEED_EVAL_NONE);
1066   if (evalNone) {
1067     ierr = CeedCalloc(nqpts*nnodes, &identity); CeedChkBackend(ierr);
1068     for (CeedInt i=0; i<(nnodes<nqpts?nnodes:nqpts); i++)
1069       identity[i*nnodes+i] = 1.0;
1070     ierr = cudaMalloc((void **)&diag->d_identity, iBytes); CeedChk_Cu(ceed, ierr);
1071     ierr = cudaMemcpy(diag->d_identity, identity, iBytes,
1072                       cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1073   }
1074 
1075   // CEED_EVAL_INTERP
1076   ierr = CeedBasisGetInterp(basisin, &interpin); CeedChkBackend(ierr);
1077   ierr = cudaMalloc((void **)&diag->d_interpin, iBytes); CeedChk_Cu(ceed, ierr);
1078   ierr = cudaMemcpy(diag->d_interpin, interpin, iBytes,
1079                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1080   ierr = CeedBasisGetInterp(basisout, &interpout); CeedChkBackend(ierr);
1081   ierr = cudaMalloc((void **)&diag->d_interpout, iBytes); CeedChk_Cu(ceed, ierr);
1082   ierr = cudaMemcpy(diag->d_interpout, interpout, iBytes,
1083                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1084 
1085   // CEED_EVAL_GRAD
1086   ierr = CeedBasisGetGrad(basisin, &gradin); CeedChkBackend(ierr);
1087   ierr = cudaMalloc((void **)&diag->d_gradin, gBytes); CeedChk_Cu(ceed, ierr);
1088   ierr = cudaMemcpy(diag->d_gradin, gradin, gBytes,
1089                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1090   ierr = CeedBasisGetGrad(basisout, &gradout); CeedChkBackend(ierr);
1091   ierr = cudaMalloc((void **)&diag->d_gradout, gBytes); CeedChk_Cu(ceed, ierr);
1092   ierr = cudaMemcpy(diag->d_gradout, gradout, gBytes,
1093                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1094 
1095   // Arrays of emodes
1096   ierr = cudaMalloc((void **)&diag->d_emodein, numemodein * eBytes);
1097   CeedChk_Cu(ceed, ierr);
1098   ierr = cudaMemcpy(diag->d_emodein, emodein, numemodein * eBytes,
1099                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1100   ierr = cudaMalloc((void **)&diag->d_emodeout, numemodeout * eBytes);
1101   CeedChk_Cu(ceed, ierr);
1102   ierr = cudaMemcpy(diag->d_emodeout, emodeout, numemodeout * eBytes,
1103                     cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1104 
1105   // Restriction
1106   diag->diagrstr = rstrout;
1107 
1108   return CEED_ERROR_SUCCESS;
1109 }
1110 
1111 //------------------------------------------------------------------------------
1112 // Assemble diagonal common code
1113 //------------------------------------------------------------------------------
1114 static inline int CeedOperatorAssembleDiagonalCore_Cuda(CeedOperator op,
1115     CeedVector assembled, CeedRequest *request, const bool pointBlock) {
1116   int ierr;
1117   Ceed ceed;
1118   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
1119   CeedOperator_Cuda *impl;
1120   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
1121 
1122   // Assemble QFunction
1123   CeedVector assembledqf;
1124   CeedElemRestriction rstr;
1125   ierr = CeedOperatorLinearAssembleQFunctionBuildOrUpdate(op, &assembledqf,
1126          &rstr, request); CeedChkBackend(ierr);
1127   ierr = CeedElemRestrictionDestroy(&rstr); CeedChkBackend(ierr);
1128   CeedScalar maxnorm = 0;
1129   ierr = CeedVectorNorm(assembledqf, CEED_NORM_MAX, &maxnorm);
1130   CeedChkBackend(ierr);
1131 
1132   // Setup
1133   if (!impl->diag) {
1134     ierr = CeedOperatorAssembleDiagonalSetup_Cuda(op, pointBlock);
1135     CeedChkBackend(ierr);
1136   }
1137   CeedOperatorDiag_Cuda *diag = impl->diag;
1138   assert(diag != NULL);
1139 
1140   // Restriction
1141   if (pointBlock && !diag->pbdiagrstr) {
1142     CeedElemRestriction pbdiagrstr;
1143     ierr = CreatePBRestriction(diag->diagrstr, &pbdiagrstr); CeedChkBackend(ierr);
1144     diag->pbdiagrstr = pbdiagrstr;
1145   }
1146   CeedElemRestriction diagrstr = pointBlock ? diag->pbdiagrstr : diag->diagrstr;
1147 
1148   // Create diagonal vector
1149   CeedVector elemdiag = pointBlock ? diag->pbelemdiag : diag->elemdiag;
1150   if (!elemdiag) {
1151     ierr = CeedElemRestrictionCreateVector(diagrstr, NULL, &elemdiag);
1152     CeedChkBackend(ierr);
1153     if (pointBlock)
1154       diag->pbelemdiag = elemdiag;
1155     else
1156       diag->elemdiag = elemdiag;
1157   }
1158   ierr = CeedVectorSetValue(elemdiag, 0.0); CeedChkBackend(ierr);
1159 
1160   // Assemble element operator diagonals
1161   CeedScalar *elemdiagarray;
1162   const CeedScalar *assembledqfarray;
1163   ierr = CeedVectorGetArray(elemdiag, CEED_MEM_DEVICE, &elemdiagarray);
1164   CeedChkBackend(ierr);
1165   ierr = CeedVectorGetArrayRead(assembledqf, CEED_MEM_DEVICE, &assembledqfarray);
1166   CeedChkBackend(ierr);
1167   CeedInt nelem;
1168   ierr = CeedElemRestrictionGetNumElements(diagrstr, &nelem);
1169   CeedChkBackend(ierr);
1170 
1171   // Compute the diagonal of B^T D B
1172   int elemsPerBlock = 1;
1173   int grid = nelem/elemsPerBlock+((nelem/elemsPerBlock*elemsPerBlock<nelem)?1:0);
1174   void *args[] = {(void *) &nelem, (void *) &maxnorm, &diag->d_identity,
1175                   &diag->d_interpin, &diag->d_gradin, &diag->d_interpout,
1176                   &diag->d_gradout, &diag->d_emodein, &diag->d_emodeout,
1177                   &assembledqfarray, &elemdiagarray
1178                  };
1179   if (pointBlock) {
1180     ierr = CeedRunKernelDimCuda(ceed, diag->linearPointBlock, grid,
1181                                 diag->nnodes, 1, elemsPerBlock, args);
1182     CeedChkBackend(ierr);
1183   } else {
1184     ierr = CeedRunKernelDimCuda(ceed, diag->linearDiagonal, grid,
1185                                 diag->nnodes, 1, elemsPerBlock, args);
1186     CeedChkBackend(ierr);
1187   }
1188 
1189   // Restore arrays
1190   ierr = CeedVectorRestoreArray(elemdiag, &elemdiagarray); CeedChkBackend(ierr);
1191   ierr = CeedVectorRestoreArrayRead(assembledqf, &assembledqfarray);
1192   CeedChkBackend(ierr);
1193 
1194   // Assemble local operator diagonal
1195   ierr = CeedElemRestrictionApply(diagrstr, CEED_TRANSPOSE, elemdiag,
1196                                   assembled, request); CeedChkBackend(ierr);
1197 
1198   // Cleanup
1199   ierr = CeedVectorDestroy(&assembledqf); CeedChkBackend(ierr);
1200 
1201   return CEED_ERROR_SUCCESS;
1202 }
1203 
1204 //------------------------------------------------------------------------------
1205 // Assemble composite diagonal common code
1206 //------------------------------------------------------------------------------
1207 static inline int CeedOperatorLinearAssembleAddDiagonalCompositeCore_Cuda(
1208   CeedOperator op, CeedVector assembled, CeedRequest *request,
1209   const bool pointBlock) {
1210   int ierr;
1211   CeedInt numSub;
1212   CeedOperator *subOperators;
1213   ierr = CeedOperatorGetNumSub(op, &numSub); CeedChkBackend(ierr);
1214   ierr = CeedOperatorGetSubList(op, &subOperators); CeedChkBackend(ierr);
1215   for (CeedInt i = 0; i < numSub; i++) {
1216     ierr = CeedOperatorAssembleDiagonalCore_Cuda(subOperators[i], assembled,
1217            request, pointBlock); CeedChkBackend(ierr);
1218   }
1219   return CEED_ERROR_SUCCESS;
1220 }
1221 
1222 //------------------------------------------------------------------------------
1223 // Assemble Linear Diagonal
1224 //------------------------------------------------------------------------------
1225 static int CeedOperatorLinearAssembleAddDiagonal_Cuda(CeedOperator op,
1226     CeedVector assembled, CeedRequest *request) {
1227   int ierr;
1228   bool isComposite;
1229   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChkBackend(ierr);
1230   if (isComposite) {
1231     return CeedOperatorLinearAssembleAddDiagonalCompositeCore_Cuda(op, assembled,
1232            request, false);
1233   } else {
1234     return CeedOperatorAssembleDiagonalCore_Cuda(op, assembled, request, false);
1235   }
1236 }
1237 
1238 //------------------------------------------------------------------------------
1239 // Assemble Linear Point Block Diagonal
1240 //------------------------------------------------------------------------------
1241 static int CeedOperatorLinearAssembleAddPointBlockDiagonal_Cuda(CeedOperator op,
1242     CeedVector assembled, CeedRequest *request) {
1243   int ierr;
1244   bool isComposite;
1245   ierr = CeedOperatorIsComposite(op, &isComposite); CeedChkBackend(ierr);
1246   if (isComposite) {
1247     return CeedOperatorLinearAssembleAddDiagonalCompositeCore_Cuda(op, assembled,
1248            request, true);
1249   } else {
1250     return CeedOperatorAssembleDiagonalCore_Cuda(op, assembled, request, true);
1251   }
1252 }
1253 
1254 //------------------------------------------------------------------------------
1255 // Matrix assembly kernel
1256 //------------------------------------------------------------------------------
1257 // *INDENT-OFF*
1258 static const char *assemblykernels = QUOTE(
1259 extern "C" __launch_bounds__(BLOCK_SIZE)
1260            __global__ void linearAssemble(const CeedScalar *B_in, const CeedScalar *B_out,
1261                    const CeedScalar *__restrict__ qf_array,
1262                    CeedScalar *__restrict__ values_array) {
1263 
1264   // This kernel assumes B_in and B_out have the same number of quadrature points and
1265   // basis points.
1266   // TODO: expand to more general cases
1267   const int i = threadIdx.x; // The output row index of each B^TDB operation
1268   const int l = threadIdx.y; // The output column index of each B^TDB operation
1269 			     // such that we have (Bout^T)_ij D_jk Bin_kl = C_il
1270 
1271   // Strides for final output ordering, determined by the reference (interface) implementation of
1272   // the symbolic assembly, slowest --> fastest: element, comp_in, comp_out, node_row, node_col
1273   const CeedInt comp_out_stride = NNODES * NNODES;
1274   const CeedInt comp_in_stride = comp_out_stride * NCOMP;
1275   const CeedInt e_stride = comp_in_stride * NCOMP;
1276   // Strides for QF array, slowest --> fastest:  emode_in, comp_in, emode_out, comp_out, elem, qpt
1277   const CeedInt qe_stride = NQPTS;
1278   const CeedInt qcomp_out_stride = NELEM * qe_stride;
1279   const CeedInt qemode_out_stride = qcomp_out_stride * NCOMP;
1280   const CeedInt qcomp_in_stride = qemode_out_stride * NUMEMODEOUT;
1281   const CeedInt qemode_in_stride = qcomp_in_stride * NCOMP;
1282 
1283   // Loop over each element (if necessary)
1284   for (CeedInt e = blockIdx.x*blockDim.z + threadIdx.z; e < NELEM;
1285          e += gridDim.x*blockDim.z) {
1286     for (CeedInt comp_in = 0; comp_in < NCOMP; comp_in++) {
1287       for (CeedInt comp_out = 0; comp_out < NCOMP; comp_out++) {
1288         CeedScalar result = 0.0;
1289         CeedInt qf_index_comp = qcomp_in_stride * comp_in + qcomp_out_stride * comp_out + qe_stride * e;
1290         for (CeedInt emode_in = 0; emode_in < NUMEMODEIN; emode_in++) {
1291           CeedInt b_in_index = emode_in * NQPTS * NNODES;
1292       	  for (CeedInt emode_out = 0; emode_out < NUMEMODEOUT; emode_out++) {
1293              CeedInt b_out_index = emode_out * NQPTS * NNODES;
1294              CeedInt qf_index = qf_index_comp + qemode_out_stride * emode_out + qemode_in_stride * emode_in;
1295  	     // Perform the B^T D B operation for this 'chunk' of D (the qf_array)
1296             for (CeedInt j = 0; j < NQPTS; j++) {
1297      	      result += B_out[b_out_index + j * NNODES  + i] * qf_array[qf_index + j] * B_in[b_in_index + j * NNODES + l];
1298 	    }
1299 
1300           }// end of emode_out
1301         } // end of emode_in
1302         CeedInt val_index = comp_in_stride * comp_in + comp_out_stride * comp_out + e_stride * e + NNODES * i + l;
1303    	values_array[val_index] = result;
1304       } // end of out component
1305     } // end of in component
1306   } // end of element loop
1307 }
1308 );
1309 // *INDENT-ON*
1310 
1311 //------------------------------------------------------------------------------
1312 // Single operator assembly setup
1313 //------------------------------------------------------------------------------
1314 static int CeedSingleOperatorAssembleSetup_Cuda(CeedOperator op) {
1315   int ierr;
1316   Ceed ceed;
1317   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
1318   CeedOperator_Cuda *impl;
1319   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
1320 
1321   // Get intput and output fields
1322   CeedInt num_input_fields, num_output_fields;
1323   CeedOperatorField *input_fields;
1324   CeedOperatorField *output_fields;
1325   ierr = CeedOperatorGetFields(op, &num_input_fields, &input_fields,
1326                                &num_output_fields, &output_fields); CeedChk(ierr);
1327 
1328   // Determine active input basis eval mode
1329   CeedQFunction qf;
1330   ierr = CeedOperatorGetQFunction(op, &qf); CeedChk(ierr);
1331   CeedQFunctionField *qf_fields;
1332   ierr = CeedQFunctionGetFields(qf, NULL, &qf_fields, NULL, NULL); CeedChk(ierr);
1333   // Note that the kernel will treat each dimension of a gradient action separately;
1334   // i.e., when an active input has a CEED_EVAL_GRAD mode, num_emode_in will increment
1335   // by dim.  However, for the purposes of loading the B matrices, it will be treated
1336   // as one mode, and we will load/copy the entire gradient matrix at once, so
1337   // num_B_in_mats_to_load will be incremented by 1.
1338   CeedInt num_emode_in = 0, dim = 1, num_B_in_mats_to_load = 0, size_B_in = 0;
1339   CeedEvalMode *eval_mode_in = NULL; //will be of size num_B_in_mats_load
1340   CeedBasis basis_in = NULL;
1341   CeedInt nqpts, esize;
1342   CeedElemRestriction rstr_in = NULL;
1343   for (CeedInt i=0; i<num_input_fields; i++) {
1344     CeedVector vec;
1345     ierr = CeedOperatorFieldGetVector(input_fields[i], &vec); CeedChk(ierr);
1346     if (vec == CEED_VECTOR_ACTIVE) {
1347       ierr = CeedOperatorFieldGetBasis(input_fields[i], &basis_in);
1348       CeedChk(ierr);
1349       ierr = CeedBasisGetDimension(basis_in, &dim); CeedChk(ierr);
1350       ierr = CeedBasisGetNumQuadraturePoints(basis_in, &nqpts); CeedChk(ierr);
1351       ierr = CeedOperatorFieldGetElemRestriction(input_fields[i], &rstr_in);
1352       ierr = CeedElemRestrictionGetElementSize(rstr_in, &esize); CeedChk(ierr);
1353       CeedChk(ierr);
1354       CeedEvalMode eval_mode;
1355       ierr = CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode);
1356       CeedChk(ierr);
1357       if (eval_mode != CEED_EVAL_NONE) {
1358         ierr = CeedRealloc(num_B_in_mats_to_load + 1, &eval_mode_in); CeedChk(ierr);
1359         eval_mode_in[num_B_in_mats_to_load] = eval_mode;
1360         num_B_in_mats_to_load += 1;
1361         if (eval_mode == CEED_EVAL_GRAD) {
1362           num_emode_in += dim;
1363           size_B_in += dim * esize * nqpts;
1364         } else {
1365           num_emode_in +=1;
1366           size_B_in += esize * nqpts;
1367         }
1368       }
1369     }
1370   }
1371 
1372   // Determine active output basis; basis_out and rstr_out only used if same as input, TODO
1373   ierr = CeedQFunctionGetFields(qf, NULL, NULL, NULL, &qf_fields); CeedChk(ierr);
1374   CeedInt num_emode_out = 0, num_B_out_mats_to_load = 0, size_B_out = 0;
1375   CeedEvalMode *eval_mode_out = NULL;
1376   CeedBasis basis_out = NULL;
1377   CeedElemRestriction rstr_out = NULL;
1378   for (CeedInt i=0; i<num_output_fields; i++) {
1379     CeedVector vec;
1380     ierr = CeedOperatorFieldGetVector(output_fields[i], &vec); CeedChk(ierr);
1381     if (vec == CEED_VECTOR_ACTIVE) {
1382       ierr = CeedOperatorFieldGetBasis(output_fields[i], &basis_out);
1383       CeedChk(ierr);
1384       ierr = CeedOperatorFieldGetElemRestriction(output_fields[i], &rstr_out);
1385       CeedChk(ierr);
1386       if (rstr_out && rstr_out != rstr_in)
1387         // LCOV_EXCL_START
1388         return CeedError(ceed, CEED_ERROR_BACKEND,
1389                          "Multi-field non-composite operator assembly not supported");
1390       // LCOV_EXCL_STOP
1391       CeedEvalMode eval_mode;
1392       ierr = CeedQFunctionFieldGetEvalMode(qf_fields[i], &eval_mode);
1393       CeedChk(ierr);
1394       if (eval_mode != CEED_EVAL_NONE) {
1395         ierr = CeedRealloc(num_B_out_mats_to_load + 1, &eval_mode_out); CeedChk(ierr);
1396         eval_mode_out[num_B_out_mats_to_load] = eval_mode;
1397         num_B_out_mats_to_load += 1;
1398         if (eval_mode == CEED_EVAL_GRAD) {
1399           num_emode_out += dim;
1400           size_B_out += dim * esize * nqpts;
1401         } else {
1402           num_emode_out +=1;
1403           size_B_out += esize * nqpts;
1404         }
1405       }
1406     }
1407   }
1408 
1409   if (num_emode_in == 0 || num_emode_out == 0)
1410     // LCOV_EXCL_START
1411     return CeedError(ceed, CEED_ERROR_UNSUPPORTED,
1412                      "Cannot assemble operator without inputs/outputs");
1413   // LCOV_EXCL_STOP
1414 
1415   CeedInt nelem, ncomp;
1416   ierr = CeedElemRestrictionGetNumElements(rstr_in, &nelem); CeedChk(ierr);
1417   ierr = CeedElemRestrictionGetNumComponents(rstr_in, &ncomp); CeedChk(ierr);
1418 
1419   ierr = CeedCalloc(1, &impl->asmb); CeedChkBackend(ierr);
1420   CeedOperatorAssemble_Cuda *asmb = impl->asmb;
1421   asmb->nelem = nelem;
1422   asmb->nnodes = esize;
1423 
1424   // Compile kernels
1425   int elemsPerBlock = 1;
1426   asmb->elemsPerBlock = elemsPerBlock;
1427   // TODO: 1D threadblock version for larger elements
1428   Ceed_Cuda *cuda_data;
1429   ierr = CeedGetData(ceed, &cuda_data); CeedChkBackend(ierr);
1430   if (esize * esize * elemsPerBlock > cuda_data->device_prop.maxThreadsPerBlock)
1431     // LCOV_EXCL_START
1432     return CeedError(ceed, CEED_ERROR_UNSUPPORTED,
1433                      "GPU assembly not currently available for elements of this size");
1434   // LCOV_EXCL_STOP
1435 
1436   ierr = CeedCompileCuda(ceed, assemblykernels, &asmb->module, 7,
1437                          "NELEM", nelem,
1438                          "NUMEMODEIN", num_emode_in,
1439                          "NUMEMODEOUT", num_emode_out,
1440                          "NQPTS", nqpts,
1441                          "NNODES", esize,
1442                          "BLOCK_SIZE", esize * esize * elemsPerBlock,
1443                          "NCOMP", ncomp
1444                         ); CeedChk_Cu(ceed, ierr);
1445   ierr = CeedGetKernelCuda(ceed, asmb->module, "linearAssemble",
1446                            &asmb->linearAssemble); CeedChk_Cu(ceed, ierr);
1447 
1448   // Build 'full' B matrices (not 1D arrays used for tensor-product matrices)
1449   const CeedScalar *interp_in, *grad_in;
1450   ierr = CeedBasisGetInterp(basis_in, &interp_in); CeedChkBackend(ierr);
1451   ierr = CeedBasisGetGrad(basis_in, &grad_in); CeedChkBackend(ierr);
1452 
1453   // Load into B_in, in order that they will be used in eval_mode
1454   const CeedInt inBytes = size_B_in * sizeof(CeedScalar);
1455   CeedInt mat_start = 0;
1456   ierr = cudaMalloc((void **) &asmb->d_B_in, inBytes); CeedChk_Cu(ceed, ierr);
1457   for (int i = 0; i < num_B_in_mats_to_load; i++) {
1458     CeedEvalMode eval_mode = eval_mode_in[i];
1459     if (eval_mode == CEED_EVAL_INTERP) {
1460       ierr = cudaMemcpy(&asmb->d_B_in[mat_start], interp_in,
1461                         esize * nqpts * sizeof(CeedScalar),
1462                         cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1463       mat_start += esize * nqpts;
1464     } else if (eval_mode == CEED_EVAL_GRAD) {
1465       ierr = cudaMemcpy(asmb->d_B_in, grad_in,
1466                         dim * esize * nqpts * sizeof(CeedScalar),
1467                         cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1468       mat_start += dim * esize * nqpts;
1469     }
1470   }
1471 
1472   const CeedScalar *interp_out, *grad_out;
1473   // Note that this function currently assumes 1 basis, so this should always be true
1474   // for now
1475   if (basis_out == basis_in) {
1476     interp_out = interp_in;
1477     grad_out = grad_in;
1478   } else {
1479     ierr = CeedBasisGetInterp(basis_out, &interp_out); CeedChkBackend(ierr);
1480     ierr = CeedBasisGetGrad(basis_out, &grad_out); CeedChkBackend(ierr);
1481   }
1482 
1483   // Load into B_out, in order that they will be used in eval_mode
1484   const CeedInt outBytes = size_B_out * sizeof(CeedScalar);
1485   mat_start = 0;
1486   ierr = cudaMalloc((void **) &asmb->d_B_out, outBytes); CeedChk_Cu(ceed, ierr);
1487   for (int i = 0; i < num_B_out_mats_to_load; i++) {
1488     CeedEvalMode eval_mode = eval_mode_out[i];
1489     if (eval_mode == CEED_EVAL_INTERP) {
1490       ierr = cudaMemcpy(&asmb->d_B_out[mat_start], interp_out,
1491                         esize * nqpts * sizeof(CeedScalar),
1492                         cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1493       mat_start += esize * nqpts;
1494     } else if (eval_mode == CEED_EVAL_GRAD) {
1495       ierr = cudaMemcpy(&asmb->d_B_out[mat_start], grad_out,
1496                         dim * esize * nqpts * sizeof(CeedScalar),
1497                         cudaMemcpyHostToDevice); CeedChk_Cu(ceed, ierr);
1498       mat_start += dim * esize * nqpts;
1499     }
1500   }
1501   return CEED_ERROR_SUCCESS;
1502 }
1503 
1504 //------------------------------------------------------------------------------
1505 // Single operator assembly
1506 //------------------------------------------------------------------------------
1507 static int CeedSingleOperatorAssemble_Cuda(CeedOperator op, CeedInt offset,
1508     CeedVector values) {
1509 
1510   int ierr;
1511   Ceed ceed;
1512   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
1513   CeedOperator_Cuda *impl;
1514   ierr = CeedOperatorGetData(op, &impl); CeedChkBackend(ierr);
1515 
1516   // Setup
1517   if (!impl->asmb) {
1518     ierr = CeedSingleOperatorAssembleSetup_Cuda(op);
1519     CeedChkBackend(ierr);
1520   }
1521 
1522   // Assemble QFunction
1523   CeedVector assembled_qf;
1524   CeedElemRestriction rstr_q;
1525   ierr = CeedOperatorLinearAssembleQFunctionBuildOrUpdate(
1526            op, &assembled_qf, &rstr_q, CEED_REQUEST_IMMEDIATE); CeedChk(ierr);
1527   ierr = CeedElemRestrictionDestroy(&rstr_q); CeedChkBackend(ierr);
1528   CeedScalar *values_array;
1529   ierr = CeedVectorGetArrayWrite(values, CEED_MEM_DEVICE, &values_array);
1530   CeedChkBackend(ierr);
1531   values_array += offset;
1532   const CeedScalar *qf_array;
1533   ierr = CeedVectorGetArrayRead(assembled_qf, CEED_MEM_DEVICE, &qf_array);
1534   CeedChkBackend(ierr);
1535 
1536   // Compute B^T D B
1537   const CeedInt nelem = impl->asmb->nelem;
1538   const CeedInt elemsPerBlock = impl->asmb->elemsPerBlock;
1539   const CeedInt nnodes = impl->asmb->nnodes;
1540   const CeedInt grid = nelem/elemsPerBlock+((
1541                          nelem/elemsPerBlock*elemsPerBlock<nelem)?1:0);
1542   void *args[] = {&impl->asmb->d_B_in, &impl->asmb->d_B_out,
1543                   &qf_array, &values_array
1544                  };
1545   ierr = CeedRunKernelDimCuda(ceed, impl->asmb->linearAssemble, grid,
1546                               nnodes, nnodes, elemsPerBlock, args);
1547   CeedChkBackend(ierr);
1548 
1549 
1550   // Restore arrays
1551   ierr = CeedVectorRestoreArray(values, &values_array); CeedChkBackend(ierr);
1552   ierr = CeedVectorRestoreArrayRead(assembled_qf, &qf_array);
1553   CeedChkBackend(ierr);
1554 
1555   // Cleanup
1556   ierr = CeedVectorDestroy(&assembled_qf); CeedChkBackend(ierr);
1557 
1558   return CEED_ERROR_SUCCESS;
1559 }
1560 
1561 //------------------------------------------------------------------------------
1562 // Assemble matrix data for COO matrix of assembled operator.
1563 // The sparsity pattern is set by CeedOperatorLinearAssembleSymbolic.
1564 //
1565 // Note that this (and other assembly routines) currently assume only one
1566 // active input restriction/basis per operator (could have multiple basis eval
1567 // modes).
1568 // TODO: allow multiple active input restrictions/basis objects
1569 //------------------------------------------------------------------------------
1570 int CeedOperatorLinearAssemble_Cuda(CeedOperator op, CeedVector values) {
1571 
1572   // As done in the default implementation, loop through suboperators
1573   // for composite operators, or call single operator assembly otherwise
1574   bool is_composite;
1575   CeedInt ierr;
1576   ierr = CeedOperatorIsComposite(op, &is_composite); CeedChk(ierr);
1577 
1578   CeedElemRestriction rstr;
1579   CeedInt num_elem, elem_size, num_comp;
1580 
1581   CeedInt offset = 0;
1582   if (is_composite) {
1583     CeedInt num_suboperators;
1584     ierr = CeedOperatorGetNumSub(op, &num_suboperators); CeedChk(ierr);
1585     CeedOperator *sub_operators;
1586     ierr = CeedOperatorGetSubList(op, &sub_operators); CeedChk(ierr);
1587     for (int k = 0; k < num_suboperators; ++k) {
1588       ierr = CeedSingleOperatorAssemble_Cuda(sub_operators[k], offset, values);
1589       CeedChk(ierr);
1590       ierr = CeedOperatorGetActiveElemRestriction(sub_operators[k], &rstr);
1591       CeedChk(ierr);
1592       ierr = CeedElemRestrictionGetNumElements(rstr, &num_elem); CeedChk(ierr);
1593       ierr = CeedElemRestrictionGetElementSize(rstr, &elem_size); CeedChk(ierr);
1594       ierr = CeedElemRestrictionGetNumComponents(rstr, &num_comp); CeedChk(ierr);
1595       offset += elem_size*num_comp * elem_size*num_comp * num_elem;
1596     }
1597   } else {
1598     ierr = CeedSingleOperatorAssemble_Cuda(op, offset, values); CeedChk(ierr);
1599   }
1600 
1601   return CEED_ERROR_SUCCESS;
1602 }
1603 //------------------------------------------------------------------------------
1604 // Create operator
1605 //------------------------------------------------------------------------------
1606 int CeedOperatorCreate_Cuda(CeedOperator op) {
1607   int ierr;
1608   Ceed ceed;
1609   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
1610   CeedOperator_Cuda *impl;
1611 
1612   ierr = CeedCalloc(1, &impl); CeedChkBackend(ierr);
1613   ierr = CeedOperatorSetData(op, impl); CeedChkBackend(ierr);
1614 
1615   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleQFunction",
1616                                 CeedOperatorLinearAssembleQFunction_Cuda);
1617   CeedChkBackend(ierr);
1618   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1619                                 "LinearAssembleQFunctionUpdate",
1620                                 CeedOperatorLinearAssembleQFunctionUpdate_Cuda);
1621   CeedChkBackend(ierr);
1622   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal",
1623                                 CeedOperatorLinearAssembleAddDiagonal_Cuda);
1624   CeedChkBackend(ierr);
1625   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1626                                 "LinearAssembleAddPointBlockDiagonal",
1627                                 CeedOperatorLinearAssembleAddPointBlockDiagonal_Cuda);
1628   CeedChkBackend(ierr);
1629   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1630                                 "LinearAssemble", CeedOperatorLinearAssemble_Cuda);
1631   CeedChkBackend(ierr);
1632   ierr = CeedSetBackendFunction(ceed, "Operator", op, "ApplyAdd",
1633                                 CeedOperatorApplyAdd_Cuda); CeedChkBackend(ierr);
1634   ierr = CeedSetBackendFunction(ceed, "Operator", op, "Destroy",
1635                                 CeedOperatorDestroy_Cuda); CeedChkBackend(ierr);
1636   return CEED_ERROR_SUCCESS;
1637 }
1638 
1639 //------------------------------------------------------------------------------
1640 // Composite Operator Create
1641 //------------------------------------------------------------------------------
1642 int CeedCompositeOperatorCreate_Cuda(CeedOperator op) {
1643   int ierr;
1644   Ceed ceed;
1645   ierr = CeedOperatorGetCeed(op, &ceed); CeedChkBackend(ierr);
1646 
1647   ierr = CeedSetBackendFunction(ceed, "Operator", op, "LinearAssembleAddDiagonal",
1648                                 CeedOperatorLinearAssembleAddDiagonal_Cuda);
1649   CeedChkBackend(ierr);
1650   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1651                                 "LinearAssembleAddPointBlockDiagonal",
1652                                 CeedOperatorLinearAssembleAddPointBlockDiagonal_Cuda);
1653   CeedChkBackend(ierr);
1654   ierr = CeedSetBackendFunction(ceed, "Operator", op,
1655                                 "LinearAssemble", CeedOperatorLinearAssemble_Cuda);
1656   CeedChkBackend(ierr);
1657   return CEED_ERROR_SUCCESS;
1658 }
1659 //------------------------------------------------------------------------------
1660