xref: /petsc/include/petscdm.h (revision 21e3ffae2f3b73c0bd738cf6d0a809700fc04bb0)
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 
12 /* SUBMANSEC = DM */
13 
14 PETSC_EXTERN PetscErrorCode DMInitializePackage(void);
15 
16 PETSC_EXTERN PetscClassId DM_CLASSID;
17 
18 #define DMLOCATEPOINT_POINT_NOT_FOUND -367
19 
20 /*J
21     DMType - String with the name of a PETSc `DM`
22 
23    Level: beginner
24 
25 .seealso: `DMSetType()`, `DM`
26 J*/
27 typedef const char *DMType;
28 #define DMDA        "da"
29 #define DMCOMPOSITE "composite"
30 #define DMSLICED    "sliced"
31 #define DMSHELL     "shell"
32 #define DMPLEX      "plex"
33 #define DMREDUNDANT "redundant"
34 #define DMPATCH     "patch"
35 #define DMMOAB      "moab"
36 #define DMNETWORK   "network"
37 #define DMFOREST    "forest"
38 #define DMP4EST     "p4est"
39 #define DMP8EST     "p8est"
40 #define DMSWARM     "swarm"
41 #define DMPRODUCT   "product"
42 #define DMSTAG      "stag"
43 
44 PETSC_EXTERN const char *const       DMBoundaryTypes[];
45 PETSC_EXTERN const char *const       DMBoundaryConditionTypes[];
46 PETSC_EXTERN const char *const       DMBlockingTypes[];
47 PETSC_EXTERN PetscFunctionList       DMList;
48 PETSC_EXTERN DMGeneratorFunctionList DMGenerateList;
49 PETSC_EXTERN PetscErrorCode          DMCreate(MPI_Comm, DM *);
50 PETSC_EXTERN PetscErrorCode          DMClone(DM, DM *);
51 PETSC_EXTERN PetscErrorCode          DMSetType(DM, DMType);
52 PETSC_EXTERN PetscErrorCode          DMGetType(DM, DMType *);
53 PETSC_EXTERN PetscErrorCode          DMRegister(const char[], PetscErrorCode (*)(DM));
54 PETSC_EXTERN PetscErrorCode          DMRegisterDestroy(void);
55 
56 PETSC_EXTERN PetscErrorCode DMView(DM, PetscViewer);
57 PETSC_EXTERN PetscErrorCode DMLoad(DM, PetscViewer);
58 PETSC_EXTERN PetscErrorCode DMDestroy(DM *);
59 PETSC_EXTERN PetscErrorCode DMCreateGlobalVector(DM, Vec *);
60 PETSC_EXTERN PetscErrorCode DMCreateLocalVector(DM, Vec *);
61 PETSC_EXTERN PetscErrorCode DMGetLocalVector(DM, Vec *);
62 PETSC_EXTERN PetscErrorCode DMRestoreLocalVector(DM, Vec *);
63 PETSC_EXTERN PetscErrorCode DMGetGlobalVector(DM, Vec *);
64 PETSC_EXTERN PetscErrorCode DMRestoreGlobalVector(DM, Vec *);
65 PETSC_EXTERN PetscErrorCode DMClearGlobalVectors(DM);
66 PETSC_EXTERN PetscErrorCode DMClearLocalVectors(DM);
67 PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
68 PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
69 PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
70 PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
71 PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
72 PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
73 PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
74 PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
75 PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
76 PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
77 PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
78 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
79 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
80 PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
81 PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
82 PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
83 PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
84 PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
85 PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
86 PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
87 PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
88 PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
89 PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
90 PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
91 PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
92 PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
93 PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
94 PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
95 PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
96 PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
97 PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
98 PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
99 PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
100 PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
101 PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
102 PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
103 PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
104 PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
105 PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
106 PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
107 PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);
108 
109 PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
110 PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
111 PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
112 PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
113 PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
114 PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);
115 
116 PETSC_EXTERN PetscErrorCode DMSetUp(DM);
117 PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
118 PETSC_EXTERN                PETSC_DEPRECATED_FUNCTION("Use DMDACreateAggregates() or DMCreateRestriction() (since version 3.12)") PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
119 PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
120 PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
121 PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
122 PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
123 PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
124 PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
125 PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
126 PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
127 PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
128 PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
129 PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);
130 
131 /* Topology support */
132 PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
133 PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
134 PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
135 PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
136 PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
137 PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);
138 
139 /* Coordinate support */
140 PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
141 PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
142 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
143 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
144 PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
145 PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
146 PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
147 PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
148 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
149 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
150 PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
151 PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
152 PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
153 PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
154 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
155 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
156 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
157 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
158 PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
159 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
160 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
161 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
162 PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
163 PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
164 PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
165 PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
166 PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
167 PETSC_EXTERN PetscErrorCode DMProjectCoordinates(DM, PetscFE);
168 PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
169 
170 /* Periodicity support */
171 PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
172 PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
173 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
174 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
175 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
176 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
177 
178 /* block hook interface */
179 PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
180 PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
181 PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);
182 
183 PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
184 PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
185 PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
186 PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
187 PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
188 PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
189 PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
190 PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
191 PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
192 PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
193 PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscErrorCode (*)(void **));
194 PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
195 PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
196 PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
197 PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
198 PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
199 PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
200 PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);
201 
202 PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
203 PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
204 PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
205 PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
206 PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
207 PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
208 PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);
209 
210 PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
211 PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
212 PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
213 PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
214 PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);
215 
216 PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
217 PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
218 PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
219 PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
220 PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);
221 
222 typedef struct NLF_DAAD *NLF;
223 
224 #define DM_FILE_CLASSID 1211221
225 
226 /* FEM support */
227 PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
228 PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
229 PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);
230 
231 PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
232 PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
233 PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
234 PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
235 
236 PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
237 PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
238 PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
239 PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
240 PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
241 PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
242 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSection() (since v3.9)") PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
243 {
244   return DMGetSection(dm, s);
245 }
246 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSection() (since v3.9)") PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
247 {
248   return DMSetSection(dm, s);
249 }
250 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetGlobalSection() (since v3.9)") PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
251 {
252   return DMGetGlobalSection(dm, s);
253 }
254 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetGlobalSection() (since v3.9)") PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
255 {
256   return DMSetGlobalSection(dm, s);
257 }
258 
259 PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
260 PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
261 PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
262 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSectionSF() (since v3.12)") PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
263 {
264   return DMGetSectionSF(dm, s);
265 }
266 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSectionSF() (since v3.12)") PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
267 {
268   return DMSetSectionSF(dm, s);
269 }
270 static inline PETSC_DEPRECATED_FUNCTION("Use DMCreateSectionSF() (since v3.12)") PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
271 {
272   return DMCreateSectionSF(dm, l, g);
273 }
274 PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
275 PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
276 PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
277 PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);
278 
279 PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
280 PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);
281 
282 PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
283 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
284 PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
285 PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);
286 
287 PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
288 PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
289 PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
290 PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
291 PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
292 PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
293 PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
294 PETSC_EXTERN PetscErrorCode DMClearFields(DM);
295 PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
296 PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
297 PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
298 PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
299 PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);
300 
301 PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
302 PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
303 PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *);
304 PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *);
305 PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS);
306 PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *);
307 PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS);
308 PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
309 PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
310 PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
311 PETSC_EXTERN PetscErrorCode DMClearDS(DM);
312 PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
313 PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
314 PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
315 PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
316 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
317 PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
318 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
319 PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
320 
321 /*MC
322   DMInterpolationInfo - Structure for holding information about interpolation on a mesh
323 
324   Level: intermediate
325 
326   Synopsis:
327     comm   - The communicator
328     dim    - The spatial dimension of points
329     nInput - The number of input points
330     points - The input point coordinates
331     cells  - The cell containing each point
332     n      - The number of local points
333     coords - The point coordinates
334     dof    - The number of components to interpolate
335 
336 .seealso: `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
337 M*/
338 struct _DMInterpolationInfo {
339   MPI_Comm   comm;
340   PetscInt   dim;    /*1 The spatial dimension of points */
341   PetscInt   nInput; /* The number of input points */
342   PetscReal *points; /* The input point coordinates */
343   PetscInt  *cells;  /* The cell containing each point */
344   PetscInt   n;      /* The number of local points */
345   Vec        coords; /* The point coordinates */
346   PetscInt   dof;    /* The number of components to interpolate */
347 };
348 typedef struct _DMInterpolationInfo *DMInterpolationInfo;
349 
350 PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
351 PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
352 PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
353 PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
354 PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
355 PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
356 PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
357 PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
358 PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
359 PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
360 PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
361 PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);
362 
363 PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
364 PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
365 PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
366 PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
367 PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
368 PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
369 PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
370 PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
371 PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
372 PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
373 PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
374 PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
375 PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);
376 
377 /*E
378    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination DMs with the same name
379 
380    Level: advanced
381 
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 E*/
387 typedef enum {
388   DM_COPY_LABELS_REPLACE,
389   DM_COPY_LABELS_KEEP,
390   DM_COPY_LABELS_FAIL
391 } DMCopyLabelsMode;
392 PETSC_EXTERN const char *const DMCopyLabelsModes[];
393 
394 PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
395 PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
396 PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
397 PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
398 PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
399 PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
400 PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
401 PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
402 PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
403 PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
404 PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);
405 
406 PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
407 PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
408 
409 PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
410 PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
411 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
412 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
413 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);
414 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);
415 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);
416 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);
417 PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
418 PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
419 PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
420 PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
421 PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
422 PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);
423 
424 PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);
425 
426 PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
427 PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
428 PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
429 PETSC_EXTERN PetscErrorCode DMMonitor(DM);
430 
431 static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
432 {
433   switch (ct) {
434   case DM_POLYTOPE_POINT:
435     return 0;
436   case DM_POLYTOPE_SEGMENT:
437   case DM_POLYTOPE_POINT_PRISM_TENSOR:
438     return 1;
439   case DM_POLYTOPE_TRIANGLE:
440   case DM_POLYTOPE_QUADRILATERAL:
441   case DM_POLYTOPE_SEG_PRISM_TENSOR:
442     return 2;
443   case DM_POLYTOPE_TETRAHEDRON:
444   case DM_POLYTOPE_HEXAHEDRON:
445   case DM_POLYTOPE_TRI_PRISM:
446   case DM_POLYTOPE_TRI_PRISM_TENSOR:
447   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
448   case DM_POLYTOPE_PYRAMID:
449     return 3;
450   default:
451     return -1;
452   }
453 }
454 
455 static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
456 {
457   switch (ct) {
458   case DM_POLYTOPE_POINT:
459     return 0;
460   case DM_POLYTOPE_SEGMENT:
461     return 2;
462   case DM_POLYTOPE_POINT_PRISM_TENSOR:
463     return 2;
464   case DM_POLYTOPE_TRIANGLE:
465     return 3;
466   case DM_POLYTOPE_QUADRILATERAL:
467     return 4;
468   case DM_POLYTOPE_SEG_PRISM_TENSOR:
469     return 4;
470   case DM_POLYTOPE_TETRAHEDRON:
471     return 4;
472   case DM_POLYTOPE_HEXAHEDRON:
473     return 6;
474   case DM_POLYTOPE_TRI_PRISM:
475     return 5;
476   case DM_POLYTOPE_TRI_PRISM_TENSOR:
477     return 5;
478   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
479     return 6;
480   case DM_POLYTOPE_PYRAMID:
481     return 5;
482   default:
483     return -1;
484   }
485 }
486 
487 static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
488 {
489   switch (ct) {
490   case DM_POLYTOPE_POINT:
491     return 1;
492   case DM_POLYTOPE_SEGMENT:
493     return 2;
494   case DM_POLYTOPE_POINT_PRISM_TENSOR:
495     return 2;
496   case DM_POLYTOPE_TRIANGLE:
497     return 3;
498   case DM_POLYTOPE_QUADRILATERAL:
499     return 4;
500   case DM_POLYTOPE_SEG_PRISM_TENSOR:
501     return 4;
502   case DM_POLYTOPE_TETRAHEDRON:
503     return 4;
504   case DM_POLYTOPE_HEXAHEDRON:
505     return 8;
506   case DM_POLYTOPE_TRI_PRISM:
507     return 6;
508   case DM_POLYTOPE_TRI_PRISM_TENSOR:
509     return 6;
510   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
511     return 8;
512   case DM_POLYTOPE_PYRAMID:
513     return 5;
514   default:
515     return -1;
516   }
517 }
518 
519 static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
520 {
521   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)));
522 }
523 
524 static inline PetscInt DMPolytopeTypeGetNumArrangments(DMPolytopeType ct)
525 {
526   switch (ct) {
527   case DM_POLYTOPE_POINT:
528     return 1;
529   case DM_POLYTOPE_SEGMENT:
530     return 2;
531   case DM_POLYTOPE_POINT_PRISM_TENSOR:
532     return 2;
533   case DM_POLYTOPE_TRIANGLE:
534     return 6;
535   case DM_POLYTOPE_QUADRILATERAL:
536     return 8;
537   case DM_POLYTOPE_SEG_PRISM_TENSOR:
538     return 4;
539   case DM_POLYTOPE_TETRAHEDRON:
540     return 24;
541   case DM_POLYTOPE_HEXAHEDRON:
542     return 48;
543   case DM_POLYTOPE_TRI_PRISM:
544     return 12;
545   case DM_POLYTOPE_TRI_PRISM_TENSOR:
546     return 12;
547   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
548     return 16;
549   case DM_POLYTOPE_PYRAMID:
550     return 8;
551   default:
552     return -1;
553   }
554 }
555 
556 /* An arrangement is a face order combined with an orientation for each face */
557 static inline const PetscInt *DMPolytopeTypeGetArrangment(DMPolytopeType ct, PetscInt o)
558 {
559   static const PetscInt pntArr[1 * 2] = {0, 0};
560   /* a: swap */
561   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
562                                              0, 0, 1, 0,
563                                              /*  0: e */};
564   /* a: swap first two
565      b: swap last two */
566   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
567                                              2, -1, 1, -1, 0, -1, /* -2: aba */
568                                              1, -1, 0, -1, 2, -1, /* -1: a */
569                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
570                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
571                                              2, 0,  0, 0,  1, 0,
572                                              /*  2: ab */};
573   /* a: forward cyclic permutation
574      b: swap first and last pairs */
575   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
576                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
577                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
578                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
579                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
580                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
581                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
582                                               3, 0,  0, 0,  1, 0,  2, 0,
583                                               /*  3: a^3 */};
584   /* r: rotate 180
585      b: swap top and bottom segments */
586   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
587                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
588                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
589                                               1, 0,  0, 0,  2, -1, 3, -1,
590                                               /*  1: b */};
591   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
592   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
593                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
594                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
595                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
596                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
597                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
598                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
599                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
600                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
601                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
602                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
603                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
604                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
605                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
606                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
607                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
608                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
609                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
610                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
611                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
612                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
613                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
614                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
615                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
616   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
617   static const PetscInt hexArr[48 * 6 * 2] = {
618     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
619     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
620     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
621     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
622     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
623     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
624     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
625     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
626     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
627     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
628     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
629     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
630     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
631     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
632     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
633     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
634     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
635     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
636     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
637     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
638     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
639     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
640     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
641     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
642     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
643     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
644     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
645     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
646     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
647     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
648     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
649     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
650     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
651     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
652     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
653     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
654     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
655     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
656     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
657     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
658     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
659     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
660     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
661     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
662     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
663     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
664     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
665     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
666   };
667   static const PetscInt tripArr[12 * 5 * 2] = {
668     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
669     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
670     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
671     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
672     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
673     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
674     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
675     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
676     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
677     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
678     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
679     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
680   };
681   /* a: rotate 120 about z
682      b: swap top and bottom segments
683      r: reflect */
684   static const PetscInt ttriArr[12 * 5 * 2] = {
685     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
686     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
687     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
688     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
689     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
690     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
691     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
692     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
693     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
694     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
695     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
696     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
697   };
698   /* a: rotate 90 about z
699      b: swap top and bottom segments
700      r: reflect */
701   static const PetscInt tquadArr[16 * 6 * 2] = {
702     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
703     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
704     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
705     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
706     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
707     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
708     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
709     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
710     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
711     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
712     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
713     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
714     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
715     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
716     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
717     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
718   };
719   static const PetscInt pyrArr[8 * 5 * 2] = {
720     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
721     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
722     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
723     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
724     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
725     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
726     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
727     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
728   };
729   switch (ct) {
730   case DM_POLYTOPE_POINT:
731     return pntArr;
732   case DM_POLYTOPE_SEGMENT:
733     return &segArr[(o + 1) * 2 * 2];
734   case DM_POLYTOPE_POINT_PRISM_TENSOR:
735     return &segArr[(o + 1) * 2 * 2];
736   case DM_POLYTOPE_TRIANGLE:
737     return &triArr[(o + 3) * 3 * 2];
738   case DM_POLYTOPE_QUADRILATERAL:
739     return &quadArr[(o + 4) * 4 * 2];
740   case DM_POLYTOPE_SEG_PRISM_TENSOR:
741     return &tsegArr[(o + 2) * 4 * 2];
742   case DM_POLYTOPE_TETRAHEDRON:
743     return &tetArr[(o + 12) * 4 * 2];
744   case DM_POLYTOPE_HEXAHEDRON:
745     return &hexArr[(o + 24) * 6 * 2];
746   case DM_POLYTOPE_TRI_PRISM:
747     return &tripArr[(o + 6) * 5 * 2];
748   case DM_POLYTOPE_TRI_PRISM_TENSOR:
749     return &ttriArr[(o + 6) * 5 * 2];
750   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
751     return &tquadArr[(o + 8) * 6 * 2];
752   case DM_POLYTOPE_PYRAMID:
753     return &pyrArr[(o + 4) * 5 * 2];
754   default:
755     return NULL;
756   }
757 }
758 
759 /* A vertex arrangement is a vertex order */
760 static inline const PetscInt *DMPolytopeTypeGetVertexArrangment(DMPolytopeType ct, PetscInt o)
761 {
762   static const PetscInt pntVerts[1]      = {0};
763   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
764   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
765   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};
766   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
767   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
768                                             3, 1, 2, 0, /* -11: (14)     p21 */
769                                             1, 2, 3, 0, /* -10: (1234)   p18 */
770                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
771                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
772                                             0, 3, 2, 1, /*  -7: (24)     p14 */
773                                             0, 1, 3, 2, /*  -6: (34)     p6  */
774                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
775                                             3, 0, 1, 2, /*  -4: (1432    p9  */
776                                             1, 0, 2, 3, /*  -3: (12)     p1  */
777                                             0, 2, 1, 3, /*  -2: (23)     p2  */
778                                             2, 1, 0, 3, /*  -1: (13)     p5  */
779                                             0, 1, 2, 3, /*   0: ()       p0  */
780                                             1, 2, 0, 3, /*   1: (123)    p4  */
781                                             2, 0, 1, 3, /*   2: (132)    p3  */
782                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
783                                             0, 3, 1, 2, /*   4: (243)    p8  */
784                                             3, 1, 0, 2, /*   5: (143)    p11 */
785                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
786                                             3, 0, 2, 1, /*   7: (142)    p15 */
787                                             0, 2, 3, 1, /*   8: (234)    p12 */
788                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
789                                             2, 1, 3, 0, /*  10: (134)    p19 */
790                                             1, 3, 2, 0 /*  11: (124)    p20 */};
791   static const PetscInt hexVerts[48 * 8] = {
792     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
793     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
794     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
795     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
796     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
797     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
798     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
799     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
800     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
801     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
802     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
803     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
804     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
805     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
806     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
807     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
808     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
809     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
810     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
811     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
812     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
813     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
814     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
815     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
816     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
817     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
818     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
819     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
820     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
821     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
822     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
823     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
824     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
825     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
826     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
827     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
828     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
829     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
830     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
831     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
832     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
833     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
834     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
835     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
836     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
837     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
838     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
839     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
840   };
841   static const PetscInt tripVerts[12 * 6] = {
842     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
843     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
844     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
845     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
846     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
847     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
848     0, 1, 2, 3, 4, 5, /*  0: identity */
849     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
850     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
851     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
852     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
853     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
854   };
855   static const PetscInt ttriVerts[12 * 6] = {
856     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
857     3, 5, 4, 0, 2, 1, /* -5: r b a */
858     5, 4, 3, 2, 1, 0, /* -4: r b */
859     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
860     0, 2, 1, 3, 5, 4, /* -2: r a */
861     2, 1, 0, 5, 4, 3, /* -1: r */
862     0, 1, 2, 3, 4, 5, /*  0: identity */
863     1, 2, 0, 4, 5, 3, /*  1: a */
864     2, 0, 1, 5, 3, 4, /*  2: a^2 */
865     3, 4, 5, 0, 1, 2, /*  3: b */
866     4, 5, 3, 1, 2, 0, /*  4: b a */
867     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
868   };
869   /* a: rotate 90 about z
870      b: swap top and bottom segments
871      r: reflect */
872   static const PetscInt tquadVerts[16 * 8] = {
873     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
874     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
875     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
876     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
877     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
878     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
879     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
880     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
881     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
882     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
883     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
884     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
885     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
886     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
887     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
888     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
889   };
890   static const PetscInt pyrVerts[8 * 5] = {
891     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
892     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
893     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
894     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
895     0, 1, 2, 3, 4, /*  0: identity */
896     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
897     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
898     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
899   };
900   switch (ct) {
901   case DM_POLYTOPE_POINT:
902     return pntVerts;
903   case DM_POLYTOPE_SEGMENT:
904     return &segVerts[(o + 1) * 2];
905   case DM_POLYTOPE_POINT_PRISM_TENSOR:
906     return &segVerts[(o + 1) * 2];
907   case DM_POLYTOPE_TRIANGLE:
908     return &triVerts[(o + 3) * 3];
909   case DM_POLYTOPE_QUADRILATERAL:
910     return &quadVerts[(o + 4) * 4];
911   case DM_POLYTOPE_SEG_PRISM_TENSOR:
912     return &tsegVerts[(o + 2) * 4];
913   case DM_POLYTOPE_TETRAHEDRON:
914     return &tetVerts[(o + 12) * 4];
915   case DM_POLYTOPE_HEXAHEDRON:
916     return &hexVerts[(o + 24) * 8];
917   case DM_POLYTOPE_TRI_PRISM:
918     return &tripVerts[(o + 6) * 6];
919   case DM_POLYTOPE_TRI_PRISM_TENSOR:
920     return &ttriVerts[(o + 6) * 6];
921   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
922     return &tquadVerts[(o + 8) * 8];
923   case DM_POLYTOPE_PYRAMID:
924     return &pyrVerts[(o + 4) * 5];
925   default:
926     return NULL;
927   }
928 }
929 
930 /* This is orientation o1 acting on orientation o2 */
931 static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
932 {
933   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
934   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};
935   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,
936                                             -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};
937   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
938   static const PetscInt tetMult[24 * 24] = {
939     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,
940     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,
941     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,
942     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,
943     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,
944     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,
945     -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,
946     -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,
947     -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,
948     -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,
949     -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,
950     -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,
951   };
952   static const PetscInt hexMult[48 * 48] = {
953     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,
954     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,
955     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,
956     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,
957     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,
958     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,
959     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,
960     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,
961     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,
962     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,
963     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,
964     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,
965     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,
966     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,
967     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,
968     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,
969     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,
970     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,
971     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,
972     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,
973     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,
974     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,
975     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,
976     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,
977     -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,
978     -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,
979     -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,
980     -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,
981     -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,
982     -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,
983     -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,
984     -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,
985     -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,
986     -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,
987     -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,
988     -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,
989     -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,
990     -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,
991     -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,
992     -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,
993     -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,
994     -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,
995     -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,
996     -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,
997     -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,
998     -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,
999     -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,
1000     -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,
1001   };
1002   static const PetscInt tripMult[12 * 12] = {
1003     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,
1004     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,
1005     -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,
1006   };
1007   static const PetscInt ttriMult[12 * 12] = {
1008     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,
1009     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,
1010     -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,
1011   };
1012   static const PetscInt tquadMult[16 * 16] = {
1013     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,
1014     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,
1015     -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,
1016     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,
1017     -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,
1018   };
1019   static const PetscInt pyrMult[8 * 8] = {
1020     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,
1021   };
1022   switch (ct) {
1023   case DM_POLYTOPE_POINT:
1024     return 0;
1025   case DM_POLYTOPE_SEGMENT:
1026   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1027     return segMult[(o1 + 1) * 2 + o2 + 1];
1028   case DM_POLYTOPE_TRIANGLE:
1029     return triMult[(o1 + 3) * 6 + o2 + 3];
1030   case DM_POLYTOPE_QUADRILATERAL:
1031     return quadMult[(o1 + 4) * 8 + o2 + 4];
1032   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1033     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1034   case DM_POLYTOPE_TETRAHEDRON:
1035     return tetMult[(o1 + 12) * 24 + o2 + 12];
1036   case DM_POLYTOPE_HEXAHEDRON:
1037     return hexMult[(o1 + 24) * 48 + o2 + 24];
1038   case DM_POLYTOPE_TRI_PRISM:
1039     return tripMult[(o1 + 6) * 12 + o2 + 6];
1040   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1041     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1042   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1043     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1044   case DM_POLYTOPE_PYRAMID:
1045     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1046   default:
1047     return 0;
1048   }
1049 }
1050 
1051 /* This is orientation o1 acting on orientation o2^{-1} */
1052 static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1053 {
1054   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1055   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1056   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};
1057   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};
1058   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1059   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1060   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1061   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1062   switch (ct) {
1063   case DM_POLYTOPE_POINT:
1064     return 0;
1065   case DM_POLYTOPE_SEGMENT:
1066   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1067     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1068   case DM_POLYTOPE_TRIANGLE:
1069     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1070   case DM_POLYTOPE_QUADRILATERAL:
1071     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1072   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1073     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1074   case DM_POLYTOPE_TETRAHEDRON:
1075     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1076   case DM_POLYTOPE_HEXAHEDRON:
1077     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1078   case DM_POLYTOPE_TRI_PRISM:
1079     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1080   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1081     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1082   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1083     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1084   case DM_POLYTOPE_PYRAMID:
1085     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1086   default:
1087     return 0;
1088   }
1089 }
1090 
1091 PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1092 PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1093 PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1094 PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1095 PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
1096 
1097 #endif
1098