xref: /petsc/include/petscdm.h (revision e907feaad8a9ad15ff003b1a1f8acb2ecb25e843)
1 /*
2       Objects to manage the interactions between the mesh data structures and the algebraic objects
3 */
4 #pragma once
5 #include <petscmat.h>
6 #include <petscdmtypes.h>
7 #include <petscfetypes.h>
8 #include <petscdstypes.h>
9 #include <petscdmlabel.h>
10 #include <petscdt.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: [](ch_dmbase), `DMSetType()`, `DMCreate()`, `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 DMClearNamedGlobalVectors(DM);
68 PETSC_EXTERN PetscErrorCode DMClearNamedLocalVectors(DM);
69 PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
70 PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
71 PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
72 PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
73 PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
74 PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
75 PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
76 PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
77 PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
78 PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
79 PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
80 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
81 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
82 PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
83 PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
84 PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
85 PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
86 PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
87 PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
88 PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
89 PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
90 PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
91 PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
92 PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
93 PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
94 PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
95 PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
96 PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
97 PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
98 PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
99 PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
100 PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
101 PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
102 PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
103 PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
104 PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
105 PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
106 PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
107 PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
108 PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
109 PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);
110 
111 PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
112 PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
113 PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
114 PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
115 PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
116 PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);
117 
118 PETSC_EXTERN PetscErrorCode DMSetUp(DM);
119 PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
120 PETSC_EXTERN PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMDACreateAggregates()", ) PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
121 PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
122 PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
123 PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
124 PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
125 PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
126 PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
127 PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
128 PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
129 PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
130 PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
131 PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);
132 
133 /* Topology support */
134 PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
135 PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
136 PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
137 PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
138 PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
139 PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);
140 
141 /* Coordinate support */
142 PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
143 PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
144 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
145 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
146 PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
147 PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
148 PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
149 PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
150 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
151 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
152 PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
153 PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
154 PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
155 PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
156 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
157 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
158 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
159 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
160 PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
161 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
162 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
163 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
164 PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
165 PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
166 PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
167 PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
168 PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
169 PETSC_EXTERN PetscErrorCode DMSetCoordinateDisc(DM, PetscFE, PetscBool);
170 PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
171 
172 /* Periodicity support */
173 PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
174 PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
175 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
176 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
177 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
178 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
179 
180 /* block hook interface */
181 PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
182 PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
183 PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);
184 
185 PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
186 PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
187 PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
188 PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
189 PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
190 PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
191 PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
192 PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
193 PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
194 PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
195 PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscErrorCode (*)(void **));
196 PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
197 PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
198 PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
199 PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
200 PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
201 PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
202 PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);
203 
204 PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
205 PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
206 PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
207 PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
208 PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
209 PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
210 PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);
211 
212 PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
213 PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
214 PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
215 PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
216 PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);
217 
218 PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
219 PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
220 PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
221 PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
222 PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);
223 
224 typedef struct NLF_DAAD *NLF;
225 
226 #define DM_FILE_CLASSID 1211221
227 
228 /* FEM support */
229 PETSC_EXTERN PetscErrorCode DMPrintCellIndices(PetscInt, const char[], PetscInt, const PetscInt[]);
230 PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
231 PETSC_EXTERN PetscErrorCode DMPrintCellVectorReal(PetscInt, const char[], PetscInt, const PetscReal[]);
232 PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
233 PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);
234 
235 PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
236 PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
237 PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
238 PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
239 
240 PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
241 PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
242 PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
243 PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
244 PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
245 PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
246 PETSC_EXTERN PetscErrorCode DMUseTensorOrder(DM, PetscBool);
247 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetSection()", ) PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
248 {
249   return DMGetSection(dm, s);
250 }
251 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetSection()", ) PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
252 {
253   return DMSetSection(dm, s);
254 }
255 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetGlobalSection()", ) PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
256 {
257   return DMGetGlobalSection(dm, s);
258 }
259 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetGlobalSection()", ) PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
260 {
261   return DMSetGlobalSection(dm, s);
262 }
263 
264 PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
265 PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
266 PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
267 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMGetSectionSF()", ) PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
268 {
269   return DMGetSectionSF(dm, s);
270 }
271 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMSetSectionSF()", ) PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
272 {
273   return DMSetSectionSF(dm, s);
274 }
275 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMCreateSectionSF()", ) PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
276 {
277   return DMCreateSectionSF(dm, l, g);
278 }
279 PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
280 PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
281 PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
282 PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);
283 
284 PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
285 PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);
286 
287 PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
288 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
289 PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
290 PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);
291 
292 PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
293 PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
294 PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
295 PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
296 PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
297 PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
298 PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
299 PETSC_EXTERN PetscErrorCode DMClearFields(DM);
300 PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
301 PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
302 PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
303 PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
304 PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);
305 
306 PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
307 PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
308 PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *, PetscDS *);
309 PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *, PetscDS *);
310 PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS, PetscDS);
311 PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *, PetscDS *);
312 PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS, PetscDS);
313 PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
314 PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
315 PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
316 PETSC_EXTERN PetscErrorCode DMClearDS(DM);
317 PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
318 PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
319 PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
320 PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
321 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
322 PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
323 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
324 PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
325 
326 /*MC
327   DMInterpolationInfo - Structure for holding information about interpolation on a mesh
328 
329   Synopsis:
330     comm   - The communicator
331     dim    - The spatial dimension of points
332     nInput - The number of input points
333     points - The input point coordinates
334     cells  - The cell containing each point
335     n      - The number of local points
336     coords - The point coordinates
337     dof    - The number of components to interpolate
338 
339   Level: intermediate
340 
341 .seealso: `DM`, `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
342 M*/
343 struct _DMInterpolationInfo {
344   MPI_Comm   comm;
345   PetscInt   dim;    /*1 The spatial dimension of points */
346   PetscInt   nInput; /* The number of input points */
347   PetscReal *points; /* The input point coordinates */
348   PetscInt  *cells;  /* The cell containing each point */
349   PetscInt   n;      /* The number of local points */
350   Vec        coords; /* The point coordinates */
351   PetscInt   dof;    /* The number of components to interpolate */
352 };
353 typedef struct _DMInterpolationInfo *DMInterpolationInfo;
354 
355 PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
356 PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
357 PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
358 PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
359 PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
360 PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
361 PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
362 PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
363 PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
364 PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
365 PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
366 PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);
367 
368 PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
369 PETSC_EXTERN PetscErrorCode DMCreateLabelAtIndex(DM, PetscInt, const char[]);
370 PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
371 PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
372 PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
373 PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
374 PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
375 PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
376 PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
377 PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
378 PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
379 PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
380 PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
381 PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);
382 
383 /*E
384    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination DMs with the same name
385 
386    Values:
387 +  `DM_COPY_LABELS_REPLACE`  - replace label in destination by label from source
388 .  `DM_COPY_LABELS_KEEP`     - keep destination label
389 -  `DM_COPY_LABELS_FAIL`     - throw error
390 
391    Level: advanced
392 
393 .seealso: `DMLabel`, `DM`, `DMCompareLabels()`, `DMRemoveLabel()`
394 E*/
395 typedef enum {
396   DM_COPY_LABELS_REPLACE,
397   DM_COPY_LABELS_KEEP,
398   DM_COPY_LABELS_FAIL
399 } DMCopyLabelsMode;
400 PETSC_EXTERN const char *const DMCopyLabelsModes[];
401 
402 PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
403 PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
404 PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
405 PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
406 PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
407 PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
408 PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
409 PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
410 PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
411 PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
412 PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);
413 
414 PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
415 PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
416 
417 PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
418 PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
419 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
420 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
421 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);
422 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);
423 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);
424 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);
425 PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
426 PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
427 PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
428 PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
429 PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
430 PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);
431 
432 PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);
433 
434 PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
435 PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
436 PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
437 PETSC_EXTERN PetscErrorCode DMMonitor(DM);
438 
439 static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
440 {
441   switch (ct) {
442   case DM_POLYTOPE_POINT:
443     return 0;
444   case DM_POLYTOPE_SEGMENT:
445   case DM_POLYTOPE_POINT_PRISM_TENSOR:
446     return 1;
447   case DM_POLYTOPE_TRIANGLE:
448   case DM_POLYTOPE_QUADRILATERAL:
449   case DM_POLYTOPE_SEG_PRISM_TENSOR:
450   case DM_POLYTOPE_UNKNOWN_FACE:
451     return 2;
452   case DM_POLYTOPE_TETRAHEDRON:
453   case DM_POLYTOPE_HEXAHEDRON:
454   case DM_POLYTOPE_TRI_PRISM:
455   case DM_POLYTOPE_TRI_PRISM_TENSOR:
456   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
457   case DM_POLYTOPE_PYRAMID:
458   case DM_POLYTOPE_UNKNOWN_CELL:
459     return 3;
460   default:
461     return -1;
462   }
463 }
464 
465 static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
466 {
467   switch (ct) {
468   case DM_POLYTOPE_POINT:
469     return 0;
470   case DM_POLYTOPE_SEGMENT:
471     return 2;
472   case DM_POLYTOPE_POINT_PRISM_TENSOR:
473     return 2;
474   case DM_POLYTOPE_TRIANGLE:
475     return 3;
476   case DM_POLYTOPE_QUADRILATERAL:
477     return 4;
478   case DM_POLYTOPE_SEG_PRISM_TENSOR:
479     return 4;
480   case DM_POLYTOPE_TETRAHEDRON:
481     return 4;
482   case DM_POLYTOPE_HEXAHEDRON:
483     return 6;
484   case DM_POLYTOPE_TRI_PRISM:
485     return 5;
486   case DM_POLYTOPE_TRI_PRISM_TENSOR:
487     return 5;
488   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
489     return 6;
490   case DM_POLYTOPE_PYRAMID:
491     return 5;
492   default:
493     return -1;
494   }
495 }
496 
497 static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
498 {
499   switch (ct) {
500   case DM_POLYTOPE_POINT:
501     return 1;
502   case DM_POLYTOPE_SEGMENT:
503     return 2;
504   case DM_POLYTOPE_POINT_PRISM_TENSOR:
505     return 2;
506   case DM_POLYTOPE_TRIANGLE:
507     return 3;
508   case DM_POLYTOPE_QUADRILATERAL:
509     return 4;
510   case DM_POLYTOPE_SEG_PRISM_TENSOR:
511     return 4;
512   case DM_POLYTOPE_TETRAHEDRON:
513     return 4;
514   case DM_POLYTOPE_HEXAHEDRON:
515     return 8;
516   case DM_POLYTOPE_TRI_PRISM:
517     return 6;
518   case DM_POLYTOPE_TRI_PRISM_TENSOR:
519     return 6;
520   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
521     return 8;
522   case DM_POLYTOPE_PYRAMID:
523     return 5;
524   default:
525     return -1;
526   }
527 }
528 
529 static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
530 {
531   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)));
532 }
533 
534 static inline PetscInt DMPolytopeTypeGetNumArrangments(DMPolytopeType ct)
535 {
536   switch (ct) {
537   case DM_POLYTOPE_POINT:
538     return 1;
539   case DM_POLYTOPE_SEGMENT:
540     return 2;
541   case DM_POLYTOPE_POINT_PRISM_TENSOR:
542     return 2;
543   case DM_POLYTOPE_TRIANGLE:
544     return 6;
545   case DM_POLYTOPE_QUADRILATERAL:
546     return 8;
547   case DM_POLYTOPE_SEG_PRISM_TENSOR:
548     return 4;
549   case DM_POLYTOPE_TETRAHEDRON:
550     return 24;
551   case DM_POLYTOPE_HEXAHEDRON:
552     return 48;
553   case DM_POLYTOPE_TRI_PRISM:
554     return 12;
555   case DM_POLYTOPE_TRI_PRISM_TENSOR:
556     return 12;
557   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
558     return 16;
559   case DM_POLYTOPE_PYRAMID:
560     return 8;
561   default:
562     return -1;
563   }
564 }
565 
566 /* An arrangement is a face order combined with an orientation for each face */
567 static inline const PetscInt *DMPolytopeTypeGetArrangment(DMPolytopeType ct, PetscInt o)
568 {
569   static const PetscInt pntArr[1 * 2] = {0, 0};
570   /* a: swap */
571   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
572                                              0, 0, 1, 0,
573                                              /*  0: e */};
574   /* a: swap first two
575      b: swap last two */
576   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
577                                              2, -1, 1, -1, 0, -1, /* -2: aba */
578                                              1, -1, 0, -1, 2, -1, /* -1: a */
579                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
580                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
581                                              2, 0,  0, 0,  1, 0,
582                                              /*  2: ab */};
583   /* a: forward cyclic permutation
584      b: swap first and last pairs */
585   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
586                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
587                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
588                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
589                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
590                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
591                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
592                                               3, 0,  0, 0,  1, 0,  2, 0,
593                                               /*  3: a^3 */};
594   /* r: rotate 180
595      b: swap top and bottom segments */
596   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
597                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
598                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
599                                               1, 0,  0, 0,  2, -1, 3, -1,
600                                               /*  1: b */};
601   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
602   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
603                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
604                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
605                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
606                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
607                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
608                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
609                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
610                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
611                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
612                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
613                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
614                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
615                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
616                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
617                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
618                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
619                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
620                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
621                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
622                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
623                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
624                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
625                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
626   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
627   static const PetscInt hexArr[48 * 6 * 2] = {
628     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
629     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
630     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
631     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
632     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
633     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
634     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
635     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
636     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
637     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
638     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
639     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
640     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
641     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
642     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
643     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
644     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
645     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
646     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
647     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
648     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
649     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
650     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
651     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
652     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
653     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
654     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
655     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
656     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
657     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
658     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
659     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
660     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
661     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
662     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
663     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
664     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
665     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
666     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
667     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
668     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
669     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
670     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
671     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
672     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
673     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
674     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
675     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
676   };
677   static const PetscInt tripArr[12 * 5 * 2] = {
678     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
679     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
680     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
681     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
682     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
683     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
684     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
685     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
686     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
687     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
688     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
689     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
690   };
691   /* a: rotate 120 about z
692      b: swap top and bottom segments
693      r: reflect */
694   static const PetscInt ttriArr[12 * 5 * 2] = {
695     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
696     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
697     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
698     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
699     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
700     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
701     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
702     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
703     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
704     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
705     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
706     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
707   };
708   /* a: rotate 90 about z
709      b: swap top and bottom segments
710      r: reflect */
711   static const PetscInt tquadArr[16 * 6 * 2] = {
712     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
713     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
714     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
715     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
716     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
717     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
718     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
719     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
720     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
721     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
722     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
723     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
724     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
725     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
726     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
727     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
728   };
729   static const PetscInt pyrArr[8 * 5 * 2] = {
730     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
731     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
732     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
733     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
734     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
735     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
736     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
737     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
738   };
739   switch (ct) {
740   case DM_POLYTOPE_POINT:
741     return pntArr;
742   case DM_POLYTOPE_SEGMENT:
743     return &segArr[(o + 1) * 2 * 2];
744   case DM_POLYTOPE_POINT_PRISM_TENSOR:
745     return &segArr[(o + 1) * 2 * 2];
746   case DM_POLYTOPE_TRIANGLE:
747     return &triArr[(o + 3) * 3 * 2];
748   case DM_POLYTOPE_QUADRILATERAL:
749     return &quadArr[(o + 4) * 4 * 2];
750   case DM_POLYTOPE_SEG_PRISM_TENSOR:
751     return &tsegArr[(o + 2) * 4 * 2];
752   case DM_POLYTOPE_TETRAHEDRON:
753     return &tetArr[(o + 12) * 4 * 2];
754   case DM_POLYTOPE_HEXAHEDRON:
755     return &hexArr[(o + 24) * 6 * 2];
756   case DM_POLYTOPE_TRI_PRISM:
757     return &tripArr[(o + 6) * 5 * 2];
758   case DM_POLYTOPE_TRI_PRISM_TENSOR:
759     return &ttriArr[(o + 6) * 5 * 2];
760   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
761     return &tquadArr[(o + 8) * 6 * 2];
762   case DM_POLYTOPE_PYRAMID:
763     return &pyrArr[(o + 4) * 5 * 2];
764   default:
765     return PETSC_NULLPTR;
766   }
767 }
768 
769 /* A vertex arrangement is a vertex order */
770 static inline const PetscInt *DMPolytopeTypeGetVertexArrangment(DMPolytopeType ct, PetscInt o)
771 {
772   static const PetscInt pntVerts[1]      = {0};
773   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
774   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
775   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};
776   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
777   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
778                                             3, 1, 2, 0, /* -11: (14)     p21 */
779                                             1, 2, 3, 0, /* -10: (1234)   p18 */
780                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
781                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
782                                             0, 3, 2, 1, /*  -7: (24)     p14 */
783                                             0, 1, 3, 2, /*  -6: (34)     p6  */
784                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
785                                             3, 0, 1, 2, /*  -4: (1432    p9  */
786                                             1, 0, 2, 3, /*  -3: (12)     p1  */
787                                             0, 2, 1, 3, /*  -2: (23)     p2  */
788                                             2, 1, 0, 3, /*  -1: (13)     p5  */
789                                             0, 1, 2, 3, /*   0: ()       p0  */
790                                             1, 2, 0, 3, /*   1: (123)    p4  */
791                                             2, 0, 1, 3, /*   2: (132)    p3  */
792                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
793                                             0, 3, 1, 2, /*   4: (243)    p8  */
794                                             3, 1, 0, 2, /*   5: (143)    p11 */
795                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
796                                             3, 0, 2, 1, /*   7: (142)    p15 */
797                                             0, 2, 3, 1, /*   8: (234)    p12 */
798                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
799                                             2, 1, 3, 0, /*  10: (134)    p19 */
800                                             1, 3, 2, 0 /*  11: (124)    p20 */};
801   static const PetscInt hexVerts[48 * 8] = {
802     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
803     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
804     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
805     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
806     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
807     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
808     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
809     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
810     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
811     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
812     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
813     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
814     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
815     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
816     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
817     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
818     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
819     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
820     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
821     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
822     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
823     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
824     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
825     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
826     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
827     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
828     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
829     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
830     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
831     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
832     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
833     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
834     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
835     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
836     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
837     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
838     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
839     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
840     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
841     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
842     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
843     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
844     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
845     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
846     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
847     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
848     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
849     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
850   };
851   static const PetscInt tripVerts[12 * 6] = {
852     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
853     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
854     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
855     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
856     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
857     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
858     0, 1, 2, 3, 4, 5, /*  0: identity */
859     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
860     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
861     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
862     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
863     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
864   };
865   static const PetscInt ttriVerts[12 * 6] = {
866     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
867     3, 5, 4, 0, 2, 1, /* -5: r b a */
868     5, 4, 3, 2, 1, 0, /* -4: r b */
869     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
870     0, 2, 1, 3, 5, 4, /* -2: r a */
871     2, 1, 0, 5, 4, 3, /* -1: r */
872     0, 1, 2, 3, 4, 5, /*  0: identity */
873     1, 2, 0, 4, 5, 3, /*  1: a */
874     2, 0, 1, 5, 3, 4, /*  2: a^2 */
875     3, 4, 5, 0, 1, 2, /*  3: b */
876     4, 5, 3, 1, 2, 0, /*  4: b a */
877     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
878   };
879   /* a: rotate 90 about z
880      b: swap top and bottom segments
881      r: reflect */
882   static const PetscInt tquadVerts[16 * 8] = {
883     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
884     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
885     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
886     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
887     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
888     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
889     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
890     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
891     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
892     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
893     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
894     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
895     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
896     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
897     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
898     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
899   };
900   static const PetscInt pyrVerts[8 * 5] = {
901     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
902     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
903     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
904     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
905     0, 1, 2, 3, 4, /*  0: identity */
906     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
907     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
908     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
909   };
910   switch (ct) {
911   case DM_POLYTOPE_POINT:
912     return pntVerts;
913   case DM_POLYTOPE_SEGMENT:
914     return &segVerts[(o + 1) * 2];
915   case DM_POLYTOPE_POINT_PRISM_TENSOR:
916     return &segVerts[(o + 1) * 2];
917   case DM_POLYTOPE_TRIANGLE:
918     return &triVerts[(o + 3) * 3];
919   case DM_POLYTOPE_QUADRILATERAL:
920     return &quadVerts[(o + 4) * 4];
921   case DM_POLYTOPE_SEG_PRISM_TENSOR:
922     return &tsegVerts[(o + 2) * 4];
923   case DM_POLYTOPE_TETRAHEDRON:
924     return &tetVerts[(o + 12) * 4];
925   case DM_POLYTOPE_HEXAHEDRON:
926     return &hexVerts[(o + 24) * 8];
927   case DM_POLYTOPE_TRI_PRISM:
928     return &tripVerts[(o + 6) * 6];
929   case DM_POLYTOPE_TRI_PRISM_TENSOR:
930     return &ttriVerts[(o + 6) * 6];
931   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
932     return &tquadVerts[(o + 8) * 8];
933   case DM_POLYTOPE_PYRAMID:
934     return &pyrVerts[(o + 4) * 5];
935   default:
936     return PETSC_NULLPTR;
937   }
938 }
939 
940 /* This is orientation o1 acting on orientation o2 */
941 static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
942 {
943   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
944   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};
945   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,
946                                             -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};
947   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
948   static const PetscInt tetMult[24 * 24] = {
949     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,
950     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,
951     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,
952     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,
953     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,
954     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,
955     -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,
956     -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,
957     -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,
958     -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,
959     -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,
960     -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,
961   };
962   static const PetscInt hexMult[48 * 48] = {
963     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,
964     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,
965     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,
966     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,
967     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,
968     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,
969     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,
970     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,
971     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,
972     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,
973     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,
974     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,
975     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,
976     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,
977     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,
978     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,
979     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,
980     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,
981     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,
982     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,
983     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,
984     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,
985     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,
986     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,
987     -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,
988     -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,
989     -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,
990     -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,
991     -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,
992     -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,
993     -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,
994     -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,
995     -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,
996     -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,
997     -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,
998     -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,
999     -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,
1000     -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,
1001     -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,
1002     -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,
1003     -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,
1004     -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,
1005     -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,
1006     -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,
1007     -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,
1008     -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,
1009     -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,
1010     -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,
1011   };
1012   static const PetscInt tripMult[12 * 12] = {
1013     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,
1014     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,
1015     -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,
1016   };
1017   static const PetscInt ttriMult[12 * 12] = {
1018     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,
1019     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,
1020     -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,
1021   };
1022   static const PetscInt tquadMult[16 * 16] = {
1023     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,
1024     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,
1025     -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,
1026     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,
1027     -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,
1028   };
1029   static const PetscInt pyrMult[8 * 8] = {
1030     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,
1031   };
1032   switch (ct) {
1033   case DM_POLYTOPE_POINT:
1034     return 0;
1035   case DM_POLYTOPE_SEGMENT:
1036   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1037     return segMult[(o1 + 1) * 2 + o2 + 1];
1038   case DM_POLYTOPE_TRIANGLE:
1039     return triMult[(o1 + 3) * 6 + o2 + 3];
1040   case DM_POLYTOPE_QUADRILATERAL:
1041     return quadMult[(o1 + 4) * 8 + o2 + 4];
1042   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1043     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1044   case DM_POLYTOPE_TETRAHEDRON:
1045     return tetMult[(o1 + 12) * 24 + o2 + 12];
1046   case DM_POLYTOPE_HEXAHEDRON:
1047     return hexMult[(o1 + 24) * 48 + o2 + 24];
1048   case DM_POLYTOPE_TRI_PRISM:
1049     return tripMult[(o1 + 6) * 12 + o2 + 6];
1050   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1051     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1052   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1053     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1054   case DM_POLYTOPE_PYRAMID:
1055     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1056   default:
1057     return 0;
1058   }
1059 }
1060 
1061 /* This is orientation o1 acting on orientation o2^{-1} */
1062 static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1063 {
1064   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1065   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1066   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};
1067   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};
1068   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1069   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1070   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1071   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1072   switch (ct) {
1073   case DM_POLYTOPE_POINT:
1074     return 0;
1075   case DM_POLYTOPE_SEGMENT:
1076   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1077     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1078   case DM_POLYTOPE_TRIANGLE:
1079     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1080   case DM_POLYTOPE_QUADRILATERAL:
1081     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1082   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1083     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1084   case DM_POLYTOPE_TETRAHEDRON:
1085     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1086   case DM_POLYTOPE_HEXAHEDRON:
1087     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1088   case DM_POLYTOPE_TRI_PRISM:
1089     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1090   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1091     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1092   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1093     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1094   case DM_POLYTOPE_PYRAMID:
1095     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1096   default:
1097     return 0;
1098   }
1099 }
1100 
1101 PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1102 PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1103 PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1104 PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1105 PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
1106