xref: /petsc/include/petscdm.h (revision 92a26154bc948bc3af330cd082baf461ef1aa548)
1 /*
2       Objects to manage the interactions between the mesh data structures and the algebraic objects
3 */
4 #pragma once
5 #include "petscsystypes.h"
6 #include <petscmat.h>
7 #include <petscdmtypes.h>
8 #include <petscfetypes.h>
9 #include <petscdstypes.h>
10 #include <petscdmlabel.h>
11 #include <petscdt.h>
12 
13 /* SUBMANSEC = DM */
14 
15 PETSC_EXTERN PetscErrorCode DMInitializePackage(void);
16 
17 PETSC_EXTERN PetscClassId DM_CLASSID;
18 
19 #define DMLOCATEPOINT_POINT_NOT_FOUND -367
20 
21 /*J
22     DMType - String with the name of a PETSc `DM`
23 
24    Level: beginner
25 
26 .seealso: [](ch_dmbase), `DMSetType()`, `DMCreate()`, `DM`
27 J*/
28 typedef const char *DMType;
29 #define DMDA        "da"
30 #define DMCOMPOSITE "composite"
31 #define DMSLICED    "sliced"
32 #define DMSHELL     "shell"
33 #define DMPLEX      "plex"
34 #define DMREDUNDANT "redundant"
35 #define DMPATCH     "patch"
36 #define DMMOAB      "moab"
37 #define DMNETWORK   "network"
38 #define DMFOREST    "forest"
39 #define DMP4EST     "p4est"
40 #define DMP8EST     "p8est"
41 #define DMSWARM     "swarm"
42 #define DMPRODUCT   "product"
43 #define DMSTAG      "stag"
44 
45 PETSC_EXTERN const char *const       DMBoundaryTypes[];
46 PETSC_EXTERN const char *const       DMBoundaryConditionTypes[];
47 PETSC_EXTERN const char *const       DMBlockingTypes[];
48 PETSC_EXTERN PetscFunctionList       DMList;
49 PETSC_EXTERN DMGeneratorFunctionList DMGenerateList;
50 PETSC_EXTERN PetscFunctionList       DMGeomModelList;
51 PETSC_EXTERN PetscErrorCode          DMCreate(MPI_Comm, DM *);
52 PETSC_EXTERN PetscErrorCode          DMClone(DM, DM *);
53 PETSC_EXTERN PetscErrorCode          DMSetType(DM, DMType);
54 PETSC_EXTERN PetscErrorCode          DMGetType(DM, DMType *);
55 PETSC_EXTERN PetscErrorCode          DMRegister(const char[], PetscErrorCode (*)(DM));
56 PETSC_EXTERN PetscErrorCode          DMRegisterDestroy(void);
57 
58 PETSC_EXTERN PetscErrorCode DMView(DM, PetscViewer);
59 PETSC_EXTERN PetscErrorCode DMLoad(DM, PetscViewer);
60 PETSC_EXTERN PetscErrorCode DMDestroy(DM *);
61 PETSC_EXTERN PetscErrorCode DMCreateGlobalVector(DM, Vec *);
62 PETSC_EXTERN PetscErrorCode DMCreateLocalVector(DM, Vec *);
63 PETSC_EXTERN PetscErrorCode DMGetLocalVector(DM, Vec *);
64 PETSC_EXTERN PetscErrorCode DMRestoreLocalVector(DM, Vec *);
65 PETSC_EXTERN PetscErrorCode DMGetGlobalVector(DM, Vec *);
66 PETSC_EXTERN PetscErrorCode DMRestoreGlobalVector(DM, Vec *);
67 PETSC_EXTERN PetscErrorCode DMClearGlobalVectors(DM);
68 PETSC_EXTERN PetscErrorCode DMClearLocalVectors(DM);
69 PETSC_EXTERN PetscErrorCode DMClearNamedGlobalVectors(DM);
70 PETSC_EXTERN PetscErrorCode DMClearNamedLocalVectors(DM);
71 PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
72 PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
73 PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
74 PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
75 PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
76 PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
77 PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
78 PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
79 PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
80 PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
81 PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
82 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
83 PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
84 PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
85 PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
86 PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
87 PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
88 PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
89 PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
90 PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
91 PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *, Vec *);
92 PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
93 PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
94 PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
95 PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
96 PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
97 PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
98 PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
99 PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
100 PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
101 PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
102 PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
103 PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
104 PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
105 PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
106 PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
107 PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
108 PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
109 PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
110 PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
111 PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);
112 
113 PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
114 PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
115 PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
116 PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
117 PETSC_EXTERN PetscErrorCode DMGeomModelRegister(const char[], PetscErrorCode (*)(DM, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]));
118 PETSC_EXTERN PetscErrorCode DMGeomModelRegisterAll(void);
119 PETSC_EXTERN PetscErrorCode DMGeomModelRegisterDestroy(void);
120 PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
121 PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);
122 
123 PETSC_EXTERN PetscErrorCode DMSetUp(DM);
124 PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
125 PETSC_EXTERN PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMDACreateAggregates()", ) PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
126 PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
127 PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
128 PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
129 PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
130 PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
131 PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
132 PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
133 PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
134 PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
135 PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
136 PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);
137 
138 /* Topology support */
139 PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
140 PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
141 PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
142 PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
143 PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
144 PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);
145 
146 /* Coordinate support */
147 PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
148 PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
149 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
150 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
151 PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
152 PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
153 PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
154 PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
155 PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
156 PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
157 PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
158 PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
159 PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
160 PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
161 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
162 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
163 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
164 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
165 PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
166 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
167 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
168 PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
169 PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
170 PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
171 PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
172 PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
173 PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
174 PETSC_EXTERN PetscErrorCode DMSetCoordinateDisc(DM, PetscFE, PetscBool);
175 PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);
176 PETSC_EXTERN PetscErrorCode DMSnapToGeomModel(DM, PetscInt, PetscInt, const PetscScalar[], PetscScalar[]);
177 PETSC_EXTERN PetscErrorCode DMSetSnapToGeomModel(DM, const char[]);
178 
179 /* Periodicity support */
180 PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
181 PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
182 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
183 PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
184 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
185 PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);
186 PETSC_EXTERN PetscErrorCode DMGetSparseLocalize(DM, PetscBool *);
187 PETSC_EXTERN PetscErrorCode DMSetSparseLocalize(DM, PetscBool);
188 
189 /* block hook interface */
190 PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
191 PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
192 PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);
193 
194 PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
195 PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
196 PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
197 PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
198 PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
199 PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
200 PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
201 PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
202 PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
203 PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
204 PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscCtxDestroyFn *);
205 PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
206 PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
207 PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
208 PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
209 PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
210 PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
211 PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);
212 
213 PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
214 PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
215 PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], const PetscInt[], const PetscInt[], IS *, DM *);
216 PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
217 PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
218 PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
219 PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);
220 
221 PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
222 PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
223 PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
224 PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
225 PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);
226 
227 PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
228 PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
229 PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
230 PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
231 PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);
232 
233 typedef struct NLF_DAAD *NLF;
234 
235 #define DM_FILE_CLASSID 1211221
236 
237 /* FEM support */
238 PETSC_EXTERN PetscErrorCode DMPrintCellIndices(PetscInt, const char[], PetscInt, const PetscInt[]);
239 PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
240 PETSC_EXTERN PetscErrorCode DMPrintCellVectorReal(PetscInt, const char[], PetscInt, const PetscReal[]);
241 PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
242 PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);
243 
244 PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
245 PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
246 PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
247 PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
248 
249 PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
250 PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
251 PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
252 PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
253 PETSC_EXTERN PetscErrorCode DMCreateSectionPermutation(DM, IS *, PetscBT *);
254 PETSC_EXTERN PetscErrorCode DMReorderSectionGetDefault(DM, DMReorderDefaultFlag *);
255 PETSC_EXTERN PetscErrorCode DMReorderSectionSetDefault(DM, DMReorderDefaultFlag);
256 PETSC_EXTERN PetscErrorCode DMReorderSectionGetType(DM, MatOrderingType *);
257 PETSC_EXTERN PetscErrorCode DMReorderSectionSetType(DM, MatOrderingType);
258 PETSC_EXTERN PetscErrorCode DMUseTensorOrder(DM, PetscBool);
259 static inline PETSC_DEPRECATED_FUNCTION(3, 23, 0, "DMGetLocalSection()", ) PetscErrorCode DMGetSection(DM dm, PetscSection *s)
260 {
261   return DMGetLocalSection(dm, s);
262 }
263 static inline PETSC_DEPRECATED_FUNCTION(3, 23, 0, "DMSetLocalSection()", ) PetscErrorCode DMSetSection(DM dm, PetscSection s)
264 {
265   return DMSetLocalSection(dm, s);
266 }
267 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetSection()", ) PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
268 {
269   return DMGetLocalSection(dm, s);
270 }
271 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetSection()", ) PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
272 {
273   return DMSetLocalSection(dm, s);
274 }
275 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetGlobalSection()", ) PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
276 {
277   return DMGetGlobalSection(dm, s);
278 }
279 static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetGlobalSection()", ) PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
280 {
281   return DMSetGlobalSection(dm, s);
282 }
283 
284 PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
285 PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
286 PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
287 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMGetSectionSF()", ) PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
288 {
289   return DMGetSectionSF(dm, s);
290 }
291 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMSetSectionSF()", ) PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
292 {
293   return DMSetSectionSF(dm, s);
294 }
295 static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMCreateSectionSF()", ) PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
296 {
297   return DMCreateSectionSF(dm, l, g);
298 }
299 PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
300 PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
301 PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
302 PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);
303 
304 PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
305 PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);
306 
307 PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
308 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
309 PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
310 PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char[], PetscInt, PetscReal *);
311 PETSC_EXTERN PetscErrorCode DMGetOutputSequenceLength(DM, PetscViewer, const char[], PetscInt *);
312 
313 PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
314 PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
315 PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
316 PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
317 PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
318 PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
319 PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
320 PETSC_EXTERN PetscErrorCode DMClearFields(DM);
321 PETSC_EXTERN PetscErrorCode DMCopyFields(DM, PetscInt, PetscInt, DM);
322 PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
323 PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
324 PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
325 PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);
326 
327 PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
328 PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
329 PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *, PetscDS *);
330 PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *, PetscDS *);
331 PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS, PetscDS);
332 PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *, PetscDS *);
333 PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS, PetscDS);
334 PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
335 PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
336 PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
337 PETSC_EXTERN PetscErrorCode DMClearDS(DM);
338 PETSC_EXTERN PetscErrorCode DMCopyDS(DM, PetscInt, PetscInt, DM);
339 PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
340 PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
341 PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
342 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
343 PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
344 PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
345 PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
346 PETSC_EXTERN PetscErrorCode DMClearAuxiliaryVec(DM);
347 
348 /*MC
349   DMInterpolationInfo - Structure for holding information about interpolation on a mesh
350 
351   Synopsis:
352     comm   - The communicator
353     dim    - The spatial dimension of points
354     nInput - The number of input points
355     points - The input point coordinates
356     cells  - The cell containing each point
357     n      - The number of local points
358     coords - The point coordinates
359     dof    - The number of components to interpolate
360 
361   Level: intermediate
362 
363 .seealso: [](ch_dmbase), `DM`, `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
364 M*/
365 struct _DMInterpolationInfo {
366   MPI_Comm   comm;
367   PetscInt   dim;    /*1 The spatial dimension of points */
368   PetscInt   nInput; /* The number of input points */
369   PetscReal *points; /* The input point coordinates */
370   PetscInt  *cells;  /* The cell containing each point */
371   PetscInt   n;      /* The number of local points */
372   Vec        coords; /* The point coordinates */
373   PetscInt   dof;    /* The number of components to interpolate */
374 };
375 typedef struct _DMInterpolationInfo *DMInterpolationInfo;
376 
377 PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
378 PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
379 PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
380 PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
381 PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
382 PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
383 PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
384 PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
385 PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
386 PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
387 PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
388 PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);
389 
390 PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
391 PETSC_EXTERN PetscErrorCode DMCreateLabelAtIndex(DM, PetscInt, const char[]);
392 PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
393 PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
394 PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
395 PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
396 PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
397 PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
398 PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
399 PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
400 PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
401 PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
402 PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
403 PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);
404 
405 /*E
406    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination `DM`s with the same name
407 
408    Values:
409 +  `DM_COPY_LABELS_REPLACE` - replace label in destination by label from source
410 .  `DM_COPY_LABELS_KEEP`    - keep destination label
411 -  `DM_COPY_LABELS_FAIL`    - generate an error
412 
413    Level: advanced
414 
415 .seealso: [](ch_dmbase), `DMLabel`, `DM`, `DMCompareLabels()`, `DMRemoveLabel()`
416 E*/
417 typedef enum {
418   DM_COPY_LABELS_REPLACE,
419   DM_COPY_LABELS_KEEP,
420   DM_COPY_LABELS_FAIL
421 } DMCopyLabelsMode;
422 PETSC_EXTERN const char *const DMCopyLabelsModes[];
423 
424 PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
425 PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
426 PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
427 PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
428 PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
429 PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
430 PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
431 PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
432 PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
433 PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
434 PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);
435 
436 PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
437 PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);
438 
439 PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
440 PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
441 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
442 PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
443 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);
444 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);
445 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);
446 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);
447 PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
448 PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
449 PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
450 PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
451 PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
452 PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);
453 
454 PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);
455 
456 PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscCtxDestroyFn *);
457 PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
458 PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
459 PETSC_EXTERN PetscErrorCode DMMonitor(DM);
460 
461 static inline PetscBool DMPolytopeTypeIsHybrid(DMPolytopeType ct)
462 {
463   switch (ct) {
464   case DM_POLYTOPE_POINT_PRISM_TENSOR:
465   case DM_POLYTOPE_SEG_PRISM_TENSOR:
466   case DM_POLYTOPE_TRI_PRISM_TENSOR:
467   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
468     return PETSC_TRUE;
469   default:
470     return PETSC_FALSE;
471   }
472 }
473 
474 static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
475 {
476   switch (ct) {
477   case DM_POLYTOPE_POINT:
478     return 0;
479   case DM_POLYTOPE_SEGMENT:
480   case DM_POLYTOPE_POINT_PRISM_TENSOR:
481     return 1;
482   case DM_POLYTOPE_TRIANGLE:
483   case DM_POLYTOPE_QUADRILATERAL:
484   case DM_POLYTOPE_SEG_PRISM_TENSOR:
485   case DM_POLYTOPE_UNKNOWN_FACE:
486     return 2;
487   case DM_POLYTOPE_TETRAHEDRON:
488   case DM_POLYTOPE_HEXAHEDRON:
489   case DM_POLYTOPE_TRI_PRISM:
490   case DM_POLYTOPE_TRI_PRISM_TENSOR:
491   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
492   case DM_POLYTOPE_PYRAMID:
493   case DM_POLYTOPE_UNKNOWN_CELL:
494     return 3;
495   default:
496     return -1;
497   }
498 }
499 
500 static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
501 {
502   switch (ct) {
503   case DM_POLYTOPE_POINT:
504     return 0;
505   case DM_POLYTOPE_SEGMENT:
506     return 2;
507   case DM_POLYTOPE_POINT_PRISM_TENSOR:
508     return 2;
509   case DM_POLYTOPE_TRIANGLE:
510     return 3;
511   case DM_POLYTOPE_QUADRILATERAL:
512     return 4;
513   case DM_POLYTOPE_SEG_PRISM_TENSOR:
514     return 4;
515   case DM_POLYTOPE_TETRAHEDRON:
516     return 4;
517   case DM_POLYTOPE_HEXAHEDRON:
518     return 6;
519   case DM_POLYTOPE_TRI_PRISM:
520     return 5;
521   case DM_POLYTOPE_TRI_PRISM_TENSOR:
522     return 5;
523   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
524     return 6;
525   case DM_POLYTOPE_PYRAMID:
526     return 5;
527   default:
528     return -1;
529   }
530 }
531 
532 static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
533 {
534   switch (ct) {
535   case DM_POLYTOPE_POINT:
536     return 1;
537   case DM_POLYTOPE_SEGMENT:
538     return 2;
539   case DM_POLYTOPE_POINT_PRISM_TENSOR:
540     return 2;
541   case DM_POLYTOPE_TRIANGLE:
542     return 3;
543   case DM_POLYTOPE_QUADRILATERAL:
544     return 4;
545   case DM_POLYTOPE_SEG_PRISM_TENSOR:
546     return 4;
547   case DM_POLYTOPE_TETRAHEDRON:
548     return 4;
549   case DM_POLYTOPE_HEXAHEDRON:
550     return 8;
551   case DM_POLYTOPE_TRI_PRISM:
552     return 6;
553   case DM_POLYTOPE_TRI_PRISM_TENSOR:
554     return 6;
555   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
556     return 8;
557   case DM_POLYTOPE_PYRAMID:
558     return 5;
559   default:
560     return -1;
561   }
562 }
563 
564 static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
565 {
566   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)));
567 }
568 
569 static inline PetscInt DMPolytopeTypeGetNumArrangements(DMPolytopeType ct)
570 {
571   switch (ct) {
572   case DM_POLYTOPE_POINT:
573     return 1;
574   case DM_POLYTOPE_SEGMENT:
575     return 2;
576   case DM_POLYTOPE_POINT_PRISM_TENSOR:
577     return 2;
578   case DM_POLYTOPE_TRIANGLE:
579     return 6;
580   case DM_POLYTOPE_QUADRILATERAL:
581     return 8;
582   case DM_POLYTOPE_SEG_PRISM_TENSOR:
583     return 4;
584   case DM_POLYTOPE_TETRAHEDRON:
585     return 24;
586   case DM_POLYTOPE_HEXAHEDRON:
587     return 48;
588   case DM_POLYTOPE_TRI_PRISM:
589     return 12;
590   case DM_POLYTOPE_TRI_PRISM_TENSOR:
591     return 12;
592   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
593     return 16;
594   case DM_POLYTOPE_PYRAMID:
595     return 8;
596   default:
597     return -1;
598   }
599 }
600 
601 /* An arrangement is a face order combined with an orientation for each face */
602 static inline const PetscInt *DMPolytopeTypeGetArrangement(DMPolytopeType ct, PetscInt o)
603 {
604   static const PetscInt pntArr[1 * 2] = {0, 0};
605   /* a: swap */
606   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
607                                              0, 0, 1, 0,
608                                              /*  0: e */};
609   /* a: swap first two
610      b: swap last two */
611   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
612                                              2, -1, 1, -1, 0, -1, /* -2: aba */
613                                              1, -1, 0, -1, 2, -1, /* -1: a */
614                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
615                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
616                                              2, 0,  0, 0,  1, 0,
617                                              /*  2: ab */};
618   /* a: forward cyclic permutation
619      b: swap first and last pairs */
620   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
621                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
622                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
623                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
624                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
625                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
626                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
627                                               3, 0,  0, 0,  1, 0,  2, 0,
628                                               /*  3: a^3 */};
629   /* r: rotate 180
630      b: swap top and bottom segments */
631   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
632                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
633                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
634                                               1, 0,  0, 0,  2, -1, 3, -1,
635                                               /*  1: b */};
636   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
637   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
638                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
639                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
640                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
641                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
642                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
643                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
644                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
645                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
646                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
647                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
648                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
649                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
650                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
651                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
652                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
653                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
654                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
655                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
656                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
657                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
658                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
659                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
660                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
661   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
662   static const PetscInt hexArr[48 * 6 * 2] = {
663     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
664     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
665     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
666     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
667     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
668     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
669     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
670     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
671     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
672     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
673     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
674     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
675     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
676     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
677     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
678     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
679     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
680     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
681     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
682     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
683     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
684     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
685     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
686     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
687     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
688     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
689     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
690     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
691     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
692     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
693     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
694     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
695     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
696     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
697     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
698     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
699     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
700     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
701     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
702     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
703     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
704     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
705     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
706     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
707     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
708     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
709     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
710     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
711   };
712   static const PetscInt tripArr[12 * 5 * 2] = {
713     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
714     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
715     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
716     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
717     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
718     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
719     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
720     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
721     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
722     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
723     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
724     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
725   };
726   /* a: rotate 120 about z
727      b: swap top and bottom segments
728      r: reflect */
729   static const PetscInt ttriArr[12 * 5 * 2] = {
730     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
731     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
732     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
733     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
734     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
735     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
736     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
737     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
738     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
739     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
740     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
741     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
742   };
743   /* a: rotate 90 about z
744      b: swap top and bottom segments
745      r: reflect */
746   static const PetscInt tquadArr[16 * 6 * 2] = {
747     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
748     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
749     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
750     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
751     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
752     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
753     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
754     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
755     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
756     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
757     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
758     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
759     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
760     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
761     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
762     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
763   };
764   static const PetscInt pyrArr[8 * 5 * 2] = {
765     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
766     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
767     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
768     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
769     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
770     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
771     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
772     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
773   };
774   switch (ct) {
775   case DM_POLYTOPE_POINT:
776     return pntArr;
777   case DM_POLYTOPE_SEGMENT:
778     return &segArr[(o + 1) * 2 * 2];
779   case DM_POLYTOPE_POINT_PRISM_TENSOR:
780     return &segArr[(o + 1) * 2 * 2];
781   case DM_POLYTOPE_TRIANGLE:
782     return &triArr[(o + 3) * 3 * 2];
783   case DM_POLYTOPE_QUADRILATERAL:
784     return &quadArr[(o + 4) * 4 * 2];
785   case DM_POLYTOPE_SEG_PRISM_TENSOR:
786     return &tsegArr[(o + 2) * 4 * 2];
787   case DM_POLYTOPE_TETRAHEDRON:
788     return &tetArr[(o + 12) * 4 * 2];
789   case DM_POLYTOPE_HEXAHEDRON:
790     return &hexArr[(o + 24) * 6 * 2];
791   case DM_POLYTOPE_TRI_PRISM:
792     return &tripArr[(o + 6) * 5 * 2];
793   case DM_POLYTOPE_TRI_PRISM_TENSOR:
794     return &ttriArr[(o + 6) * 5 * 2];
795   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
796     return &tquadArr[(o + 8) * 6 * 2];
797   case DM_POLYTOPE_PYRAMID:
798     return &pyrArr[(o + 4) * 5 * 2];
799   default:
800     return PETSC_NULLPTR;
801   }
802 }
803 
804 /* A vertex arrangement is a vertex order */
805 static inline const PetscInt *DMPolytopeTypeGetVertexArrangement(DMPolytopeType ct, PetscInt o)
806 {
807   static const PetscInt pntVerts[1]      = {0};
808   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
809   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
810   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};
811   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
812   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
813                                             3, 1, 2, 0, /* -11: (14)     p21 */
814                                             1, 2, 3, 0, /* -10: (1234)   p18 */
815                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
816                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
817                                             0, 3, 2, 1, /*  -7: (24)     p14 */
818                                             0, 1, 3, 2, /*  -6: (34)     p6  */
819                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
820                                             3, 0, 1, 2, /*  -4: (1432    p9  */
821                                             1, 0, 2, 3, /*  -3: (12)     p1  */
822                                             0, 2, 1, 3, /*  -2: (23)     p2  */
823                                             2, 1, 0, 3, /*  -1: (13)     p5  */
824                                             0, 1, 2, 3, /*   0: ()       p0  */
825                                             1, 2, 0, 3, /*   1: (123)    p4  */
826                                             2, 0, 1, 3, /*   2: (132)    p3  */
827                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
828                                             0, 3, 1, 2, /*   4: (243)    p8  */
829                                             3, 1, 0, 2, /*   5: (143)    p11 */
830                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
831                                             3, 0, 2, 1, /*   7: (142)    p15 */
832                                             0, 2, 3, 1, /*   8: (234)    p12 */
833                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
834                                             2, 1, 3, 0, /*  10: (134)    p19 */
835                                             1, 3, 2, 0 /*  11: (124)    p20 */};
836   static const PetscInt hexVerts[48 * 8] = {
837     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
838     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
839     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
840     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
841     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
842     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
843     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
844     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
845     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
846     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
847     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
848     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
849     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
850     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
851     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
852     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
853     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
854     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
855     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
856     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
857     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
858     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
859     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
860     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
861     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
862     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
863     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
864     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
865     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
866     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
867     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
868     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
869     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
870     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
871     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
872     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
873     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
874     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
875     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
876     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
877     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
878     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
879     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
880     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
881     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
882     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
883     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
884     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
885   };
886   static const PetscInt tripVerts[12 * 6] = {
887     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
888     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
889     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
890     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
891     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
892     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
893     0, 1, 2, 3, 4, 5, /*  0: identity */
894     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
895     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
896     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
897     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
898     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
899   };
900   static const PetscInt ttriVerts[12 * 6] = {
901     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
902     3, 5, 4, 0, 2, 1, /* -5: r b a */
903     5, 4, 3, 2, 1, 0, /* -4: r b */
904     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
905     0, 2, 1, 3, 5, 4, /* -2: r a */
906     2, 1, 0, 5, 4, 3, /* -1: r */
907     0, 1, 2, 3, 4, 5, /*  0: identity */
908     1, 2, 0, 4, 5, 3, /*  1: a */
909     2, 0, 1, 5, 3, 4, /*  2: a^2 */
910     3, 4, 5, 0, 1, 2, /*  3: b */
911     4, 5, 3, 1, 2, 0, /*  4: b a */
912     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
913   };
914   /* a: rotate 90 about z
915      b: swap top and bottom segments
916      r: reflect */
917   static const PetscInt tquadVerts[16 * 8] = {
918     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
919     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
920     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
921     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
922     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
923     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
924     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
925     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
926     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
927     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
928     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
929     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
930     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
931     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
932     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
933     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
934   };
935   static const PetscInt pyrVerts[8 * 5] = {
936     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
937     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
938     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
939     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
940     0, 1, 2, 3, 4, /*  0: identity */
941     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
942     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
943     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
944   };
945   switch (ct) {
946   case DM_POLYTOPE_POINT:
947     return pntVerts;
948   case DM_POLYTOPE_SEGMENT:
949     return &segVerts[(o + 1) * 2];
950   case DM_POLYTOPE_POINT_PRISM_TENSOR:
951     return &segVerts[(o + 1) * 2];
952   case DM_POLYTOPE_TRIANGLE:
953     return &triVerts[(o + 3) * 3];
954   case DM_POLYTOPE_QUADRILATERAL:
955     return &quadVerts[(o + 4) * 4];
956   case DM_POLYTOPE_SEG_PRISM_TENSOR:
957     return &tsegVerts[(o + 2) * 4];
958   case DM_POLYTOPE_TETRAHEDRON:
959     return &tetVerts[(o + 12) * 4];
960   case DM_POLYTOPE_HEXAHEDRON:
961     return &hexVerts[(o + 24) * 8];
962   case DM_POLYTOPE_TRI_PRISM:
963     return &tripVerts[(o + 6) * 6];
964   case DM_POLYTOPE_TRI_PRISM_TENSOR:
965     return &ttriVerts[(o + 6) * 6];
966   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
967     return &tquadVerts[(o + 8) * 8];
968   case DM_POLYTOPE_PYRAMID:
969     return &pyrVerts[(o + 4) * 5];
970   default:
971     return PETSC_NULLPTR;
972   }
973 }
974 
975 /* This is orientation o1 acting on orientation o2 */
976 static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
977 {
978   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
979   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};
980   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,
981                                             -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};
982   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
983   static const PetscInt tetMult[24 * 24] = {
984     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,
985     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,
986     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,
987     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,
988     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,
989     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,
990     -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,
991     -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,
992     -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,
993     -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,
994     -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,
995     -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,
996   };
997   static const PetscInt hexMult[48 * 48] = {
998     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,
999     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,
1000     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,
1001     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,
1002     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,
1003     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,
1004     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,
1005     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,
1006     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,
1007     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,
1008     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,
1009     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,
1010     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,
1011     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,
1012     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,
1013     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,
1014     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,
1015     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,
1016     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,
1017     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,
1018     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,
1019     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,
1020     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,
1021     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,
1022     -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,
1023     -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,
1024     -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,
1025     -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,
1026     -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,
1027     -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,
1028     -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,
1029     -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,
1030     -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,
1031     -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,
1032     -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,
1033     -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,
1034     -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,
1035     -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,
1036     -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,
1037     -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,
1038     -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,
1039     -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,
1040     -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,
1041     -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,
1042     -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,
1043     -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,
1044     -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,
1045     -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,
1046   };
1047   static const PetscInt tripMult[12 * 12] = {
1048     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,
1049     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,
1050     -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,
1051   };
1052   static const PetscInt ttriMult[12 * 12] = {
1053     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,
1054     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,
1055     -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,
1056   };
1057   static const PetscInt tquadMult[16 * 16] = {
1058     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,
1059     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,
1060     -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,
1061     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,
1062     -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,
1063   };
1064   static const PetscInt pyrMult[8 * 8] = {
1065     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,
1066   };
1067   switch (ct) {
1068   case DM_POLYTOPE_POINT:
1069     return 0;
1070   case DM_POLYTOPE_SEGMENT:
1071   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1072     return segMult[(o1 + 1) * 2 + o2 + 1];
1073   case DM_POLYTOPE_TRIANGLE:
1074     return triMult[(o1 + 3) * 6 + o2 + 3];
1075   case DM_POLYTOPE_QUADRILATERAL:
1076     return quadMult[(o1 + 4) * 8 + o2 + 4];
1077   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1078     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1079   case DM_POLYTOPE_TETRAHEDRON:
1080     return tetMult[(o1 + 12) * 24 + o2 + 12];
1081   case DM_POLYTOPE_HEXAHEDRON:
1082     return hexMult[(o1 + 24) * 48 + o2 + 24];
1083   case DM_POLYTOPE_TRI_PRISM:
1084     return tripMult[(o1 + 6) * 12 + o2 + 6];
1085   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1086     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1087   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1088     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1089   case DM_POLYTOPE_PYRAMID:
1090     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1091   default:
1092     return 0;
1093   }
1094 }
1095 
1096 /* This is orientation o1 acting on orientation o2^{-1} */
1097 static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1098 {
1099   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1100   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1101   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};
1102   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};
1103   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1104   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1105   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1106   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1107   switch (ct) {
1108   case DM_POLYTOPE_POINT:
1109     return 0;
1110   case DM_POLYTOPE_SEGMENT:
1111   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1112     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1113   case DM_POLYTOPE_TRIANGLE:
1114     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1115   case DM_POLYTOPE_QUADRILATERAL:
1116     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1117   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1118     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1119   case DM_POLYTOPE_TETRAHEDRON:
1120     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1121   case DM_POLYTOPE_HEXAHEDRON:
1122     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1123   case DM_POLYTOPE_TRI_PRISM:
1124     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1125   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1126     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1127   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1128     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1129   case DM_POLYTOPE_PYRAMID:
1130     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1131   default:
1132     return 0;
1133   }
1134 }
1135 
1136 PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1137 PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1138 PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1139 PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1140 PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);
1141