xref: /petsc/include/petscdm.h (revision f1580f4e3ce5d5b2393648fd039d0d41b440385d)
1 /*
2       Objects to manage the interactions between the mesh data structures and the algebraic objects
3 */
4 #if !defined(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 PETSC_EXTERN PetscClassId DMLABEL_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: `DMSetType()`, `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 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 DMCreateInterpolation(DM, DM, Mat *, Vec *);
82 PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
83 PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
84 PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
85 PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
86 PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
87 PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
88 PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
89 PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
90 PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
91 PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
92 PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
93 PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
94 PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
95 PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
96 PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
97 PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
98 PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
99 PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
100 PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
101 PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
102 PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
103 PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
104 PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
105 PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);
106 
107 PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
108 PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
109 PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
110 PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
111 PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
112 PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);
113 
114 PETSC_EXTERN PetscErrorCode DMSetUp(DM);
115 PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
116 PETSC_EXTERN                PETSC_DEPRECATED_FUNCTION("Use DMDACreateAggregates() or DMCreateRestriction() (since version 3.12)") PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
117 PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
118 PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
119 PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
120 PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
121 PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
122 PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
123 PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
124 PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
125 PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
126 PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
127 PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);
128 
129 /* Topology support */
130 PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
131 PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
132 PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
133 PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
134 PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
135 PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);
136 
137 /* Coordinate support */
138 PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
139 PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
140 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
141 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
142 PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
143 PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
144 PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
145 PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
146 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
147 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
148 PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
149 PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
150 PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
151 PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
152 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
153 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
154 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
155 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
156 PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
157 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
158 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
159 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
160 PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
161 PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
162 PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
163 PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
164 PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
165 PETSC_EXTERN PetscErrorCode DMProjectCoordinates(DM, PetscFE);
166 PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
167 
168 /* Periodicity support */
169 PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
170 PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
171 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
172 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
173 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
174 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
175 
176 /* block hook interface */
177 PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
178 PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
179 PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);
180 
181 PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
182 PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
183 PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
184 PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
185 PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
186 PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
187 PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
188 PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
189 PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
190 PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
191 PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscErrorCode (*)(void **));
192 PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
193 PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
194 PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
195 PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
196 PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
197 PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
198 PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);
199 
200 PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
201 PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
202 PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
203 PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
204 PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
205 PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
206 PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);
207 
208 PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
209 PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
210 PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
211 PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
212 PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);
213 
214 PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
215 PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
216 PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
217 PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
218 PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);
219 
220 typedef struct NLF_DAAD *NLF;
221 
222 #define DM_FILE_CLASSID 1211221
223 
224 /* FEM support */
225 PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
226 PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
227 PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);
228 
229 PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
230 PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
231 PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
232 PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
233 
234 PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
235 PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
236 PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
237 PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
238 PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
239 PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
240 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSection() (since v3.9)") PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s) {
241   return DMGetSection(dm, s);
242 }
243 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSection() (since v3.9)") PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s) {
244   return DMSetSection(dm, s);
245 }
246 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetGlobalSection() (since v3.9)") PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s) {
247   return DMGetGlobalSection(dm, s);
248 }
249 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetGlobalSection() (since v3.9)") PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s) {
250   return DMSetGlobalSection(dm, s);
251 }
252 
253 PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
254 PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
255 PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
256 static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSectionSF() (since v3.12)") PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s) {
257   return DMGetSectionSF(dm, s);
258 }
259 static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSectionSF() (since v3.12)") PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s) {
260   return DMSetSectionSF(dm, s);
261 }
262 static inline PETSC_DEPRECATED_FUNCTION("Use DMCreateSectionSF() (since v3.12)") PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g) {
263   return DMCreateSectionSF(dm, l, g);
264 }
265 PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
266 PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
267 PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
268 PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);
269 
270 PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
271 PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);
272 
273 PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
274 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
275 PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
276 PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);
277 
278 PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
279 PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
280 PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
281 PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
282 PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
283 PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
284 PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
285 PETSC_EXTERN PetscErrorCode DMClearFields(DM);
286 PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
287 PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
288 PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
289 PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
290 PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);
291 
292 PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
293 PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
294 PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *);
295 PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *);
296 PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS);
297 PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *);
298 PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS);
299 PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
300 PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
301 PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
302 PETSC_EXTERN PetscErrorCode DMClearDS(DM);
303 PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
304 PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
305 PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
306 PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
307 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
308 PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
309 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
310 PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
311 
312 /*MC
313   DMInterpolationInfo - Structure for holding information about interpolation on a mesh
314 
315   Level: intermediate
316 
317   Synopsis:
318     comm   - The communicator
319     dim    - The spatial dimension of points
320     nInput - The number of input points
321     points - The input point coordinates
322     cells  - The cell containing each point
323     n      - The number of local points
324     coords - The point coordinates
325     dof    - The number of components to interpolate
326 
327 .seealso: `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
328 M*/
329 struct _DMInterpolationInfo {
330   MPI_Comm   comm;
331   PetscInt   dim;    /*1 The spatial dimension of points */
332   PetscInt   nInput; /* The number of input points */
333   PetscReal *points; /* The input point coordinates */
334   PetscInt  *cells;  /* The cell containing each point */
335   PetscInt   n;      /* The number of local points */
336   Vec        coords; /* The point coordinates */
337   PetscInt   dof;    /* The number of components to interpolate */
338 };
339 typedef struct _DMInterpolationInfo *DMInterpolationInfo;
340 
341 PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
342 PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
343 PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
344 PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
345 PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
346 PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
347 PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
348 PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
349 PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
350 PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
351 PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
352 PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);
353 
354 PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
355 PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
356 PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
357 PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
358 PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
359 PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
360 PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
361 PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
362 PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
363 PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
364 PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
365 PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
366 PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);
367 
368 /*E
369    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination DMs with the same name
370 
371    Level: advanced
372 
373 $ DM_COPY_LABELS_REPLACE  - replace label in destination by label from source
374 $ DM_COPY_LABELS_KEEP     - keep destination label
375 $ DM_COPY_LABELS_FAIL     - throw error
376 
377 E*/
378 typedef enum {
379   DM_COPY_LABELS_REPLACE,
380   DM_COPY_LABELS_KEEP,
381   DM_COPY_LABELS_FAIL
382 } DMCopyLabelsMode;
383 PETSC_EXTERN const char *const DMCopyLabelsModes[];
384 
385 PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
386 PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
387 PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
388 PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
389 PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
390 PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
391 PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
392 PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
393 PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
394 PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
395 PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);
396 
397 PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
398 PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
399 
400 PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
401 PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
402 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
403 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
404 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);
405 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);
406 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);
407 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);
408 PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
409 PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
410 PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
411 PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
412 PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
413 PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);
414 
415 PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);
416 
417 PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
418 PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
419 PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
420 PETSC_EXTERN PetscErrorCode DMMonitor(DM);
421 
422 static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct) {
423   switch (ct) {
424   case DM_POLYTOPE_POINT: return 0;
425   case DM_POLYTOPE_SEGMENT:
426   case DM_POLYTOPE_POINT_PRISM_TENSOR: return 1;
427   case DM_POLYTOPE_TRIANGLE:
428   case DM_POLYTOPE_QUADRILATERAL:
429   case DM_POLYTOPE_SEG_PRISM_TENSOR: return 2;
430   case DM_POLYTOPE_TETRAHEDRON:
431   case DM_POLYTOPE_HEXAHEDRON:
432   case DM_POLYTOPE_TRI_PRISM:
433   case DM_POLYTOPE_TRI_PRISM_TENSOR:
434   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
435   case DM_POLYTOPE_PYRAMID: return 3;
436   default: return -1;
437   }
438 }
439 
440 static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct) {
441   switch (ct) {
442   case DM_POLYTOPE_POINT: return 0;
443   case DM_POLYTOPE_SEGMENT: return 2;
444   case DM_POLYTOPE_POINT_PRISM_TENSOR: return 2;
445   case DM_POLYTOPE_TRIANGLE: return 3;
446   case DM_POLYTOPE_QUADRILATERAL: return 4;
447   case DM_POLYTOPE_SEG_PRISM_TENSOR: return 4;
448   case DM_POLYTOPE_TETRAHEDRON: return 4;
449   case DM_POLYTOPE_HEXAHEDRON: return 6;
450   case DM_POLYTOPE_TRI_PRISM: return 5;
451   case DM_POLYTOPE_TRI_PRISM_TENSOR: return 5;
452   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return 6;
453   case DM_POLYTOPE_PYRAMID: return 5;
454   default: return -1;
455   }
456 }
457 
458 static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct) {
459   switch (ct) {
460   case DM_POLYTOPE_POINT: return 1;
461   case DM_POLYTOPE_SEGMENT: return 2;
462   case DM_POLYTOPE_POINT_PRISM_TENSOR: return 2;
463   case DM_POLYTOPE_TRIANGLE: return 3;
464   case DM_POLYTOPE_QUADRILATERAL: return 4;
465   case DM_POLYTOPE_SEG_PRISM_TENSOR: return 4;
466   case DM_POLYTOPE_TETRAHEDRON: return 4;
467   case DM_POLYTOPE_HEXAHEDRON: return 8;
468   case DM_POLYTOPE_TRI_PRISM: return 6;
469   case DM_POLYTOPE_TRI_PRISM_TENSOR: return 6;
470   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return 8;
471   case DM_POLYTOPE_PYRAMID: return 5;
472   default: return -1;
473   }
474 }
475 
476 static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex) {
477   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)));
478 }
479 
480 static inline PetscInt DMPolytopeTypeGetNumArrangments(DMPolytopeType ct) {
481   switch (ct) {
482   case DM_POLYTOPE_POINT: return 1;
483   case DM_POLYTOPE_SEGMENT: return 2;
484   case DM_POLYTOPE_POINT_PRISM_TENSOR: return 2;
485   case DM_POLYTOPE_TRIANGLE: return 6;
486   case DM_POLYTOPE_QUADRILATERAL: return 8;
487   case DM_POLYTOPE_SEG_PRISM_TENSOR: return 4;
488   case DM_POLYTOPE_TETRAHEDRON: return 24;
489   case DM_POLYTOPE_HEXAHEDRON: return 48;
490   case DM_POLYTOPE_TRI_PRISM: return 12;
491   case DM_POLYTOPE_TRI_PRISM_TENSOR: return 12;
492   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return 16;
493   case DM_POLYTOPE_PYRAMID: return 8;
494   default: return -1;
495   }
496 }
497 
498 /* An arrangement is a face order combined with an orientation for each face */
499 static inline const PetscInt *DMPolytopeTypeGetArrangment(DMPolytopeType ct, PetscInt o) {
500   static const PetscInt pntArr[1 * 2]      = {0, 0};
501   /* a: swap */
502   static const PetscInt segArr[2 * 2 * 2]  = {1, 0, 0, 0, /* -1: a */
503                                               0, 0, 1, 0,
504                                               /*  0: e */};
505   /* a: swap first two
506      b: swap last two */
507   static const PetscInt triArr[6 * 3 * 2]  = {0, -1, 2, -1, 1, -1, /* -3: b */
508                                               2, -1, 1, -1, 0, -1, /* -2: aba */
509                                               1, -1, 0, -1, 2, -1, /* -1: a */
510                                               0, 0,  1, 0,  2, 0,  /*  0: identity */
511                                               1, 0,  2, 0,  0, 0,  /*  1: ba */
512                                               2, 0,  0, 0,  1, 0,
513                                               /*  2: ab */};
514   /* a: forward cyclic permutation
515      b: swap first and last pairs */
516   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
517                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
518                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
519                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
520                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
521                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
522                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
523                                               3, 0,  0, 0,  1, 0,  2, 0,
524                                               /*  3: a^3 */};
525   /* r: rotate 180
526      b: swap top and bottom segments */
527   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
528                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
529                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
530                                               1, 0,  0, 0,  2, -1, 3, -1,
531                                               /*  1: b */};
532   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
533   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
534                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
535                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
536                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
537                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
538                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
539                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
540                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
541                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
542                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
543                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
544                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
545                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
546                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
547                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
548                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
549                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
550                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
551                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
552                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
553                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
554                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
555                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
556                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
557   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
558   static const PetscInt hexArr[48 * 6 * 2] = {
559     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
560     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
561     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
562     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
563     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
564     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
565     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
566     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
567     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
568     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
569     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
570     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
571     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
572     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
573     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
574     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
575     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
576     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
577     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
578     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
579     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
580     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
581     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
582     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
583     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
584     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
585     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
586     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
587     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
588     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
589     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
590     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
591     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
592     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
593     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
594     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
595     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
596     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
597     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
598     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
599     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
600     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
601     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
602     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
603     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
604     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
605     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
606     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
607   };
608   static const PetscInt tripArr[12 * 5 * 2] = {
609     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
610     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
611     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
612     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
613     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
614     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
615     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
616     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
617     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
618     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
619     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
620     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
621   };
622   /* a: rotate 120 about z
623      b: swap top and bottom segments
624      r: reflect */
625   static const PetscInt ttriArr[12 * 5 * 2] = {
626     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
627     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
628     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
629     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
630     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
631     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
632     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
633     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
634     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
635     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
636     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
637     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
638   };
639   /* a: rotate 90 about z
640      b: swap top and bottom segments
641      r: reflect */
642   static const PetscInt tquadArr[16 * 6 * 2] = {
643     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
644     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
645     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
646     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
647     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
648     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
649     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
650     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
651     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
652     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
653     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
654     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
655     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
656     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
657     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
658     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
659   };
660   static const PetscInt pyrArr[8 * 5 * 2] = {
661     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
662     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
663     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
664     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
665     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
666     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
667     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
668     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
669   };
670   switch (ct) {
671   case DM_POLYTOPE_POINT: return pntArr;
672   case DM_POLYTOPE_SEGMENT: return &segArr[(o + 1) * 2 * 2];
673   case DM_POLYTOPE_POINT_PRISM_TENSOR: return &segArr[(o + 1) * 2 * 2];
674   case DM_POLYTOPE_TRIANGLE: return &triArr[(o + 3) * 3 * 2];
675   case DM_POLYTOPE_QUADRILATERAL: return &quadArr[(o + 4) * 4 * 2];
676   case DM_POLYTOPE_SEG_PRISM_TENSOR: return &tsegArr[(o + 2) * 4 * 2];
677   case DM_POLYTOPE_TETRAHEDRON: return &tetArr[(o + 12) * 4 * 2];
678   case DM_POLYTOPE_HEXAHEDRON: return &hexArr[(o + 24) * 6 * 2];
679   case DM_POLYTOPE_TRI_PRISM: return &tripArr[(o + 6) * 5 * 2];
680   case DM_POLYTOPE_TRI_PRISM_TENSOR: return &ttriArr[(o + 6) * 5 * 2];
681   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return &tquadArr[(o + 8) * 6 * 2];
682   case DM_POLYTOPE_PYRAMID: return &pyrArr[(o + 4) * 5 * 2];
683   default: return NULL;
684   }
685 }
686 
687 /* A vertex arrangment is a vertex order */
688 static inline const PetscInt *DMPolytopeTypeGetVertexArrangment(DMPolytopeType ct, PetscInt o) {
689   static const PetscInt pntVerts[1]      = {0};
690   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
691   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
692   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};
693   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
694   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
695                                             3, 1, 2, 0, /* -11: (14)     p21 */
696                                             1, 2, 3, 0, /* -10: (1234)   p18 */
697                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
698                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
699                                             0, 3, 2, 1, /*  -7: (24)     p14 */
700                                             0, 1, 3, 2, /*  -6: (34)     p6  */
701                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
702                                             3, 0, 1, 2, /*  -4: (1432    p9  */
703                                             1, 0, 2, 3, /*  -3: (12)     p1  */
704                                             0, 2, 1, 3, /*  -2: (23)     p2  */
705                                             2, 1, 0, 3, /*  -1: (13)     p5  */
706                                             0, 1, 2, 3, /*   0: ()       p0  */
707                                             1, 2, 0, 3, /*   1: (123)    p4  */
708                                             2, 0, 1, 3, /*   2: (132)    p3  */
709                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
710                                             0, 3, 1, 2, /*   4: (243)    p8  */
711                                             3, 1, 0, 2, /*   5: (143)    p11 */
712                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
713                                             3, 0, 2, 1, /*   7: (142)    p15 */
714                                             0, 2, 3, 1, /*   8: (234)    p12 */
715                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
716                                             2, 1, 3, 0, /*  10: (134)    p19 */
717                                             1, 3, 2, 0 /*  11: (124)    p20 */};
718   static const PetscInt hexVerts[48 * 8] = {
719     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
720     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
721     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
722     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
723     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
724     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
725     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
726     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
727     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
728     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
729     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
730     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
731     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
732     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
733     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
734     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
735     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
736     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
737     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
738     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
739     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
740     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
741     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
742     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
743     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
744     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
745     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
746     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
747     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
748     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
749     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
750     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
751     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
752     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
753     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
754     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
755     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
756     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
757     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
758     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
759     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
760     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
761     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
762     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
763     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
764     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
765     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
766     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
767   };
768   static const PetscInt tripVerts[12 * 6] = {
769     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
770     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
771     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
772     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
773     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
774     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
775     0, 1, 2, 3, 4, 5, /*  0: identity */
776     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
777     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
778     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
779     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
780     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
781   };
782   static const PetscInt ttriVerts[12 * 6] = {
783     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
784     3, 5, 4, 0, 2, 1, /* -5: r b a */
785     5, 4, 3, 2, 1, 0, /* -4: r b */
786     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
787     0, 2, 1, 3, 5, 4, /* -2: r a */
788     2, 1, 0, 5, 4, 3, /* -1: r */
789     0, 1, 2, 3, 4, 5, /*  0: identity */
790     1, 2, 0, 4, 5, 3, /*  1: a */
791     2, 0, 1, 5, 3, 4, /*  2: a^2 */
792     3, 4, 5, 0, 1, 2, /*  3: b */
793     4, 5, 3, 1, 2, 0, /*  4: b a */
794     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
795   };
796   /* a: rotate 90 about z
797      b: swap top and bottom segments
798      r: reflect */
799   static const PetscInt tquadVerts[16 * 8] = {
800     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
801     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
802     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
803     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
804     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
805     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
806     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
807     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
808     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
809     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
810     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
811     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
812     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
813     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
814     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
815     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
816   };
817   static const PetscInt pyrVerts[8 * 5] = {
818     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
819     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
820     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
821     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
822     0, 1, 2, 3, 4, /*  0: identity */
823     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
824     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
825     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
826   };
827   switch (ct) {
828   case DM_POLYTOPE_POINT: return pntVerts;
829   case DM_POLYTOPE_SEGMENT: return &segVerts[(o + 1) * 2];
830   case DM_POLYTOPE_POINT_PRISM_TENSOR: return &segVerts[(o + 1) * 2];
831   case DM_POLYTOPE_TRIANGLE: return &triVerts[(o + 3) * 3];
832   case DM_POLYTOPE_QUADRILATERAL: return &quadVerts[(o + 4) * 4];
833   case DM_POLYTOPE_SEG_PRISM_TENSOR: return &tsegVerts[(o + 2) * 4];
834   case DM_POLYTOPE_TETRAHEDRON: return &tetVerts[(o + 12) * 4];
835   case DM_POLYTOPE_HEXAHEDRON: return &hexVerts[(o + 24) * 8];
836   case DM_POLYTOPE_TRI_PRISM: return &tripVerts[(o + 6) * 6];
837   case DM_POLYTOPE_TRI_PRISM_TENSOR: return &ttriVerts[(o + 6) * 6];
838   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return &tquadVerts[(o + 8) * 8];
839   case DM_POLYTOPE_PYRAMID: return &pyrVerts[(o + 4) * 5];
840   default: return NULL;
841   }
842 }
843 
844 /* This is orientation o1 acting on orientation o2 */
845 static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2) {
846   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
847   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};
848   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,
849                                             -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};
850   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
851   static const PetscInt tetMult[24 * 24] = {
852     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,
853     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,
854     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,
855     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,
856     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,
857     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,
858     -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,
859     -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,
860     -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,
861     -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,
862     -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,
863     -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,
864   };
865   static const PetscInt hexMult[48 * 48] = {
866     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,
867     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,
868     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,
869     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,
870     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,
871     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,
872     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,
873     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,
874     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,
875     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,
876     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,
877     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,
878     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,
879     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,
880     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,
881     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,
882     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,
883     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,
884     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,
885     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,
886     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,
887     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,
888     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,
889     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,
890     -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,
891     -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,
892     -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,
893     -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,
894     -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,
895     -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,
896     -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,
897     -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,
898     -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,
899     -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,
900     -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,
901     -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,
902     -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,
903     -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,
904     -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,
905     -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,
906     -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,
907     -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,
908     -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,
909     -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,
910     -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,
911     -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,
912     -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,
913     -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,
914   };
915   static const PetscInt tripMult[12 * 12] = {
916     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,
917     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,
918     -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,
919   };
920   static const PetscInt ttriMult[12 * 12] = {
921     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,
922     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,
923     -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,
924   };
925   static const PetscInt tquadMult[16 * 16] = {
926     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,
927     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,
928     -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,
929     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,
930     -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,
931   };
932   static const PetscInt pyrMult[8 * 8] = {
933     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,
934   };
935   switch (ct) {
936   case DM_POLYTOPE_POINT: return 0;
937   case DM_POLYTOPE_SEGMENT:
938   case DM_POLYTOPE_POINT_PRISM_TENSOR: return segMult[(o1 + 1) * 2 + o2 + 1];
939   case DM_POLYTOPE_TRIANGLE: return triMult[(o1 + 3) * 6 + o2 + 3];
940   case DM_POLYTOPE_QUADRILATERAL: return quadMult[(o1 + 4) * 8 + o2 + 4];
941   case DM_POLYTOPE_SEG_PRISM_TENSOR: return tsegMult[(o1 + 2) * 4 + o2 + 2];
942   case DM_POLYTOPE_TETRAHEDRON: return tetMult[(o1 + 12) * 24 + o2 + 12];
943   case DM_POLYTOPE_HEXAHEDRON: return hexMult[(o1 + 24) * 48 + o2 + 24];
944   case DM_POLYTOPE_TRI_PRISM: return tripMult[(o1 + 6) * 12 + o2 + 6];
945   case DM_POLYTOPE_TRI_PRISM_TENSOR: return ttriMult[(o1 + 6) * 12 + o2 + 6];
946   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return tquadMult[(o1 + 8) * 16 + o2 + 8];
947   case DM_POLYTOPE_PYRAMID: return pyrMult[(o1 + 4) * 8 + o2 + 4];
948   default: return 0;
949   }
950 }
951 
952 /* This is orientation o1 acting on orientation o2^{-1} */
953 static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2) {
954   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
955   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
956   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};
957   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};
958   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
959   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
960   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
961   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
962   switch (ct) {
963   case DM_POLYTOPE_POINT: return 0;
964   case DM_POLYTOPE_SEGMENT:
965   case DM_POLYTOPE_POINT_PRISM_TENSOR: return DMPolytopeTypeComposeOrientation(ct, o1, o2);
966   case DM_POLYTOPE_TRIANGLE: return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
967   case DM_POLYTOPE_QUADRILATERAL: return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
968   case DM_POLYTOPE_SEG_PRISM_TENSOR: return DMPolytopeTypeComposeOrientation(ct, o1, o2);
969   case DM_POLYTOPE_TETRAHEDRON: return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
970   case DM_POLYTOPE_HEXAHEDRON: return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
971   case DM_POLYTOPE_TRI_PRISM: return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
972   case DM_POLYTOPE_TRI_PRISM_TENSOR: return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
973   case DM_POLYTOPE_QUAD_PRISM_TENSOR: return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
974   case DM_POLYTOPE_PYRAMID: return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
975   default: return 0;
976   }
977 }
978 
979 PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
980 PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
981 PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
982 PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
983 PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
984 
985 #endif
986