xref: /petsc/include/petscdm.h (revision bcee047adeeb73090d7e36cc71e39fc287cdbb97)
1 /*
2       Objects to manage the interactions between the mesh data structures and the algebraic objects
3 */
4 #ifndef PETSCDM_H
5 #define PETSCDM_H
6 #include <petscmat.h>
7 #include <petscdmtypes.h>
8 #include <petscfetypes.h>
9 #include <petscdstypes.h>
10 #include <petscdmlabel.h>
11 #include <petscdt.h>
12 
13 /* SUBMANSEC = DM */
14 
15 PETSC_EXTERN PetscErrorCode DMInitializePackage(void);
16 
17 PETSC_EXTERN PetscClassId DM_CLASSID;
18 
19 #define DMLOCATEPOINT_POINT_NOT_FOUND -367
20 
21 /*J
22     DMType - String with the name of a PETSc `DM`
23 
24    Level: beginner
25 
26 .seealso: [](ch_dmbase), `DMSetType()`, `DMCreate()`, `DM`
27 J*/
28 typedef const char *DMType;
29 #define DMDA        "da"
30 #define DMCOMPOSITE "composite"
31 #define DMSLICED    "sliced"
32 #define DMSHELL     "shell"
33 #define DMPLEX      "plex"
34 #define DMREDUNDANT "redundant"
35 #define DMPATCH     "patch"
36 #define DMMOAB      "moab"
37 #define DMNETWORK   "network"
38 #define DMFOREST    "forest"
39 #define DMP4EST     "p4est"
40 #define DMP8EST     "p8est"
41 #define DMSWARM     "swarm"
42 #define DMPRODUCT   "product"
43 #define DMSTAG      "stag"
44 
45 PETSC_EXTERN const char *const       DMBoundaryTypes[];
46 PETSC_EXTERN const char *const       DMBoundaryConditionTypes[];
47 PETSC_EXTERN const char *const       DMBlockingTypes[];
48 PETSC_EXTERN PetscFunctionList       DMList;
49 PETSC_EXTERN DMGeneratorFunctionList DMGenerateList;
50 PETSC_EXTERN PetscErrorCode          DMCreate(MPI_Comm, DM *);
51 PETSC_EXTERN PetscErrorCode          DMClone(DM, DM *);
52 PETSC_EXTERN PetscErrorCode          DMSetType(DM, DMType);
53 PETSC_EXTERN PetscErrorCode          DMGetType(DM, DMType *);
54 PETSC_EXTERN PetscErrorCode          DMRegister(const char[], PetscErrorCode (*)(DM));
55 PETSC_EXTERN PetscErrorCode          DMRegisterDestroy(void);
56 
57 PETSC_EXTERN PetscErrorCode DMView(DM, PetscViewer);
58 PETSC_EXTERN PetscErrorCode DMLoad(DM, PetscViewer);
59 PETSC_EXTERN PetscErrorCode DMDestroy(DM *);
60 PETSC_EXTERN PetscErrorCode DMCreateGlobalVector(DM, Vec *);
61 PETSC_EXTERN PetscErrorCode DMCreateLocalVector(DM, Vec *);
62 PETSC_EXTERN PetscErrorCode DMGetLocalVector(DM, Vec *);
63 PETSC_EXTERN PetscErrorCode DMRestoreLocalVector(DM, Vec *);
64 PETSC_EXTERN PetscErrorCode DMGetGlobalVector(DM, Vec *);
65 PETSC_EXTERN PetscErrorCode DMRestoreGlobalVector(DM, Vec *);
66 PETSC_EXTERN PetscErrorCode DMClearGlobalVectors(DM);
67 PETSC_EXTERN PetscErrorCode DMClearLocalVectors(DM);
68 PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
69 PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
70 PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
71 PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
72 PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
73 PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
74 PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
75 PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
76 PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
77 PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
78 PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
79 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
80 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
81 PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
82 PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
83 PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
84 PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
85 PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
86 PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
87 PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
88 PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
89 PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
90 PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
91 PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
92 PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
93 PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
94 PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
95 PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
96 PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
97 PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
98 PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
99 PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
100 PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
101 PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
102 PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
103 PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
104 PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
105 PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
106 PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
107 PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
108 PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);
109 
110 PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
111 PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
112 PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
113 PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
114 PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
115 PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);
116 
117 PETSC_EXTERN PetscErrorCode DMSetUp(DM);
118 PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
119 PETSC_EXTERN                PETSC_DEPRECATED_FUNCTION("Use DMDACreateAggregates() or DMCreateRestriction() (since version 3.12)") PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
120 PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
121 PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
122 PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
123 PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
124 PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
125 PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
126 PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
127 PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
128 PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
129 PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
130 PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);
131 
132 /* Topology support */
133 PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
134 PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
135 PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
136 PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
137 PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
138 PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);
139 
140 /* Coordinate support */
141 PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
142 PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
143 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
144 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
145 PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
146 PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
147 PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
148 PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
149 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
150 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
151 PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
152 PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
153 PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
154 PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
155 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
156 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
157 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
158 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
159 PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
160 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
161 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
162 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
163 PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
164 PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
165 PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
166 PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
167 PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
168 PETSC_EXTERN PetscErrorCode DMProjectCoordinates(DM, PetscFE);
169 PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
170 
171 /* Periodicity support */
172 PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
173 PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
174 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
175 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
176 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
177 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
178 
179 /* block hook interface */
180 PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
181 PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
182 PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);
183 
184 PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
185 PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
186 PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
187 PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
188 PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
189 PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
190 PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
191 PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
192 PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
193 PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
194 PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscErrorCode (*)(void **));
195 PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
196 PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
197 PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
198 PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
199 PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
200 PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
201 PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);
202 
203 PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
204 PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
205 PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
206 PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
207 PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
208 PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
209 PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);
210 
211 PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
212 PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
213 PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
214 PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
215 PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);
216 
217 PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
218 PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
219 PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
220 PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
221 PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);
222 
223 typedef struct NLF_DAAD *NLF;
224 
225 #define DM_FILE_CLASSID 1211221
226 
227 /* FEM support */
228 PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
229 PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
230 PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);
231 
232 PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
233 PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
234 PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
235 PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
236 
237 PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
238 PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
239 PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
240 PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
241 PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
242 PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
243 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSection() (since v3.9)") PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
244 {
245   return DMGetSection(dm, s);
246 }
247 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSection() (since v3.9)") PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
248 {
249   return DMSetSection(dm, s);
250 }
251 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetGlobalSection() (since v3.9)") PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
252 {
253   return DMGetGlobalSection(dm, s);
254 }
255 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetGlobalSection() (since v3.9)") PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
256 {
257   return DMSetGlobalSection(dm, s);
258 }
259 
260 PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
261 PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
262 PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
263 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSectionSF() (since v3.12)") PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
264 {
265   return DMGetSectionSF(dm, s);
266 }
267 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSectionSF() (since v3.12)") PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
268 {
269   return DMSetSectionSF(dm, s);
270 }
271 static inline PETSC_DEPRECATED_FUNCTION("Use DMCreateSectionSF() (since v3.12)") PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
272 {
273   return DMCreateSectionSF(dm, l, g);
274 }
275 PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
276 PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
277 PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
278 PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);
279 
280 PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
281 PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);
282 
283 PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
284 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
285 PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
286 PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);
287 
288 PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
289 PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
290 PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
291 PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
292 PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
293 PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
294 PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
295 PETSC_EXTERN PetscErrorCode DMClearFields(DM);
296 PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
297 PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
298 PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
299 PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
300 PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);
301 
302 PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
303 PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
304 PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *, PetscDS *);
305 PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *, PetscDS *);
306 PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS, PetscDS);
307 PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *, PetscDS *);
308 PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS, PetscDS);
309 PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
310 PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
311 PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
312 PETSC_EXTERN PetscErrorCode DMClearDS(DM);
313 PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
314 PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
315 PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
316 PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
317 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
318 PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
319 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
320 PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
321 
322 /*MC
323   DMInterpolationInfo - Structure for holding information about interpolation on a mesh
324 
325   Synopsis:
326     comm   - The communicator
327     dim    - The spatial dimension of points
328     nInput - The number of input points
329     points - The input point coordinates
330     cells  - The cell containing each point
331     n      - The number of local points
332     coords - The point coordinates
333     dof    - The number of components to interpolate
334 
335   Level: intermediate
336 
337 .seealso: `DM`, `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
338 M*/
339 struct _DMInterpolationInfo {
340   MPI_Comm   comm;
341   PetscInt   dim;    /*1 The spatial dimension of points */
342   PetscInt   nInput; /* The number of input points */
343   PetscReal *points; /* The input point coordinates */
344   PetscInt  *cells;  /* The cell containing each point */
345   PetscInt   n;      /* The number of local points */
346   Vec        coords; /* The point coordinates */
347   PetscInt   dof;    /* The number of components to interpolate */
348 };
349 typedef struct _DMInterpolationInfo *DMInterpolationInfo;
350 
351 PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
352 PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
353 PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
354 PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
355 PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
356 PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
357 PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
358 PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
359 PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
360 PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
361 PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
362 PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);
363 
364 PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
365 PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
366 PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
367 PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
368 PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
369 PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
370 PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
371 PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
372 PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
373 PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
374 PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
375 PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
376 PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);
377 
378 /*E
379    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination DMs with the same name
380 
381    Values:
382 +  `DM_COPY_LABELS_REPLACE`  - replace label in destination by label from source
383 .  `DM_COPY_LABELS_KEEP`     - keep destination label
384 -  `DM_COPY_LABELS_FAIL`     - throw error
385 
386    Level: advanced
387 
388 .seealso: `DMLabel`, `DM`, `DMCompareLabels()`, `DMRemoveLabel()`
389 E*/
390 typedef enum {
391   DM_COPY_LABELS_REPLACE,
392   DM_COPY_LABELS_KEEP,
393   DM_COPY_LABELS_FAIL
394 } DMCopyLabelsMode;
395 PETSC_EXTERN const char *const DMCopyLabelsModes[];
396 
397 PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
398 PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
399 PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
400 PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
401 PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
402 PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
403 PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
404 PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
405 PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
406 PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
407 PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);
408 
409 PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
410 PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
411 
412 PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
413 PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
414 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
415 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
416 PETSC_EXTERN PetscErrorCode DMProjectFieldLocal(DM, PetscReal, Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
417 PETSC_EXTERN PetscErrorCode DMProjectFieldLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**funcs)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
418 PETSC_EXTERN PetscErrorCode DMProjectFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
419 PETSC_EXTERN PetscErrorCode DMProjectBdFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
420 PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
421 PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
422 PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
423 PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
424 PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
425 PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);
426 
427 PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);
428 
429 PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
430 PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
431 PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
432 PETSC_EXTERN PetscErrorCode DMMonitor(DM);
433 
434 static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
435 {
436   switch (ct) {
437   case DM_POLYTOPE_POINT:
438     return 0;
439   case DM_POLYTOPE_SEGMENT:
440   case DM_POLYTOPE_POINT_PRISM_TENSOR:
441     return 1;
442   case DM_POLYTOPE_TRIANGLE:
443   case DM_POLYTOPE_QUADRILATERAL:
444   case DM_POLYTOPE_SEG_PRISM_TENSOR:
445     return 2;
446   case DM_POLYTOPE_TETRAHEDRON:
447   case DM_POLYTOPE_HEXAHEDRON:
448   case DM_POLYTOPE_TRI_PRISM:
449   case DM_POLYTOPE_TRI_PRISM_TENSOR:
450   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
451   case DM_POLYTOPE_PYRAMID:
452     return 3;
453   default:
454     return -1;
455   }
456 }
457 
458 static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
459 {
460   switch (ct) {
461   case DM_POLYTOPE_POINT:
462     return 0;
463   case DM_POLYTOPE_SEGMENT:
464     return 2;
465   case DM_POLYTOPE_POINT_PRISM_TENSOR:
466     return 2;
467   case DM_POLYTOPE_TRIANGLE:
468     return 3;
469   case DM_POLYTOPE_QUADRILATERAL:
470     return 4;
471   case DM_POLYTOPE_SEG_PRISM_TENSOR:
472     return 4;
473   case DM_POLYTOPE_TETRAHEDRON:
474     return 4;
475   case DM_POLYTOPE_HEXAHEDRON:
476     return 6;
477   case DM_POLYTOPE_TRI_PRISM:
478     return 5;
479   case DM_POLYTOPE_TRI_PRISM_TENSOR:
480     return 5;
481   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
482     return 6;
483   case DM_POLYTOPE_PYRAMID:
484     return 5;
485   default:
486     return -1;
487   }
488 }
489 
490 static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
491 {
492   switch (ct) {
493   case DM_POLYTOPE_POINT:
494     return 1;
495   case DM_POLYTOPE_SEGMENT:
496     return 2;
497   case DM_POLYTOPE_POINT_PRISM_TENSOR:
498     return 2;
499   case DM_POLYTOPE_TRIANGLE:
500     return 3;
501   case DM_POLYTOPE_QUADRILATERAL:
502     return 4;
503   case DM_POLYTOPE_SEG_PRISM_TENSOR:
504     return 4;
505   case DM_POLYTOPE_TETRAHEDRON:
506     return 4;
507   case DM_POLYTOPE_HEXAHEDRON:
508     return 8;
509   case DM_POLYTOPE_TRI_PRISM:
510     return 6;
511   case DM_POLYTOPE_TRI_PRISM_TENSOR:
512     return 6;
513   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
514     return 8;
515   case DM_POLYTOPE_PYRAMID:
516     return 5;
517   default:
518     return -1;
519   }
520 }
521 
522 static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
523 {
524   return dim == 0 ? DM_POLYTOPE_POINT : (dim == 1 ? DM_POLYTOPE_SEGMENT : (dim == 2 ? (simplex ? DM_POLYTOPE_TRIANGLE : DM_POLYTOPE_QUADRILATERAL) : (dim == 3 ? (simplex ? DM_POLYTOPE_TETRAHEDRON : DM_POLYTOPE_HEXAHEDRON) : DM_POLYTOPE_UNKNOWN)));
525 }
526 
527 static inline PetscInt DMPolytopeTypeGetNumArrangments(DMPolytopeType ct)
528 {
529   switch (ct) {
530   case DM_POLYTOPE_POINT:
531     return 1;
532   case DM_POLYTOPE_SEGMENT:
533     return 2;
534   case DM_POLYTOPE_POINT_PRISM_TENSOR:
535     return 2;
536   case DM_POLYTOPE_TRIANGLE:
537     return 6;
538   case DM_POLYTOPE_QUADRILATERAL:
539     return 8;
540   case DM_POLYTOPE_SEG_PRISM_TENSOR:
541     return 4;
542   case DM_POLYTOPE_TETRAHEDRON:
543     return 24;
544   case DM_POLYTOPE_HEXAHEDRON:
545     return 48;
546   case DM_POLYTOPE_TRI_PRISM:
547     return 12;
548   case DM_POLYTOPE_TRI_PRISM_TENSOR:
549     return 12;
550   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
551     return 16;
552   case DM_POLYTOPE_PYRAMID:
553     return 8;
554   default:
555     return -1;
556   }
557 }
558 
559 /* An arrangement is a face order combined with an orientation for each face */
560 static inline const PetscInt *DMPolytopeTypeGetArrangment(DMPolytopeType ct, PetscInt o)
561 {
562   static const PetscInt pntArr[1 * 2] = {0, 0};
563   /* a: swap */
564   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
565                                              0, 0, 1, 0,
566                                              /*  0: e */};
567   /* a: swap first two
568      b: swap last two */
569   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
570                                              2, -1, 1, -1, 0, -1, /* -2: aba */
571                                              1, -1, 0, -1, 2, -1, /* -1: a */
572                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
573                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
574                                              2, 0,  0, 0,  1, 0,
575                                              /*  2: ab */};
576   /* a: forward cyclic permutation
577      b: swap first and last pairs */
578   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
579                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
580                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
581                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
582                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
583                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
584                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
585                                               3, 0,  0, 0,  1, 0,  2, 0,
586                                               /*  3: a^3 */};
587   /* r: rotate 180
588      b: swap top and bottom segments */
589   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
590                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
591                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
592                                               1, 0,  0, 0,  2, -1, 3, -1,
593                                               /*  1: b */};
594   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
595   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
596                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
597                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
598                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
599                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
600                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
601                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
602                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
603                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
604                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
605                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
606                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
607                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
608                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
609                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
610                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
611                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
612                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
613                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
614                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
615                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
616                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
617                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
618                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
619   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
620   static const PetscInt hexArr[48 * 6 * 2] = {
621     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
622     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
623     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
624     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
625     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
626     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
627     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
628     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
629     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
630     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
631     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
632     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
633     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
634     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
635     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
636     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
637     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
638     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
639     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
640     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
641     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
642     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
643     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
644     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
645     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
646     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
647     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
648     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
649     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
650     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
651     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
652     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
653     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
654     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
655     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
656     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
657     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
658     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
659     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
660     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
661     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
662     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
663     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
664     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
665     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
666     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
667     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
668     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
669   };
670   static const PetscInt tripArr[12 * 5 * 2] = {
671     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
672     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
673     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
674     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
675     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
676     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
677     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
678     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
679     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
680     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
681     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
682     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
683   };
684   /* a: rotate 120 about z
685      b: swap top and bottom segments
686      r: reflect */
687   static const PetscInt ttriArr[12 * 5 * 2] = {
688     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
689     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
690     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
691     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
692     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
693     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
694     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
695     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
696     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
697     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
698     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
699     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
700   };
701   /* a: rotate 90 about z
702      b: swap top and bottom segments
703      r: reflect */
704   static const PetscInt tquadArr[16 * 6 * 2] = {
705     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
706     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
707     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
708     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
709     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
710     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
711     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
712     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
713     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
714     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
715     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
716     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
717     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
718     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
719     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
720     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
721   };
722   static const PetscInt pyrArr[8 * 5 * 2] = {
723     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
724     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
725     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
726     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
727     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
728     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
729     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
730     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
731   };
732   switch (ct) {
733   case DM_POLYTOPE_POINT:
734     return pntArr;
735   case DM_POLYTOPE_SEGMENT:
736     return &segArr[(o + 1) * 2 * 2];
737   case DM_POLYTOPE_POINT_PRISM_TENSOR:
738     return &segArr[(o + 1) * 2 * 2];
739   case DM_POLYTOPE_TRIANGLE:
740     return &triArr[(o + 3) * 3 * 2];
741   case DM_POLYTOPE_QUADRILATERAL:
742     return &quadArr[(o + 4) * 4 * 2];
743   case DM_POLYTOPE_SEG_PRISM_TENSOR:
744     return &tsegArr[(o + 2) * 4 * 2];
745   case DM_POLYTOPE_TETRAHEDRON:
746     return &tetArr[(o + 12) * 4 * 2];
747   case DM_POLYTOPE_HEXAHEDRON:
748     return &hexArr[(o + 24) * 6 * 2];
749   case DM_POLYTOPE_TRI_PRISM:
750     return &tripArr[(o + 6) * 5 * 2];
751   case DM_POLYTOPE_TRI_PRISM_TENSOR:
752     return &ttriArr[(o + 6) * 5 * 2];
753   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
754     return &tquadArr[(o + 8) * 6 * 2];
755   case DM_POLYTOPE_PYRAMID:
756     return &pyrArr[(o + 4) * 5 * 2];
757   default:
758     return PETSC_NULLPTR;
759   }
760 }
761 
762 /* A vertex arrangement is a vertex order */
763 static inline const PetscInt *DMPolytopeTypeGetVertexArrangment(DMPolytopeType ct, PetscInt o)
764 {
765   static const PetscInt pntVerts[1]      = {0};
766   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
767   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
768   static const PetscInt quadVerts[8 * 4] = {2, 1, 0, 3, 1, 0, 3, 2, 0, 3, 2, 1, 3, 2, 1, 0, 0, 1, 2, 3, 1, 2, 3, 0, 2, 3, 0, 1, 3, 0, 1, 2};
769   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
770   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
771                                             3, 1, 2, 0, /* -11: (14)     p21 */
772                                             1, 2, 3, 0, /* -10: (1234)   p18 */
773                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
774                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
775                                             0, 3, 2, 1, /*  -7: (24)     p14 */
776                                             0, 1, 3, 2, /*  -6: (34)     p6  */
777                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
778                                             3, 0, 1, 2, /*  -4: (1432    p9  */
779                                             1, 0, 2, 3, /*  -3: (12)     p1  */
780                                             0, 2, 1, 3, /*  -2: (23)     p2  */
781                                             2, 1, 0, 3, /*  -1: (13)     p5  */
782                                             0, 1, 2, 3, /*   0: ()       p0  */
783                                             1, 2, 0, 3, /*   1: (123)    p4  */
784                                             2, 0, 1, 3, /*   2: (132)    p3  */
785                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
786                                             0, 3, 1, 2, /*   4: (243)    p8  */
787                                             3, 1, 0, 2, /*   5: (143)    p11 */
788                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
789                                             3, 0, 2, 1, /*   7: (142)    p15 */
790                                             0, 2, 3, 1, /*   8: (234)    p12 */
791                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
792                                             2, 1, 3, 0, /*  10: (134)    p19 */
793                                             1, 3, 2, 0 /*  11: (124)    p20 */};
794   static const PetscInt hexVerts[48 * 8] = {
795     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
796     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
797     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
798     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
799     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
800     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
801     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
802     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
803     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
804     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
805     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
806     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
807     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
808     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
809     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
810     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
811     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
812     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
813     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
814     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
815     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
816     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
817     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
818     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
819     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
820     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
821     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
822     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
823     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
824     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
825     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
826     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
827     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
828     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
829     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
830     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
831     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
832     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
833     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
834     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
835     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
836     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
837     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
838     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
839     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
840     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
841     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
842     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
843   };
844   static const PetscInt tripVerts[12 * 6] = {
845     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
846     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
847     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
848     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
849     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
850     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
851     0, 1, 2, 3, 4, 5, /*  0: identity */
852     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
853     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
854     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
855     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
856     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
857   };
858   static const PetscInt ttriVerts[12 * 6] = {
859     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
860     3, 5, 4, 0, 2, 1, /* -5: r b a */
861     5, 4, 3, 2, 1, 0, /* -4: r b */
862     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
863     0, 2, 1, 3, 5, 4, /* -2: r a */
864     2, 1, 0, 5, 4, 3, /* -1: r */
865     0, 1, 2, 3, 4, 5, /*  0: identity */
866     1, 2, 0, 4, 5, 3, /*  1: a */
867     2, 0, 1, 5, 3, 4, /*  2: a^2 */
868     3, 4, 5, 0, 1, 2, /*  3: b */
869     4, 5, 3, 1, 2, 0, /*  4: b a */
870     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
871   };
872   /* a: rotate 90 about z
873      b: swap top and bottom segments
874      r: reflect */
875   static const PetscInt tquadVerts[16 * 8] = {
876     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
877     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
878     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
879     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
880     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
881     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
882     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
883     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
884     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
885     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
886     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
887     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
888     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
889     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
890     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
891     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
892   };
893   static const PetscInt pyrVerts[8 * 5] = {
894     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
895     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
896     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
897     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
898     0, 1, 2, 3, 4, /*  0: identity */
899     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
900     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
901     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
902   };
903   switch (ct) {
904   case DM_POLYTOPE_POINT:
905     return pntVerts;
906   case DM_POLYTOPE_SEGMENT:
907     return &segVerts[(o + 1) * 2];
908   case DM_POLYTOPE_POINT_PRISM_TENSOR:
909     return &segVerts[(o + 1) * 2];
910   case DM_POLYTOPE_TRIANGLE:
911     return &triVerts[(o + 3) * 3];
912   case DM_POLYTOPE_QUADRILATERAL:
913     return &quadVerts[(o + 4) * 4];
914   case DM_POLYTOPE_SEG_PRISM_TENSOR:
915     return &tsegVerts[(o + 2) * 4];
916   case DM_POLYTOPE_TETRAHEDRON:
917     return &tetVerts[(o + 12) * 4];
918   case DM_POLYTOPE_HEXAHEDRON:
919     return &hexVerts[(o + 24) * 8];
920   case DM_POLYTOPE_TRI_PRISM:
921     return &tripVerts[(o + 6) * 6];
922   case DM_POLYTOPE_TRI_PRISM_TENSOR:
923     return &ttriVerts[(o + 6) * 6];
924   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
925     return &tquadVerts[(o + 8) * 8];
926   case DM_POLYTOPE_PYRAMID:
927     return &pyrVerts[(o + 4) * 5];
928   default:
929     return PETSC_NULLPTR;
930   }
931 }
932 
933 /* This is orientation o1 acting on orientation o2 */
934 static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
935 {
936   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
937   static const PetscInt triMult[6 * 6]   = {0, 2, 1, -3, -1, -2, 1, 0, 2, -2, -3, -1, 2, 1, 0, -1, -2, -3, -3, -2, -1, 0, 1, 2, -2, -1, -3, 1, 2, 0, -1, -3, -2, 2, 0, 1};
938   static const PetscInt quadMult[8 * 8]  = {0,  3,  2,  1,  -4, -1, -2, -3, 1,  0,  3,  2,  -3, -4, -1, -2, 2,  1,  0,  3,  -2, -3, -4, -1, 3,  2,  1,  0,  -1, -2, -3, -4,
939                                             -4, -3, -2, -1, 0,  1,  2,  3,  -3, -2, -1, -4, 1,  2,  3,  0,  -2, -1, -4, -3, 2,  3,  0,  1,  -1, -4, -3, -2, 3,  0,  1,  2};
940   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
941   static const PetscInt tetMult[24 * 24] = {
942     3,   2,   7,   0,   5,   10,  9,   8,   1,   6,   11,  4,   -12, -7,  -5,  -9,  -10, -2,  -6,  -1,  -11, -3,  -4,  -8,  4,   0,   8,   1,   3,   11,  10,  6,   2,   7,   9,   5,   -11, -9,  -4,  -8,  -12, -1,  -5,  -3,  -10, -2,  -6,  -7,
943     5,   1,   6,   2,   4,   9,   11,  7,   0,   8,   10,  3,   -10, -8,  -6,  -7,  -11, -3,  -4,  -2,  -12, -1,  -5,  -9,  0,   8,   4,   3,   11,  1,   6,   2,   10,  9,   5,   7,   -9,  -4,  -11, -12, -1,  -8,  -3,  -10, -5,  -6,  -7,  -2,
944     1,   6,   5,   4,   9,   2,   7,   0,   11,  10,  3,   8,   -8,  -6,  -10, -11, -3,  -7,  -2,  -12, -4,  -5,  -9,  -1,  2,   7,   3,   5,   10,  0,   8,   1,   9,   11,  4,   6,   -7,  -5,  -12, -10, -2,  -9,  -1,  -11, -6,  -4,  -8,  -3,
945     6,   5,   1,   9,   2,   4,   0,   11,  7,   3,   8,   10,  -6,  -10, -8,  -3,  -7,  -11, -12, -4,  -2,  -9,  -1,  -5,  7,   3,   2,   10,  0,   5,   1,   9,   8,   4,   6,   11,  -5,  -12, -7,  -2,  -9,  -10, -11, -6,  -1,  -8,  -3,  -4,
946     8,   4,   0,   11,  1,   3,   2,   10,  6,   5,   7,   9,   -4,  -11, -9,  -1,  -8,  -12, -10, -5,  -3,  -7,  -2,  -6,  9,   11,  10,  6,   8,   7,   3,   5,   4,   0,   2,   1,   -3,  -1,  -2,  -6,  -4,  -5,  -9,  -7,  -8,  -12, -10, -11,
947     10,  9,   11,  7,   6,   8,   4,   3,   5,   1,   0,   2,   -2,  -3,  -1,  -5,  -6,  -4,  -8,  -9,  -7,  -11, -12, -10, 11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12,
948     -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  -11, -10, -12, -8,  -7,  -9,  -5,  -4,  -6,  -2,  -1,  -3,  1,   2,   0,   4,   5,   3,   7,   8,   6,   10,  11,  9,
949     -10, -12, -11, -7,  -9,  -8,  -4,  -6,  -5,  -1,  -3,  -2,  2,   0,   1,   5,   3,   4,   8,   6,   7,   11,  9,   10,  -9,  -5,  -1,  -12, -2,  -4,  -3,  -11, -7,  -6,  -8,  -10, 3,   10,  8,   0,   7,   11,  9,   4,   2,   6,   1,   5,
950     -8,  -4,  -3,  -11, -1,  -6,  -2,  -10, -9,  -5,  -7,  -12, 4,   11,  6,   1,   8,   9,   10,  5,   0,   7,   2,   3,   -7,  -6,  -2,  -10, -3,  -5,  -1,  -12, -8,  -4,  -9,  -11, 5,   9,   7,   2,   6,   10,  11,  3,   1,   8,   0,   4,
951     -3,  -8,  -4,  -6,  -11, -1,  -9,  -2,  -10, -12, -5,  -7,  6,   4,   11,  9,   1,   8,   0,   10,  5,   3,   7,   2,   -2,  -7,  -6,  -5,  -10, -3,  -8,  -1,  -12, -11, -4,  -9,  7,   5,   9,   10,  2,   6,   1,   11,  3,   4,   8,   0,
952     -1,  -9,  -5,  -4,  -12, -2,  -7,  -3,  -11, -10, -6,  -8,  8,   3,   10,  11,  0,   7,   2,   9,   4,   5,   6,   1,   -6,  -2,  -7,  -3,  -5,  -10, -12, -8,  -1,  -9,  -11, -4,  9,   7,   5,   6,   10,  2,   3,   1,   11,  0,   4,   8,
953     -5,  -1,  -9,  -2,  -4,  -12, -11, -7,  -3,  -8,  -10, -6,  10,  8,   3,   7,   11,  0,   4,   2,   9,   1,   5,   6,   -4,  -3,  -8,  -1,  -6,  -11, -10, -9,  -2,  -7,  -12, -5,  11,  6,   4,   8,   9,   1,   5,   0,   10,  2,   3,   7,
954   };
955   static const PetscInt hexMult[48 * 48] = {
956     18,  2,   5,   22,  21,  8,   16,  0,   13,  6,   11,  3,   15,  9,   4,   23,  12,  1,   19,  10,  7,   20,  14,  17,  -24, -10, -20, -16, -12, -21, -4,  -5,  -18, -13, -15, -8,  -2,  -11, -14, -7,  -3,  -22, -6,  -17, -19, -9,  -1,  -23,
957     8,   20,  19,  2,   5,   23,  0,   17,  11,  1,   15,  7,   13,  4,   10,  18,  3,   14,  21,  9,   12,  22,  6,   16,  -23, -13, -17, -7,  -8,  -19, -16, -12, -22, -2,  -14, -5,  -10, -15, -11, -4,  -20, -9,  -21, -3,  -6,  -18, -24, -1,
958     2,   17,  23,  8,   0,   19,  5,   20,  1,   11,  9,   14,  12,  6,   3,   16,  10,  7,   22,  15,  13,  21,  4,   18,  -22, -14, -19, -5,  -15, -17, -10, -2,  -23, -12, -13, -7,  -16, -8,  -4,  -11, -24, -3,  -18, -9,  -1,  -21, -20, -6,
959     21,  5,   2,   16,  18,  0,   22,  8,   4,   12,  3,   11,  14,  7,   13,  20,  6,   10,  17,  1,   9,   23,  15,  19,  -21, -8,  -18, -15, -4,  -24, -12, -14, -20, -7,  -16, -10, -11, -2,  -5,  -13, -6,  -19, -3,  -23, -22, -1,  -9,  -17,
960     16,  8,   0,   21,  22,  2,   18,  5,   12,  4,   1,   10,  9,   15,  6,   19,  13,  11,  23,  3,   14,  17,  7,   20,  -20, -16, -24, -10, -2,  -18, -11, -7,  -21, -14, -8,  -15, -12, -4,  -13, -5,  -9,  -23, -1,  -19, -17, -3,  -6,  -22,
961     5,   19,  20,  0,   8,   17,  2,   23,  10,  3,   7,   15,  6,   12,  11,  22,  1,   9,   16,  14,  4,   18,  13,  21,  -19, -5,  -22, -14, -16, -23, -8,  -11, -17, -4,  -7,  -13, -15, -10, -12, -2,  -21, -6,  -20, -1,  -9,  -24, -18, -3,
962     22,  0,   8,   18,  16,  5,   21,  2,   6,   13,  10,  1,   7,   14,  12,  17,  4,   3,   20,  11,  15,  19,  9,   23,  -18, -15, -21, -8,  -11, -20, -2,  -13, -24, -5,  -10, -16, -4,  -12, -7,  -14, -1,  -17, -9,  -22, -23, -6,  -3,  -19,
963     0,   23,  17,  5,   2,   20,  8,   19,  3,   10,  14,  9,   4,   13,  1,   21,  11,  15,  18,  7,   6,   16,  12,  22,  -17, -7,  -23, -13, -10, -22, -15, -4,  -19, -11, -5,  -14, -8,  -16, -2,  -12, -18, -1,  -24, -6,  -3,  -20, -21, -9,
964     10,  13,  6,   1,   11,  12,  3,   4,   8,   0,   22,  18,  19,  23,  5,   15,  2,   21,  9,   16,  17,  7,   20,  14,  -16, -24, -10, -20, -23, -8,  -19, -6,  -15, -3,  -21, -18, -22, -17, -9,  -1,  -14, -12, -7,  -4,  -11, -13, -5,  -2,
965     1,   4,   12,  10,  3,   6,   11,  13,  0,   8,   16,  21,  17,  20,  2,   14,  5,   18,  7,   22,  19,  9,   23,  15,  -15, -21, -8,  -18, -17, -10, -22, -3,  -16, -6,  -24, -20, -19, -23, -1,  -9,  -5,  -4,  -13, -12, -2,  -7,  -14, -11,
966     14,  10,  3,   9,   7,   1,   15,  11,  17,  23,  0,   5,   16,  22,  20,  6,   19,  8,   12,  2,   21,  4,   18,  13,  -14, -19, -5,  -22, -3,  -13, -9,  -20, -7,  -21, -23, -17, -6,  -1,  -24, -18, -12, -16, -2,  -8,  -10, -4,  -11, -15,
967     7,   3,   10,  15,  14,  11,  9,   1,   20,  19,  5,   0,   18,  21,  17,  4,   23,  2,   13,  8,   22,  6,   16,  12,  -13, -17, -7,  -23, -9,  -14, -3,  -24, -5,  -18, -22, -19, -1,  -6,  -20, -21, -2,  -10, -12, -15, -16, -11, -4,  -8,
968     13,  14,  15,  12,  4,   9,   6,   7,   21,  22,  23,  20,  2,   0,   18,  3,   16,  17,  1,   19,  8,   11,  5,   10,  -12, -9,  -11, -6,  -21, -4,  -24, -22, -2,  -23, -3,  -1,  -20, -18, -19, -17, -16, -14, -15, -13, -5,  -8,  -10, -7,
969     6,   9,   7,   4,   12,  14,  13,  15,  16,  18,  17,  19,  0,   2,   22,  1,   21,  23,  3,   20,  5,   10,  8,   11,  -11, -6,  -12, -9,  -20, -2,  -18, -17, -4,  -19, -1,  -3,  -21, -24, -23, -22, -8,  -7,  -10, -5,  -13, -16, -15, -14,
970     3,   12,  4,   11,  1,   13,  10,  6,   2,   5,   21,  16,  23,  19,  0,   9,   8,   22,  15,  18,  20,  14,  17,  7,   -10, -20, -16, -24, -22, -15, -17, -1,  -8,  -9,  -18, -21, -23, -19, -3,  -6,  -13, -2,  -5,  -11, -4,  -14, -7,  -12,
971     20,  16,  18,  23,  17,  21,  19,  22,  14,  15,  4,   6,   3,   1,   7,   0,   9,   12,  2,   13,  11,  5,   10,  8,   -9,  -11, -6,  -12, -14, -3,  -13, -10, -1,  -8,  -2,  -4,  -7,  -5,  -16, -15, -23, -20, -22, -18, -24, -19, -17, -21,
972     11,  6,   13,  3,   10,  4,   1,   12,  5,   2,   18,  22,  20,  17,  8,   7,   0,   16,  14,  21,  23,  15,  19,  9,   -8,  -18, -15, -21, -19, -16, -23, -9,  -10, -1,  -20, -24, -17, -22, -6,  -3,  -7,  -11, -14, -2,  -12, -5,  -13, -4,
973     9,   11,  1,   14,  15,  3,   7,   10,  23,  17,  2,   8,   21,  18,  19,  13,  20,  5,   4,   0,   16,  12,  22,  6,   -7,  -23, -13, -17, -1,  -5,  -6,  -21, -14, -20, -19, -22, -9,  -3,  -18, -24, -11, -8,  -4,  -16, -15, -2,  -12, -10,
974     19,  21,  22,  17,  23,  16,  20,  18,  9,   7,   12,  13,  1,   3,   15,  2,   14,  4,   0,   6,   10,  8,   11,  5,   -6,  -12, -9,  -11, -7,  -1,  -5,  -15, -3,  -16, -4,  -2,  -14, -13, -8,  -10, -19, -21, -17, -24, -18, -23, -22, -20,
975     15,  1,   11,  7,   9,   10,  14,  3,   19,  20,  8,   2,   22,  16,  23,  12,  17,  0,   6,   5,   18,  13,  21,  4,   -5,  -22, -14, -19, -6,  -7,  -1,  -18, -13, -24, -17, -23, -3,  -9,  -21, -20, -4,  -15, -11, -10, -8,  -12, -2,  -16,
976     4,   15,  14,  6,   13,  7,   12,  9,   18,  16,  20,  23,  5,   8,   21,  11,  22,  19,  10,  17,  0,   3,   2,   1,   -4,  -1,  -2,  -3,  -24, -12, -21, -19, -11, -17, -6,  -9,  -18, -20, -22, -23, -15, -5,  -16, -7,  -14, -10, -8,  -13,
977     17,  18,  16,  19,  20,  22,  23,  21,  7,   9,   6,   4,   10,  11,  14,  5,   15,  13,  8,   12,  1,   0,   3,   2,   -3,  -4,  -1,  -2,  -13, -9,  -14, -16, -6,  -15, -12, -11, -5,  -7,  -10, -8,  -22, -24, -23, -21, -20, -17, -19, -18,
978     12,  7,   9,   13,  6,   15,  4,   14,  22,  21,  19,  17,  8,   5,   16,  10,  18,  20,  11,  23,  2,   1,   0,   3,   -2,  -3,  -4,  -1,  -18, -11, -20, -23, -12, -22, -9,  -6,  -24, -21, -17, -19, -10, -13, -8,  -14, -7,  -15, -16, -5,
979     23,  22,  21,  20,  19,  18,  17,  16,  15,  14,  13,  12,  11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24,
980     -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  12,  13,  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,
981     -13, -8,  -10, -14, -7,  -16, -5,  -15, -23, -22, -20, -18, -9,  -6,  -17, -11, -19, -21, -12, -24, -3,  -2,  -1,  -4,  1,   2,   3,   0,   17,  10,  19,  22,  11,  21,  8,   5,   23,  20,  16,  18,  9,   12,  7,   13,  6,   14,  15,  4,
982     -18, -19, -17, -20, -21, -23, -24, -22, -8,  -10, -7,  -5,  -11, -12, -15, -6,  -16, -14, -9,  -13, -2,  -1,  -4,  -3,  2,   3,   0,   1,   12,  8,   13,  15,  5,   14,  11,  10,  4,   6,   9,   7,   21,  23,  22,  20,  19,  16,  18,  17,
983     -5,  -16, -15, -7,  -14, -8,  -13, -10, -19, -17, -21, -24, -6,  -9,  -22, -12, -23, -20, -11, -18, -1,  -4,  -3,  -2,  3,   0,   1,   2,   23,  11,  20,  18,  10,  16,  5,   8,   17,  19,  21,  22,  14,  4,   15,  6,   13,  9,   7,   12,
984     -16, -2,  -12, -8,  -10, -11, -15, -4,  -20, -21, -9,  -3,  -23, -17, -24, -13, -18, -1,  -7,  -6,  -19, -14, -22, -5,  4,   21,  13,  18,  5,   6,   0,   17,  12,  23,  16,  22,  2,   8,   20,  19,  3,   14,  10,  9,   7,   11,  1,   15,
985     -20, -22, -23, -18, -24, -17, -21, -19, -10, -8,  -13, -14, -2,  -4,  -16, -3,  -15, -5,  -1,  -7,  -11, -9,  -12, -6,  5,   11,  8,   10,  6,   0,   4,   14,  2,   15,  3,   1,   13,  12,  7,   9,   18,  20,  16,  23,  17,  22,  21,  19,
986     -10, -12, -2,  -15, -16, -4,  -8,  -11, -24, -18, -3,  -9,  -22, -19, -20, -14, -21, -6,  -5,  -1,  -17, -13, -23, -7,  6,   22,  12,  16,  0,   4,   5,   20,  13,  19,  18,  21,  8,   2,   17,  23,  10,  7,   3,   15,  14,  1,   11,  9,
987     -12, -7,  -14, -4,  -11, -5,  -2,  -13, -6,  -3,  -19, -23, -21, -18, -9,  -8,  -1,  -17, -15, -22, -24, -16, -20, -10, 7,   17,  14,  20,  18,  15,  22,  8,   9,   0,   19,  23,  16,  21,  5,   2,   6,   10,  13,  1,   11,  4,   12,  3,
988     -21, -17, -19, -24, -18, -22, -20, -23, -15, -16, -5,  -7,  -4,  -2,  -8,  -1,  -10, -13, -3,  -14, -12, -6,  -11, -9,  8,   10,  5,   11,  13,  2,   12,  9,   0,   7,   1,   3,   6,   4,   15,  14,  22,  19,  21,  17,  23,  18,  16,  20,
989     -4,  -13, -5,  -12, -2,  -14, -11, -7,  -3,  -6,  -22, -17, -24, -20, -1,  -10, -9,  -23, -16, -19, -21, -15, -18, -8,  9,   19,  15,  23,  21,  14,  16,  0,   7,   8,   17,  20,  22,  18,  2,   5,   12,  1,   4,   10,  3,   13,  6,   11,
990     -7,  -10, -8,  -5,  -13, -15, -14, -16, -17, -19, -18, -20, -1,  -3,  -23, -2,  -22, -24, -4,  -21, -6,  -11, -9,  -12, 10,  5,   11,  8,   19,  1,   17,  16,  3,   18,  0,   2,   20,  23,  22,  21,  7,   6,   9,   4,   12,  15,  14,  13,
991     -14, -15, -16, -13, -5,  -10, -7,  -8,  -22, -23, -24, -21, -3,  -1,  -19, -4,  -17, -18, -2,  -20, -9,  -12, -6,  -11, 11,  8,   10,  5,   20,  3,   23,  21,  1,   22,  2,   0,   19,  17,  18,  16,  15,  13,  14,  12,  4,   7,   9,   6,
992     -8,  -4,  -11, -16, -15, -12, -10, -2,  -21, -20, -6,  -1,  -19, -22, -18, -5,  -24, -3,  -14, -9,  -23, -7,  -17, -13, 12,  16,  6,   22,  8,   13,  2,   23,  4,   17,  21,  18,  0,   5,   19,  20,  1,   9,   11,  14,  15,  10,  3,   7,
993     -15, -11, -4,  -10, -8,  -2,  -16, -12, -18, -24, -1,  -6,  -17, -23, -21, -7,  -20, -9,  -13, -3,  -22, -5,  -19, -14, 13,  18,  4,   21,  2,   12,  8,   19,  6,   20,  22,  16,  5,   0,   23,  17,  11,  15,  1,   7,   9,   3,   10,  14,
994     -2,  -5,  -13, -11, -4,  -7,  -12, -14, -1,  -9,  -17, -22, -18, -21, -3,  -15, -6,  -19, -8,  -23, -20, -10, -24, -16, 14,  20,  7,   17,  16,  9,   21,  2,   15,  5,   23,  19,  18,  22,  0,   8,   4,   3,   12,  11,  1,   6,   13,  10,
995     -11, -14, -7,  -2,  -12, -13, -4,  -5,  -9,  -1,  -23, -19, -20, -24, -6,  -16, -3,  -22, -10, -17, -18, -8,  -21, -15, 15,  23,  9,   19,  22,  7,   18,  5,   14,  2,   20,  17,  21,  16,  8,   0,   13,  11,  6,   3,   10,  12,  4,   1,
996     -1,  -24, -18, -6,  -3,  -21, -9,  -20, -4,  -11, -15, -10, -5,  -14, -2,  -22, -12, -16, -19, -8,  -7,  -17, -13, -23, 16,  6,   22,  12,  9,   21,  14,  3,   18,  10,  4,   13,  7,   15,  1,   11,  17,  0,   23,  5,   2,   19,  20,  8,
997     -23, -1,  -9,  -19, -17, -6,  -22, -3,  -7,  -14, -11, -2,  -8,  -15, -13, -18, -5,  -4,  -21, -12, -16, -20, -10, -24, 17,  14,  20,  7,   10,  19,  1,   12,  23,  4,   9,   15,  3,   11,  6,   13,  0,   16,  8,   21,  22,  5,   2,   18,
998     -6,  -20, -21, -1,  -9,  -18, -3,  -24, -11, -4,  -8,  -16, -7,  -13, -12, -23, -2,  -10, -17, -15, -5,  -19, -14, -22, 18,  4,   21,  13,  15,  22,  7,   10,  16,  3,   6,   12,  14,  9,   11,  1,   20,  5,   19,  0,   8,   23,  17,  2,
999     -17, -9,  -1,  -22, -23, -3,  -19, -6,  -13, -5,  -2,  -11, -10, -16, -7,  -20, -14, -12, -24, -4,  -15, -18, -8,  -21, 19,  15,  23,  9,   1,   17,  10,  6,   20,  13,  7,   14,  11,  3,   12,  4,   8,   22,  0,   18,  16,  2,   5,   21,
1000     -22, -6,  -3,  -17, -19, -1,  -23, -9,  -5,  -13, -4,  -12, -15, -8,  -14, -21, -7,  -11, -18, -2,  -10, -24, -16, -20, 20,  7,   17,  14,  3,   23,  11,  13,  19,  6,   15,  9,   10,  1,   4,   12,  5,   18,  2,   22,  21,  0,   8,   16,
1001     -3,  -18, -24, -9,  -1,  -20, -6,  -21, -2,  -12, -10, -15, -13, -7,  -4,  -17, -11, -8,  -23, -16, -14, -22, -5,  -19, 21,  13,  18,  4,   14,  16,  9,   1,   22,  11,  12,  6,   15,  7,   3,   10,  23,  2,   17,  8,   0,   20,  19,  5,
1002     -9,  -21, -20, -3,  -6,  -24, -1,  -18, -12, -2,  -16, -8,  -14, -5,  -11, -19, -4,  -15, -22, -10, -13, -23, -7,  -17, 22,  12,  16,  6,   7,   18,  15,  11,  21,  1,   13,  4,   9,   14,  10,  3,   19,  8,   20,  2,   5,   17,  23,  0,
1003     -19, -3,  -6,  -23, -22, -9,  -17, -1,  -14, -7,  -12, -4,  -16, -10, -5,  -24, -13, -2,  -20, -11, -8,  -21, -15, -18, 23,  9,   19,  15,  11,  20,  3,   4,   17,  12,  14,  7,   1,   10,  13,  6,   2,   21,  5,   16,  18,  8,   0,   22,
1004   };
1005   static const PetscInt tripMult[12 * 12] = {
1006     1,  0,  2,  3,  5,  4,  -6, -4, -5, -2, -3, -1, 0,  2,  1,  4,  3,  5,  -5, -6, -4, -3, -1, -2, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 4,  3,  5,  0,  2,  1,  -3, -1, -2, -5, -6, -4,
1007     3,  5,  4,  1,  0,  2,  -2, -3, -1, -6, -4, -5, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -4, -6, -5, -2, -1, -3, 1,  2,  0,  5,  3,  4,
1008     -5, -4, -6, -1, -3, -2, 2,  0,  1,  4,  5,  3,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -1, -3, -2, -5, -4, -6, 4,  5,  3,  2,  0,  1,  -2, -1, -3, -4, -6, -5, 5,  3,  4,  1,  2,  0,
1009   };
1010   static const PetscInt ttriMult[12 * 12] = {
1011     0,  2,  1,  3,  5,  4,  -6, -4, -5, -3, -1, -2, 1,  0,  2,  4,  3,  5,  -5, -6, -4, -2, -3, -1, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 3,  5,  4,  0,  2,  1,  -3, -1, -2, -6, -4, -5,
1012     4,  3,  5,  1,  0,  2,  -2, -3, -1, -5, -6, -4, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -5, -4, -6, -2, -1, -3, 1,  2,  0,  4,  5,  3,
1013     -4, -6, -5, -1, -3, -2, 2,  0,  1,  5,  3,  4,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -2, -1, -3, -5, -4, -6, 4,  5,  3,  1,  2,  0,  -1, -3, -2, -4, -6, -5, 5,  3,  4,  2,  0,  1,
1014   };
1015   static const PetscInt tquadMult[16 * 16] = {
1016     0,  3,  2,  1,  4,  7,  6,  5,  -8, -5, -6, -7, -4, -1, -2, -3, 1,  0,  3,  2,  5,  4,  7,  6,  -7, -8, -5, -6, -3, -4, -1, -2, 2,  1,  0,  3,  6,  5,  4,  7,  -6, -7, -8, -5, -2, -3, -4, -1, 3, 2, 1, 0,
1017     7,  6,  5,  4,  -5, -6, -7, -8, -1, -2, -3, -4, 4,  7,  6,  5,  0,  3,  2,  1,  -4, -1, -2, -3, -8, -5, -6, -7, 5,  4,  7,  6,  1,  0,  3,  2,  -3, -4, -1, -2, -7, -8, -5, -6, 6,  5,  4,  7,  2, 1, 0, 3,
1018     -2, -3, -4, -1, -6, -7, -8, -5, 7,  6,  5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -7, -8, -8, -7, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  6,  7,  -7, -6, -5, -8, -3, -2, -1, -4, 1, 2, 3, 0,
1019     5,  6,  7,  4,  -6, -5, -8, -7, -2, -1, -4, -3, 2,  3,  0,  1,  6,  7,  4,  5,  -5, -8, -7, -6, -1, -4, -3, -2, 3,  0,  1,  2,  7,  4,  5,  6,  -4, -3, -2, -1, -8, -7, -6, -5, 4,  5,  6,  7,  0, 1, 2, 3,
1020     -3, -2, -1, -4, -7, -6, -5, -8, 5,  6,  7,  4,  1,  2,  3,  0,  -2, -1, -4, -3, -6, -5, -8, -7, 6,  7,  4,  5,  2,  3,  0,  1,  -1, -4, -3, -2, -5, -8, -7, -6, 7,  4,  5,  6,  3,  0,  1,  2,
1021   };
1022   static const PetscInt pyrMult[8 * 8] = {
1023     0, 3, 2, 1, -4, -1, -2, -3, 1, 0, 3, 2, -3, -4, -1, -2, 2, 1, 0, 3, -2, -3, -4, -1, 3, 2, 1, 0, -1, -2, -3, -4, -4, -3, -2, -1, 0, 1, 2, 3, -3, -2, -1, -4, 1, 2, 3, 0, -2, -1, -4, -3, 2, 3, 0, 1, -1, -4, -3, -2, 3, 0, 1, 2,
1024   };
1025   switch (ct) {
1026   case DM_POLYTOPE_POINT:
1027     return 0;
1028   case DM_POLYTOPE_SEGMENT:
1029   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1030     return segMult[(o1 + 1) * 2 + o2 + 1];
1031   case DM_POLYTOPE_TRIANGLE:
1032     return triMult[(o1 + 3) * 6 + o2 + 3];
1033   case DM_POLYTOPE_QUADRILATERAL:
1034     return quadMult[(o1 + 4) * 8 + o2 + 4];
1035   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1036     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1037   case DM_POLYTOPE_TETRAHEDRON:
1038     return tetMult[(o1 + 12) * 24 + o2 + 12];
1039   case DM_POLYTOPE_HEXAHEDRON:
1040     return hexMult[(o1 + 24) * 48 + o2 + 24];
1041   case DM_POLYTOPE_TRI_PRISM:
1042     return tripMult[(o1 + 6) * 12 + o2 + 6];
1043   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1044     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1045   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1046     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1047   case DM_POLYTOPE_PYRAMID:
1048     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1049   default:
1050     return 0;
1051   }
1052 }
1053 
1054 /* This is orientation o1 acting on orientation o2^{-1} */
1055 static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1056 {
1057   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1058   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1059   static const PetscInt tetInv[24]   = {-9, -11, -4, -12, -5, -7, -6, -8, -10, -3, -2, -1, 0, 2, 1, 3, 8, 10, 6, 11, 4, 9, 5, 7};
1060   static const PetscInt hexInv[48]   = {-17, -18, -20, -19, -22, -21, -23, -24, -15, -16, -14, -13, -11, -12, -10, -9, -8, -5, -6, -7, -4, -3, -2, -1, 0, 3, 2, 1, 6, 5, 4, 9, 8, 7, 10, 11, 12, 13, 14, 15, 17, 16, 19, 18, 21, 20, 23, 22};
1061   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1062   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1063   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1064   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1065   switch (ct) {
1066   case DM_POLYTOPE_POINT:
1067     return 0;
1068   case DM_POLYTOPE_SEGMENT:
1069   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1070     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1071   case DM_POLYTOPE_TRIANGLE:
1072     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1073   case DM_POLYTOPE_QUADRILATERAL:
1074     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1075   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1076     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1077   case DM_POLYTOPE_TETRAHEDRON:
1078     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1079   case DM_POLYTOPE_HEXAHEDRON:
1080     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1081   case DM_POLYTOPE_TRI_PRISM:
1082     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1083   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1084     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1085   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1086     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1087   case DM_POLYTOPE_PYRAMID:
1088     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1089   default:
1090     return 0;
1091   }
1092 }
1093 
1094 PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1095 PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1096 PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1097 PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1098 PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
1099 
1100 PETSC_EXTERN PetscErrorCode PetscDTComputeFaceQuadPermutation(DMPolytopeType, PetscQuadrature, PetscInt *, IS *[]);
1101 
1102 #endif
1103