Actual source code: petscdm.h

  1: /*
  2:       Objects to manage the interactions between the mesh data structures and the algebraic objects
  3: */
  4: #ifndef PETSCDM_H
  5: #define PETSCDM_H
  6: #include <petscmat.h>
  7: #include <petscdmtypes.h>
  8: #include <petscfetypes.h>
  9: #include <petscdstypes.h>
 10: #include <petscdmlabel.h>

 12: /* SUBMANSEC = DM */

 14: PETSC_EXTERN PetscErrorCode DMInitializePackage(void);

 16: PETSC_EXTERN PetscClassId DM_CLASSID;

 18: #define DMLOCATEPOINT_POINT_NOT_FOUND -367

 20: /*J
 21:     DMType - String with the name of a PETSc `DM`

 23:    Level: beginner

 25: .seealso: `DMSetType()`, `DM`
 26: J*/
 27: typedef const char *DMType;
 28: #define DMDA        "da"
 29: #define DMCOMPOSITE "composite"
 30: #define DMSLICED    "sliced"
 31: #define DMSHELL     "shell"
 32: #define DMPLEX      "plex"
 33: #define DMREDUNDANT "redundant"
 34: #define DMPATCH     "patch"
 35: #define DMMOAB      "moab"
 36: #define DMNETWORK   "network"
 37: #define DMFOREST    "forest"
 38: #define DMP4EST     "p4est"
 39: #define DMP8EST     "p8est"
 40: #define DMSWARM     "swarm"
 41: #define DMPRODUCT   "product"
 42: #define DMSTAG      "stag"

 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);

 56: PETSC_EXTERN PetscErrorCode DMView(DM, PetscViewer);
 57: PETSC_EXTERN PetscErrorCode DMLoad(DM, PetscViewer);
 58: PETSC_EXTERN PetscErrorCode DMDestroy(DM *);
 59: PETSC_EXTERN PetscErrorCode DMCreateGlobalVector(DM, Vec *);
 60: PETSC_EXTERN PetscErrorCode DMCreateLocalVector(DM, Vec *);
 61: PETSC_EXTERN PetscErrorCode DMGetLocalVector(DM, Vec *);
 62: PETSC_EXTERN PetscErrorCode DMRestoreLocalVector(DM, Vec *);
 63: PETSC_EXTERN PetscErrorCode DMGetGlobalVector(DM, Vec *);
 64: PETSC_EXTERN PetscErrorCode DMRestoreGlobalVector(DM, Vec *);
 65: PETSC_EXTERN PetscErrorCode DMClearGlobalVectors(DM);
 66: PETSC_EXTERN PetscErrorCode DMClearLocalVectors(DM);
 67: PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
 68: PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
 69: PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
 70: PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
 71: PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
 72: PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
 73: PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
 74: PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
 75: PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
 76: PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
 77: PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
 78: PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
 79: PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
 80: PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
 81: PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
 82: PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
 83: PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
 84: PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
 85: PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
 86: PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
 87: PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
 88: PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
 89: PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
 90: PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
 91: PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
 92: PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
 93: PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
 94: PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
 95: PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
 96: PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
 97: PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
 98: PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
 99: PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
100: PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
101: PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
102: PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
103: PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
104: PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
105: PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
106: PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
107: PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);

109: PETSC_EXTERN PetscErrorCode DMGenerate(DM, const char[], PetscBool, DM *);
110: PETSC_EXTERN PetscErrorCode DMGenerateRegister(const char[], PetscErrorCode (*)(DM, PetscBool, DM *), PetscErrorCode (*)(DM, PetscReal *, DM *), PetscErrorCode (*)(DM, Vec, DMLabel, DMLabel, DM *), PetscInt);
111: PETSC_EXTERN PetscErrorCode DMGenerateRegisterAll(void);
112: PETSC_EXTERN PetscErrorCode DMGenerateRegisterDestroy(void);
113: PETSC_EXTERN PetscErrorCode DMAdaptLabel(DM, DMLabel, DM *);
114: PETSC_EXTERN PetscErrorCode DMAdaptMetric(DM, Vec, DMLabel, DMLabel, DM *);

116: PETSC_EXTERN PetscErrorCode DMSetUp(DM);
117: PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
118: PETSC_EXTERN                PETSC_DEPRECATED_FUNCTION("Use DMDACreateAggregates() or DMCreateRestriction() (since version 3.12)") PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
119: PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
120: PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
121: PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
122: PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
123: PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
124: PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
125: PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
126: PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
127: PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
128: PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
129: PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);

131: /* Topology support */
132: PETSC_EXTERN PetscErrorCode DMGetDimension(DM, PetscInt *);
133: PETSC_EXTERN PetscErrorCode DMSetDimension(DM, PetscInt);
134: PETSC_EXTERN PetscErrorCode DMGetDimPoints(DM, PetscInt, PetscInt *, PetscInt *);
135: PETSC_EXTERN PetscErrorCode DMGetUseNatural(DM, PetscBool *);
136: PETSC_EXTERN PetscErrorCode DMSetUseNatural(DM, PetscBool);
137: PETSC_EXTERN PetscErrorCode DMGetNeighbors(DM, PetscInt *, const PetscMPIInt **);

139: /* Coordinate support */
140: PETSC_EXTERN PetscErrorCode DMGetCoordinateDM(DM, DM *);
141: PETSC_EXTERN PetscErrorCode DMSetCoordinateDM(DM, DM);
142: PETSC_EXTERN PetscErrorCode DMGetCellCoordinateDM(DM, DM *);
143: PETSC_EXTERN PetscErrorCode DMSetCellCoordinateDM(DM, DM);
144: PETSC_EXTERN PetscErrorCode DMGetCoordinateDim(DM, PetscInt *);
145: PETSC_EXTERN PetscErrorCode DMSetCoordinateDim(DM, PetscInt);
146: PETSC_EXTERN PetscErrorCode DMGetCoordinateSection(DM, PetscSection *);
147: PETSC_EXTERN PetscErrorCode DMSetCoordinateSection(DM, PetscInt, PetscSection);
148: PETSC_EXTERN PetscErrorCode DMGetCellCoordinateSection(DM, PetscSection *);
149: PETSC_EXTERN PetscErrorCode DMSetCellCoordinateSection(DM, PetscInt, PetscSection);
150: PETSC_EXTERN PetscErrorCode DMGetCoordinates(DM, Vec *);
151: PETSC_EXTERN PetscErrorCode DMSetCoordinates(DM, Vec);
152: PETSC_EXTERN PetscErrorCode DMGetCellCoordinates(DM, Vec *);
153: PETSC_EXTERN PetscErrorCode DMSetCellCoordinates(DM, Vec);
154: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalSetUp(DM);
155: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocal(DM, Vec *);
156: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalNoncollective(DM, Vec *);
157: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalTuple(DM, IS, PetscSection *, Vec *);
158: PETSC_EXTERN PetscErrorCode DMSetCoordinatesLocal(DM, Vec);
159: PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalSetUp(DM);
160: PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocal(DM, Vec *);
161: PETSC_EXTERN PetscErrorCode DMGetCellCoordinatesLocalNoncollective(DM, Vec *);
162: PETSC_EXTERN PetscErrorCode DMSetCellCoordinatesLocal(DM, Vec);
163: PETSC_EXTERN PetscErrorCode DMGetCoordinateField(DM, DMField *);
164: PETSC_EXTERN PetscErrorCode DMSetCoordinateField(DM, DMField);
165: PETSC_EXTERN PetscErrorCode DMGetLocalBoundingBox(DM, PetscReal[], PetscReal[]);
166: PETSC_EXTERN PetscErrorCode DMGetBoundingBox(DM, PetscReal[], PetscReal[]);
167: PETSC_EXTERN PetscErrorCode DMProjectCoordinates(DM, PetscFE);
168: PETSC_EXTERN PetscErrorCode DMLocatePoints(DM, Vec, DMPointLocationType, PetscSF *);

170: /* Periodicity support */
171: PETSC_EXTERN PetscErrorCode DMGetPeriodicity(DM, const PetscReal *[], const PetscReal *[], const PetscReal *[]);
172: PETSC_EXTERN PetscErrorCode DMSetPeriodicity(DM, const PetscReal[], const PetscReal[], const PetscReal[]);
173: PETSC_EXTERN PetscErrorCode DMLocalizeCoordinate(DM, const PetscScalar[], PetscBool, PetscScalar[]);
174: PETSC_EXTERN PetscErrorCode DMLocalizeCoordinates(DM);
175: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalized(DM, PetscBool *);
176: PETSC_EXTERN PetscErrorCode DMGetCoordinatesLocalizedLocal(DM, PetscBool *);

178: /* block hook interface */
179: PETSC_EXTERN PetscErrorCode DMSubDomainHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
180: PETSC_EXTERN PetscErrorCode DMSubDomainHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, VecScatter, VecScatter, DM, void *), void *);
181: PETSC_EXTERN PetscErrorCode DMSubDomainRestrict(DM, VecScatter, VecScatter, DM);

183: PETSC_EXTERN PetscErrorCode DMSetOptionsPrefix(DM, const char[]);
184: PETSC_EXTERN PetscErrorCode DMAppendOptionsPrefix(DM, const char[]);
185: PETSC_EXTERN PetscErrorCode DMGetOptionsPrefix(DM, const char *[]);
186: PETSC_EXTERN PetscErrorCode DMSetVecType(DM, VecType);
187: PETSC_EXTERN PetscErrorCode DMGetVecType(DM, VecType *);
188: PETSC_EXTERN PetscErrorCode DMSetMatType(DM, MatType);
189: PETSC_EXTERN PetscErrorCode DMGetMatType(DM, MatType *);
190: PETSC_EXTERN PetscErrorCode DMSetISColoringType(DM, ISColoringType);
191: PETSC_EXTERN PetscErrorCode DMGetISColoringType(DM, ISColoringType *);
192: PETSC_EXTERN PetscErrorCode DMSetApplicationContext(DM, void *);
193: PETSC_EXTERN PetscErrorCode DMSetApplicationContextDestroy(DM, PetscErrorCode (*)(void **));
194: PETSC_EXTERN PetscErrorCode DMGetApplicationContext(DM, void *);
195: PETSC_EXTERN PetscErrorCode DMSetVariableBounds(DM, PetscErrorCode (*)(DM, Vec, Vec));
196: PETSC_EXTERN PetscErrorCode DMHasVariableBounds(DM, PetscBool *);
197: PETSC_EXTERN PetscErrorCode DMHasColoring(DM, PetscBool *);
198: PETSC_EXTERN PetscErrorCode DMHasCreateRestriction(DM, PetscBool *);
199: PETSC_EXTERN PetscErrorCode DMHasCreateInjection(DM, PetscBool *);
200: PETSC_EXTERN PetscErrorCode DMComputeVariableBounds(DM, Vec, Vec);

202: PETSC_EXTERN PetscErrorCode DMCreateSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
203: PETSC_EXTERN PetscErrorCode DMCreateSuperDM(DM[], PetscInt, IS **, DM *);
204: PETSC_EXTERN PetscErrorCode DMCreateSectionSubDM(DM, PetscInt, const PetscInt[], IS *, DM *);
205: PETSC_EXTERN PetscErrorCode DMCreateSectionSuperDM(DM[], PetscInt, IS **, DM *);
206: PETSC_EXTERN PetscErrorCode DMCreateFieldDecomposition(DM, PetscInt *, char ***, IS **, DM **);
207: PETSC_EXTERN PetscErrorCode DMCreateDomainDecomposition(DM, PetscInt *, char ***, IS **, IS **, DM **);
208: PETSC_EXTERN PetscErrorCode DMCreateDomainDecompositionScatters(DM, PetscInt, DM *, VecScatter **, VecScatter **, VecScatter **);

210: PETSC_EXTERN PetscErrorCode DMGetRefineLevel(DM, PetscInt *);
211: PETSC_EXTERN PetscErrorCode DMSetRefineLevel(DM, PetscInt);
212: PETSC_EXTERN PetscErrorCode DMGetCoarsenLevel(DM, PetscInt *);
213: PETSC_EXTERN PetscErrorCode DMSetCoarsenLevel(DM, PetscInt);
214: PETSC_EXTERN PetscErrorCode DMFinalizePackage(void);

216: PETSC_EXTERN PetscErrorCode VecGetDM(Vec, DM *);
217: PETSC_EXTERN PetscErrorCode VecSetDM(Vec, DM);
218: PETSC_EXTERN PetscErrorCode MatGetDM(Mat, DM *);
219: PETSC_EXTERN PetscErrorCode MatSetDM(Mat, DM);
220: PETSC_EXTERN PetscErrorCode MatFDColoringUseDM(Mat, MatFDColoring);

222: typedef struct NLF_DAAD *NLF;

224: #define DM_FILE_CLASSID 1211221

226: /* FEM support */
227: PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
228: PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
229: PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);

231: PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
232: PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
233: PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
234: PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));

236: PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
237: PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
238: PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
239: PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
240: PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
241: PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
242: static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSection() (since v3.9)") PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
243: {
244:   return DMGetSection(dm, s);
245: }
246: static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSection() (since v3.9)") PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
247: {
248:   return DMSetSection(dm, s);
249: }
250: static inline PETSC_DEPRECATED_FUNCTION("Use DMGetGlobalSection() (since v3.9)") PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
251: {
252:   return DMGetGlobalSection(dm, s);
253: }
254: static inline PETSC_DEPRECATED_FUNCTION("Use DMSetGlobalSection() (since v3.9)") PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
255: {
256:   return DMSetGlobalSection(dm, s);
257: }

259: PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
260: PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
261: PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
262: static inline PETSC_DEPRECATED_FUNCTION("Use DMGetSectionSF() (since v3.12)") PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
263: {
264:   return DMGetSectionSF(dm, s);
265: }
266: static inline PETSC_DEPRECATED_FUNCTION("Use DMSetSectionSF() (since v3.12)") PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
267: {
268:   return DMSetSectionSF(dm, s);
269: }
270: static inline PETSC_DEPRECATED_FUNCTION("Use DMCreateSectionSF() (since v3.12)") PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
271: {
272:   return DMCreateSectionSF(dm, l, g);
273: }
274: PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
275: PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
276: PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
277: PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);

279: PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
280: PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);

282: PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
283: PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
284: PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
285: PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);

287: PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
288: PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
289: PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
290: PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
291: PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
292: PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
293: PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
294: PETSC_EXTERN PetscErrorCode DMClearFields(DM);
295: PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
296: PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
297: PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
298: PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
299: PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);

301: PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
302: PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
303: PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *);
304: PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *);
305: PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS);
306: PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *);
307: PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS);
308: PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
309: PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
310: PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
311: PETSC_EXTERN PetscErrorCode DMClearDS(DM);
312: PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
313: PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
314: PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
315: PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
316: PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
317: PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
318: PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
319: PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);

321: /*MC
322:   DMInterpolationInfo - Structure for holding information about interpolation on a mesh

324:   Level: intermediate

326:   Synopsis:
327:     comm   - The communicator
328:     dim    - The spatial dimension of points
329:     nInput - The number of input points
330:     points - The input point coordinates
331:     cells  - The cell containing each point
332:     n      - The number of local points
333:     coords - The point coordinates
334:     dof    - The number of components to interpolate

336: .seealso: `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
337: M*/
338: struct _DMInterpolationInfo {
339:   MPI_Comm   comm;
340:   PetscInt   dim;    /*1 The spatial dimension of points */
341:   PetscInt   nInput; /* The number of input points */
342:   PetscReal *points; /* The input point coordinates */
343:   PetscInt  *cells;  /* The cell containing each point */
344:   PetscInt   n;      /* The number of local points */
345:   Vec        coords; /* The point coordinates */
346:   PetscInt   dof;    /* The number of components to interpolate */
347: };
348: typedef struct _DMInterpolationInfo *DMInterpolationInfo;

350: PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
351: PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
352: PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
353: PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
354: PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
355: PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
356: PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
357: PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
358: PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
359: PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
360: PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
361: PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);

363: PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
364: PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
365: PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
366: PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
367: PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
368: PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
369: PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
370: PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
371: PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
372: PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
373: PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
374: PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
375: PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);

377: /*E
378:    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination DMs with the same name

380:    Level: advanced

382: $ DM_COPY_LABELS_REPLACE  - replace label in destination by label from source
383: $ DM_COPY_LABELS_KEEP     - keep destination label
384: $ DM_COPY_LABELS_FAIL     - throw error

386: E*/
387: typedef enum {
388:   DM_COPY_LABELS_REPLACE,
389:   DM_COPY_LABELS_KEEP,
390:   DM_COPY_LABELS_FAIL
391: } DMCopyLabelsMode;
392: PETSC_EXTERN const char *const DMCopyLabelsModes[];

394: PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
395: PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
396: PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
397: PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
398: PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
399: PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
400: PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
401: PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
402: PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
403: PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
404: PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);

406: PETSC_EXTERN PetscErrorCode DMAddBoundary(DM, DMBoundaryConditionType, const char[], DMLabel, PetscInt, const PetscInt[], PetscInt, PetscInt, const PetscInt[], void (*)(void), void (*)(void), void *, PetscInt *);
407: PETSC_EXTERN PetscErrorCode DMIsBoundaryPoint(DM, PetscInt, PetscBool *);

409: PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
410: PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
411: PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
412: PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
413: PETSC_EXTERN PetscErrorCode DMProjectFieldLocal(DM, PetscReal, Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
414: PETSC_EXTERN PetscErrorCode DMProjectFieldLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**funcs)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
415: PETSC_EXTERN PetscErrorCode DMProjectFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
416: PETSC_EXTERN PetscErrorCode DMProjectBdFieldLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], Vec, void (**)(PetscInt, PetscInt, PetscInt, const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], const PetscInt[], const PetscInt[], const PetscScalar[], const PetscScalar[], const PetscScalar[], PetscReal, const PetscReal[], const PetscReal[], PetscInt, const PetscScalar[], PetscScalar[]), InsertMode, Vec);
417: PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
418: PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
419: PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
420: PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
421: PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
422: PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);

424: PETSC_EXTERN PetscErrorCode DMGetCompatibility(DM, DM, PetscBool *, PetscBool *);

426: PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
427: PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
428: PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
429: PETSC_EXTERN PetscErrorCode DMMonitor(DM);

431: static inline PetscInt DMPolytopeTypeGetDim(DMPolytopeType ct)
432: {
433:   switch (ct) {
434:   case DM_POLYTOPE_POINT:
435:     return 0;
436:   case DM_POLYTOPE_SEGMENT:
437:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
438:     return 1;
439:   case DM_POLYTOPE_TRIANGLE:
440:   case DM_POLYTOPE_QUADRILATERAL:
441:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
442:     return 2;
443:   case DM_POLYTOPE_TETRAHEDRON:
444:   case DM_POLYTOPE_HEXAHEDRON:
445:   case DM_POLYTOPE_TRI_PRISM:
446:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
447:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
448:   case DM_POLYTOPE_PYRAMID:
449:     return 3;
450:   default:
451:     return -1;
452:   }
453: }

455: static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
456: {
457:   switch (ct) {
458:   case DM_POLYTOPE_POINT:
459:     return 0;
460:   case DM_POLYTOPE_SEGMENT:
461:     return 2;
462:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
463:     return 2;
464:   case DM_POLYTOPE_TRIANGLE:
465:     return 3;
466:   case DM_POLYTOPE_QUADRILATERAL:
467:     return 4;
468:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
469:     return 4;
470:   case DM_POLYTOPE_TETRAHEDRON:
471:     return 4;
472:   case DM_POLYTOPE_HEXAHEDRON:
473:     return 6;
474:   case DM_POLYTOPE_TRI_PRISM:
475:     return 5;
476:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
477:     return 5;
478:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
479:     return 6;
480:   case DM_POLYTOPE_PYRAMID:
481:     return 5;
482:   default:
483:     return -1;
484:   }
485: }

487: static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
488: {
489:   switch (ct) {
490:   case DM_POLYTOPE_POINT:
491:     return 1;
492:   case DM_POLYTOPE_SEGMENT:
493:     return 2;
494:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
495:     return 2;
496:   case DM_POLYTOPE_TRIANGLE:
497:     return 3;
498:   case DM_POLYTOPE_QUADRILATERAL:
499:     return 4;
500:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
501:     return 4;
502:   case DM_POLYTOPE_TETRAHEDRON:
503:     return 4;
504:   case DM_POLYTOPE_HEXAHEDRON:
505:     return 8;
506:   case DM_POLYTOPE_TRI_PRISM:
507:     return 6;
508:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
509:     return 6;
510:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
511:     return 8;
512:   case DM_POLYTOPE_PYRAMID:
513:     return 5;
514:   default:
515:     return -1;
516:   }
517: }

519: static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
520: {
521:   return dim == 0 ? DM_POLYTOPE_POINT : (dim == 1 ? DM_POLYTOPE_SEGMENT : (dim == 2 ? (simplex ? DM_POLYTOPE_TRIANGLE : DM_POLYTOPE_QUADRILATERAL) : (dim == 3 ? (simplex ? DM_POLYTOPE_TETRAHEDRON : DM_POLYTOPE_HEXAHEDRON) : DM_POLYTOPE_UNKNOWN)));
522: }

524: static inline PetscInt DMPolytopeTypeGetNumArrangments(DMPolytopeType ct)
525: {
526:   switch (ct) {
527:   case DM_POLYTOPE_POINT:
528:     return 1;
529:   case DM_POLYTOPE_SEGMENT:
530:     return 2;
531:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
532:     return 2;
533:   case DM_POLYTOPE_TRIANGLE:
534:     return 6;
535:   case DM_POLYTOPE_QUADRILATERAL:
536:     return 8;
537:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
538:     return 4;
539:   case DM_POLYTOPE_TETRAHEDRON:
540:     return 24;
541:   case DM_POLYTOPE_HEXAHEDRON:
542:     return 48;
543:   case DM_POLYTOPE_TRI_PRISM:
544:     return 12;
545:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
546:     return 12;
547:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
548:     return 16;
549:   case DM_POLYTOPE_PYRAMID:
550:     return 8;
551:   default:
552:     return -1;
553:   }
554: }

556: /* An arrangement is a face order combined with an orientation for each face */
557: static inline const PetscInt *DMPolytopeTypeGetArrangment(DMPolytopeType ct, PetscInt o)
558: {
559:   static const PetscInt pntArr[1 * 2] = {0, 0};
560:   /* a: swap */
561:   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
562:                                              0, 0, 1, 0,
563:                                              /*  0: e */};
564:   /* a: swap first two
565:      b: swap last two */
566:   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
567:                                              2, -1, 1, -1, 0, -1, /* -2: aba */
568:                                              1, -1, 0, -1, 2, -1, /* -1: a */
569:                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
570:                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
571:                                              2, 0,  0, 0,  1, 0,
572:                                              /*  2: ab */};
573:   /* a: forward cyclic permutation
574:      b: swap first and last pairs */
575:   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
576:                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
577:                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
578:                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
579:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
580:                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
581:                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
582:                                               3, 0,  0, 0,  1, 0,  2, 0,
583:                                               /*  3: a^3 */};
584:   /* r: rotate 180
585:      b: swap top and bottom segments */
586:   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
587:                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
588:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
589:                                               1, 0,  0, 0,  2, -1, 3, -1,
590:                                               /*  1: b */};
591:   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
592:   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
593:                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
594:                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
595:                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
596:                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
597:                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
598:                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
599:                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
600:                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
601:                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
602:                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
603:                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
604:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
605:                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
606:                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
607:                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
608:                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
609:                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
610:                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
611:                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
612:                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
613:                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
614:                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
615:                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
616:   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
617:   static const PetscInt hexArr[48 * 6 * 2] = {
618:     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
619:     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
620:     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
621:     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
622:     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
623:     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
624:     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
625:     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
626:     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
627:     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
628:     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
629:     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
630:     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
631:     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
632:     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
633:     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
634:     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
635:     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
636:     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
637:     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
638:     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
639:     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
640:     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
641:     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
642:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
643:     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
644:     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
645:     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
646:     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
647:     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
648:     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
649:     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
650:     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
651:     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
652:     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
653:     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
654:     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
655:     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
656:     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
657:     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
658:     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
659:     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
660:     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
661:     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
662:     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
663:     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
664:     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
665:     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
666:   };
667:   static const PetscInt tripArr[12 * 5 * 2] = {
668:     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
669:     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
670:     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
671:     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
672:     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
673:     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
674:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
675:     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
676:     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
677:     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
678:     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
679:     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
680:   };
681:   /* a: rotate 120 about z
682:      b: swap top and bottom segments
683:      r: reflect */
684:   static const PetscInt ttriArr[12 * 5 * 2] = {
685:     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
686:     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
687:     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
688:     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
689:     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
690:     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
691:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
692:     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
693:     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
694:     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
695:     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
696:     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
697:   };
698:   /* a: rotate 90 about z
699:      b: swap top and bottom segments
700:      r: reflect */
701:   static const PetscInt tquadArr[16 * 6 * 2] = {
702:     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
703:     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
704:     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
705:     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
706:     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
707:     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
708:     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
709:     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
710:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
711:     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
712:     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
713:     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
714:     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
715:     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
716:     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
717:     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
718:   };
719:   static const PetscInt pyrArr[8 * 5 * 2] = {
720:     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
721:     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
722:     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
723:     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
724:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
725:     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
726:     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
727:     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
728:   };
729:   switch (ct) {
730:   case DM_POLYTOPE_POINT:
731:     return pntArr;
732:   case DM_POLYTOPE_SEGMENT:
733:     return &segArr[(o + 1) * 2 * 2];
734:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
735:     return &segArr[(o + 1) * 2 * 2];
736:   case DM_POLYTOPE_TRIANGLE:
737:     return &triArr[(o + 3) * 3 * 2];
738:   case DM_POLYTOPE_QUADRILATERAL:
739:     return &quadArr[(o + 4) * 4 * 2];
740:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
741:     return &tsegArr[(o + 2) * 4 * 2];
742:   case DM_POLYTOPE_TETRAHEDRON:
743:     return &tetArr[(o + 12) * 4 * 2];
744:   case DM_POLYTOPE_HEXAHEDRON:
745:     return &hexArr[(o + 24) * 6 * 2];
746:   case DM_POLYTOPE_TRI_PRISM:
747:     return &tripArr[(o + 6) * 5 * 2];
748:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
749:     return &ttriArr[(o + 6) * 5 * 2];
750:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
751:     return &tquadArr[(o + 8) * 6 * 2];
752:   case DM_POLYTOPE_PYRAMID:
753:     return &pyrArr[(o + 4) * 5 * 2];
754:   default:
755:     return NULL;
756:   }
757: }

759: /* A vertex arrangement is a vertex order */
760: static inline const PetscInt *DMPolytopeTypeGetVertexArrangment(DMPolytopeType ct, PetscInt o)
761: {
762:   static const PetscInt pntVerts[1]      = {0};
763:   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
764:   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
765:   static const PetscInt quadVerts[8 * 4] = {2, 1, 0, 3, 1, 0, 3, 2, 0, 3, 2, 1, 3, 2, 1, 0, 0, 1, 2, 3, 1, 2, 3, 0, 2, 3, 0, 1, 3, 0, 1, 2};
766:   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
767:   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
768:                                             3, 1, 2, 0, /* -11: (14)     p21 */
769:                                             1, 2, 3, 0, /* -10: (1234)   p18 */
770:                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
771:                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
772:                                             0, 3, 2, 1, /*  -7: (24)     p14 */
773:                                             0, 1, 3, 2, /*  -6: (34)     p6  */
774:                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
775:                                             3, 0, 1, 2, /*  -4: (1432    p9  */
776:                                             1, 0, 2, 3, /*  -3: (12)     p1  */
777:                                             0, 2, 1, 3, /*  -2: (23)     p2  */
778:                                             2, 1, 0, 3, /*  -1: (13)     p5  */
779:                                             0, 1, 2, 3, /*   0: ()       p0  */
780:                                             1, 2, 0, 3, /*   1: (123)    p4  */
781:                                             2, 0, 1, 3, /*   2: (132)    p3  */
782:                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
783:                                             0, 3, 1, 2, /*   4: (243)    p8  */
784:                                             3, 1, 0, 2, /*   5: (143)    p11 */
785:                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
786:                                             3, 0, 2, 1, /*   7: (142)    p15 */
787:                                             0, 2, 3, 1, /*   8: (234)    p12 */
788:                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
789:                                             2, 1, 3, 0, /*  10: (134)    p19 */
790:                                             1, 3, 2, 0 /*  11: (124)    p20 */};
791:   static const PetscInt hexVerts[48 * 8] = {
792:     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
793:     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
794:     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
795:     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
796:     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
797:     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
798:     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
799:     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
800:     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
801:     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
802:     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
803:     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
804:     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
805:     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
806:     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
807:     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
808:     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
809:     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
810:     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
811:     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
812:     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
813:     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
814:     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
815:     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
816:     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
817:     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
818:     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
819:     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
820:     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
821:     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
822:     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
823:     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
824:     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
825:     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
826:     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
827:     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
828:     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
829:     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
830:     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
831:     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
832:     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
833:     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
834:     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
835:     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
836:     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
837:     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
838:     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
839:     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
840:   };
841:   static const PetscInt tripVerts[12 * 6] = {
842:     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
843:     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
844:     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
845:     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
846:     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
847:     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
848:     0, 1, 2, 3, 4, 5, /*  0: identity */
849:     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
850:     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
851:     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
852:     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
853:     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
854:   };
855:   static const PetscInt ttriVerts[12 * 6] = {
856:     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
857:     3, 5, 4, 0, 2, 1, /* -5: r b a */
858:     5, 4, 3, 2, 1, 0, /* -4: r b */
859:     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
860:     0, 2, 1, 3, 5, 4, /* -2: r a */
861:     2, 1, 0, 5, 4, 3, /* -1: r */
862:     0, 1, 2, 3, 4, 5, /*  0: identity */
863:     1, 2, 0, 4, 5, 3, /*  1: a */
864:     2, 0, 1, 5, 3, 4, /*  2: a^2 */
865:     3, 4, 5, 0, 1, 2, /*  3: b */
866:     4, 5, 3, 1, 2, 0, /*  4: b a */
867:     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
868:   };
869:   /* a: rotate 90 about z
870:      b: swap top and bottom segments
871:      r: reflect */
872:   static const PetscInt tquadVerts[16 * 8] = {
873:     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
874:     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
875:     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
876:     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
877:     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
878:     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
879:     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
880:     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
881:     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
882:     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
883:     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
884:     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
885:     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
886:     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
887:     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
888:     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
889:   };
890:   static const PetscInt pyrVerts[8 * 5] = {
891:     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
892:     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
893:     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
894:     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
895:     0, 1, 2, 3, 4, /*  0: identity */
896:     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
897:     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
898:     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
899:   };
900:   switch (ct) {
901:   case DM_POLYTOPE_POINT:
902:     return pntVerts;
903:   case DM_POLYTOPE_SEGMENT:
904:     return &segVerts[(o + 1) * 2];
905:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
906:     return &segVerts[(o + 1) * 2];
907:   case DM_POLYTOPE_TRIANGLE:
908:     return &triVerts[(o + 3) * 3];
909:   case DM_POLYTOPE_QUADRILATERAL:
910:     return &quadVerts[(o + 4) * 4];
911:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
912:     return &tsegVerts[(o + 2) * 4];
913:   case DM_POLYTOPE_TETRAHEDRON:
914:     return &tetVerts[(o + 12) * 4];
915:   case DM_POLYTOPE_HEXAHEDRON:
916:     return &hexVerts[(o + 24) * 8];
917:   case DM_POLYTOPE_TRI_PRISM:
918:     return &tripVerts[(o + 6) * 6];
919:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
920:     return &ttriVerts[(o + 6) * 6];
921:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
922:     return &tquadVerts[(o + 8) * 8];
923:   case DM_POLYTOPE_PYRAMID:
924:     return &pyrVerts[(o + 4) * 5];
925:   default:
926:     return NULL;
927:   }
928: }

930: /* This is orientation o1 acting on orientation o2 */
931: static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
932: {
933:   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
934:   static const PetscInt triMult[6 * 6]   = {0, 2, 1, -3, -1, -2, 1, 0, 2, -2, -3, -1, 2, 1, 0, -1, -2, -3, -3, -2, -1, 0, 1, 2, -2, -1, -3, 1, 2, 0, -1, -3, -2, 2, 0, 1};
935:   static const PetscInt quadMult[8 * 8]  = {0,  3,  2,  1,  -4, -1, -2, -3, 1,  0,  3,  2,  -3, -4, -1, -2, 2,  1,  0,  3,  -2, -3, -4, -1, 3,  2,  1,  0,  -1, -2, -3, -4,
936:                                             -4, -3, -2, -1, 0,  1,  2,  3,  -3, -2, -1, -4, 1,  2,  3,  0,  -2, -1, -4, -3, 2,  3,  0,  1,  -1, -4, -3, -2, 3,  0,  1,  2};
937:   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
938:   static const PetscInt tetMult[24 * 24] = {
939:     3,   2,   7,   0,   5,   10,  9,   8,   1,   6,   11,  4,   -12, -7,  -5,  -9,  -10, -2,  -6,  -1,  -11, -3,  -4,  -8,  4,   0,   8,   1,   3,   11,  10,  6,   2,   7,   9,   5,   -11, -9,  -4,  -8,  -12, -1,  -5,  -3,  -10, -2,  -6,  -7,
940:     5,   1,   6,   2,   4,   9,   11,  7,   0,   8,   10,  3,   -10, -8,  -6,  -7,  -11, -3,  -4,  -2,  -12, -1,  -5,  -9,  0,   8,   4,   3,   11,  1,   6,   2,   10,  9,   5,   7,   -9,  -4,  -11, -12, -1,  -8,  -3,  -10, -5,  -6,  -7,  -2,
941:     1,   6,   5,   4,   9,   2,   7,   0,   11,  10,  3,   8,   -8,  -6,  -10, -11, -3,  -7,  -2,  -12, -4,  -5,  -9,  -1,  2,   7,   3,   5,   10,  0,   8,   1,   9,   11,  4,   6,   -7,  -5,  -12, -10, -2,  -9,  -1,  -11, -6,  -4,  -8,  -3,
942:     6,   5,   1,   9,   2,   4,   0,   11,  7,   3,   8,   10,  -6,  -10, -8,  -3,  -7,  -11, -12, -4,  -2,  -9,  -1,  -5,  7,   3,   2,   10,  0,   5,   1,   9,   8,   4,   6,   11,  -5,  -12, -7,  -2,  -9,  -10, -11, -6,  -1,  -8,  -3,  -4,
943:     8,   4,   0,   11,  1,   3,   2,   10,  6,   5,   7,   9,   -4,  -11, -9,  -1,  -8,  -12, -10, -5,  -3,  -7,  -2,  -6,  9,   11,  10,  6,   8,   7,   3,   5,   4,   0,   2,   1,   -3,  -1,  -2,  -6,  -4,  -5,  -9,  -7,  -8,  -12, -10, -11,
944:     10,  9,   11,  7,   6,   8,   4,   3,   5,   1,   0,   2,   -2,  -3,  -1,  -5,  -6,  -4,  -8,  -9,  -7,  -11, -12, -10, 11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12,
945:     -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  -11, -10, -12, -8,  -7,  -9,  -5,  -4,  -6,  -2,  -1,  -3,  1,   2,   0,   4,   5,   3,   7,   8,   6,   10,  11,  9,
946:     -10, -12, -11, -7,  -9,  -8,  -4,  -6,  -5,  -1,  -3,  -2,  2,   0,   1,   5,   3,   4,   8,   6,   7,   11,  9,   10,  -9,  -5,  -1,  -12, -2,  -4,  -3,  -11, -7,  -6,  -8,  -10, 3,   10,  8,   0,   7,   11,  9,   4,   2,   6,   1,   5,
947:     -8,  -4,  -3,  -11, -1,  -6,  -2,  -10, -9,  -5,  -7,  -12, 4,   11,  6,   1,   8,   9,   10,  5,   0,   7,   2,   3,   -7,  -6,  -2,  -10, -3,  -5,  -1,  -12, -8,  -4,  -9,  -11, 5,   9,   7,   2,   6,   10,  11,  3,   1,   8,   0,   4,
948:     -3,  -8,  -4,  -6,  -11, -1,  -9,  -2,  -10, -12, -5,  -7,  6,   4,   11,  9,   1,   8,   0,   10,  5,   3,   7,   2,   -2,  -7,  -6,  -5,  -10, -3,  -8,  -1,  -12, -11, -4,  -9,  7,   5,   9,   10,  2,   6,   1,   11,  3,   4,   8,   0,
949:     -1,  -9,  -5,  -4,  -12, -2,  -7,  -3,  -11, -10, -6,  -8,  8,   3,   10,  11,  0,   7,   2,   9,   4,   5,   6,   1,   -6,  -2,  -7,  -3,  -5,  -10, -12, -8,  -1,  -9,  -11, -4,  9,   7,   5,   6,   10,  2,   3,   1,   11,  0,   4,   8,
950:     -5,  -1,  -9,  -2,  -4,  -12, -11, -7,  -3,  -8,  -10, -6,  10,  8,   3,   7,   11,  0,   4,   2,   9,   1,   5,   6,   -4,  -3,  -8,  -1,  -6,  -11, -10, -9,  -2,  -7,  -12, -5,  11,  6,   4,   8,   9,   1,   5,   0,   10,  2,   3,   7,
951:   };
952:   static const PetscInt hexMult[48 * 48] = {
953:     18,  2,   5,   22,  21,  8,   16,  0,   13,  6,   11,  3,   15,  9,   4,   23,  12,  1,   19,  10,  7,   20,  14,  17,  -24, -10, -20, -16, -12, -21, -4,  -5,  -18, -13, -15, -8,  -2,  -11, -14, -7,  -3,  -22, -6,  -17, -19, -9,  -1,  -23,
954:     8,   20,  19,  2,   5,   23,  0,   17,  11,  1,   15,  7,   13,  4,   10,  18,  3,   14,  21,  9,   12,  22,  6,   16,  -23, -13, -17, -7,  -8,  -19, -16, -12, -22, -2,  -14, -5,  -10, -15, -11, -4,  -20, -9,  -21, -3,  -6,  -18, -24, -1,
955:     2,   17,  23,  8,   0,   19,  5,   20,  1,   11,  9,   14,  12,  6,   3,   16,  10,  7,   22,  15,  13,  21,  4,   18,  -22, -14, -19, -5,  -15, -17, -10, -2,  -23, -12, -13, -7,  -16, -8,  -4,  -11, -24, -3,  -18, -9,  -1,  -21, -20, -6,
956:     21,  5,   2,   16,  18,  0,   22,  8,   4,   12,  3,   11,  14,  7,   13,  20,  6,   10,  17,  1,   9,   23,  15,  19,  -21, -8,  -18, -15, -4,  -24, -12, -14, -20, -7,  -16, -10, -11, -2,  -5,  -13, -6,  -19, -3,  -23, -22, -1,  -9,  -17,
957:     16,  8,   0,   21,  22,  2,   18,  5,   12,  4,   1,   10,  9,   15,  6,   19,  13,  11,  23,  3,   14,  17,  7,   20,  -20, -16, -24, -10, -2,  -18, -11, -7,  -21, -14, -8,  -15, -12, -4,  -13, -5,  -9,  -23, -1,  -19, -17, -3,  -6,  -22,
958:     5,   19,  20,  0,   8,   17,  2,   23,  10,  3,   7,   15,  6,   12,  11,  22,  1,   9,   16,  14,  4,   18,  13,  21,  -19, -5,  -22, -14, -16, -23, -8,  -11, -17, -4,  -7,  -13, -15, -10, -12, -2,  -21, -6,  -20, -1,  -9,  -24, -18, -3,
959:     22,  0,   8,   18,  16,  5,   21,  2,   6,   13,  10,  1,   7,   14,  12,  17,  4,   3,   20,  11,  15,  19,  9,   23,  -18, -15, -21, -8,  -11, -20, -2,  -13, -24, -5,  -10, -16, -4,  -12, -7,  -14, -1,  -17, -9,  -22, -23, -6,  -3,  -19,
960:     0,   23,  17,  5,   2,   20,  8,   19,  3,   10,  14,  9,   4,   13,  1,   21,  11,  15,  18,  7,   6,   16,  12,  22,  -17, -7,  -23, -13, -10, -22, -15, -4,  -19, -11, -5,  -14, -8,  -16, -2,  -12, -18, -1,  -24, -6,  -3,  -20, -21, -9,
961:     10,  13,  6,   1,   11,  12,  3,   4,   8,   0,   22,  18,  19,  23,  5,   15,  2,   21,  9,   16,  17,  7,   20,  14,  -16, -24, -10, -20, -23, -8,  -19, -6,  -15, -3,  -21, -18, -22, -17, -9,  -1,  -14, -12, -7,  -4,  -11, -13, -5,  -2,
962:     1,   4,   12,  10,  3,   6,   11,  13,  0,   8,   16,  21,  17,  20,  2,   14,  5,   18,  7,   22,  19,  9,   23,  15,  -15, -21, -8,  -18, -17, -10, -22, -3,  -16, -6,  -24, -20, -19, -23, -1,  -9,  -5,  -4,  -13, -12, -2,  -7,  -14, -11,
963:     14,  10,  3,   9,   7,   1,   15,  11,  17,  23,  0,   5,   16,  22,  20,  6,   19,  8,   12,  2,   21,  4,   18,  13,  -14, -19, -5,  -22, -3,  -13, -9,  -20, -7,  -21, -23, -17, -6,  -1,  -24, -18, -12, -16, -2,  -8,  -10, -4,  -11, -15,
964:     7,   3,   10,  15,  14,  11,  9,   1,   20,  19,  5,   0,   18,  21,  17,  4,   23,  2,   13,  8,   22,  6,   16,  12,  -13, -17, -7,  -23, -9,  -14, -3,  -24, -5,  -18, -22, -19, -1,  -6,  -20, -21, -2,  -10, -12, -15, -16, -11, -4,  -8,
965:     13,  14,  15,  12,  4,   9,   6,   7,   21,  22,  23,  20,  2,   0,   18,  3,   16,  17,  1,   19,  8,   11,  5,   10,  -12, -9,  -11, -6,  -21, -4,  -24, -22, -2,  -23, -3,  -1,  -20, -18, -19, -17, -16, -14, -15, -13, -5,  -8,  -10, -7,
966:     6,   9,   7,   4,   12,  14,  13,  15,  16,  18,  17,  19,  0,   2,   22,  1,   21,  23,  3,   20,  5,   10,  8,   11,  -11, -6,  -12, -9,  -20, -2,  -18, -17, -4,  -19, -1,  -3,  -21, -24, -23, -22, -8,  -7,  -10, -5,  -13, -16, -15, -14,
967:     3,   12,  4,   11,  1,   13,  10,  6,   2,   5,   21,  16,  23,  19,  0,   9,   8,   22,  15,  18,  20,  14,  17,  7,   -10, -20, -16, -24, -22, -15, -17, -1,  -8,  -9,  -18, -21, -23, -19, -3,  -6,  -13, -2,  -5,  -11, -4,  -14, -7,  -12,
968:     20,  16,  18,  23,  17,  21,  19,  22,  14,  15,  4,   6,   3,   1,   7,   0,   9,   12,  2,   13,  11,  5,   10,  8,   -9,  -11, -6,  -12, -14, -3,  -13, -10, -1,  -8,  -2,  -4,  -7,  -5,  -16, -15, -23, -20, -22, -18, -24, -19, -17, -21,
969:     11,  6,   13,  3,   10,  4,   1,   12,  5,   2,   18,  22,  20,  17,  8,   7,   0,   16,  14,  21,  23,  15,  19,  9,   -8,  -18, -15, -21, -19, -16, -23, -9,  -10, -1,  -20, -24, -17, -22, -6,  -3,  -7,  -11, -14, -2,  -12, -5,  -13, -4,
970:     9,   11,  1,   14,  15,  3,   7,   10,  23,  17,  2,   8,   21,  18,  19,  13,  20,  5,   4,   0,   16,  12,  22,  6,   -7,  -23, -13, -17, -1,  -5,  -6,  -21, -14, -20, -19, -22, -9,  -3,  -18, -24, -11, -8,  -4,  -16, -15, -2,  -12, -10,
971:     19,  21,  22,  17,  23,  16,  20,  18,  9,   7,   12,  13,  1,   3,   15,  2,   14,  4,   0,   6,   10,  8,   11,  5,   -6,  -12, -9,  -11, -7,  -1,  -5,  -15, -3,  -16, -4,  -2,  -14, -13, -8,  -10, -19, -21, -17, -24, -18, -23, -22, -20,
972:     15,  1,   11,  7,   9,   10,  14,  3,   19,  20,  8,   2,   22,  16,  23,  12,  17,  0,   6,   5,   18,  13,  21,  4,   -5,  -22, -14, -19, -6,  -7,  -1,  -18, -13, -24, -17, -23, -3,  -9,  -21, -20, -4,  -15, -11, -10, -8,  -12, -2,  -16,
973:     4,   15,  14,  6,   13,  7,   12,  9,   18,  16,  20,  23,  5,   8,   21,  11,  22,  19,  10,  17,  0,   3,   2,   1,   -4,  -1,  -2,  -3,  -24, -12, -21, -19, -11, -17, -6,  -9,  -18, -20, -22, -23, -15, -5,  -16, -7,  -14, -10, -8,  -13,
974:     17,  18,  16,  19,  20,  22,  23,  21,  7,   9,   6,   4,   10,  11,  14,  5,   15,  13,  8,   12,  1,   0,   3,   2,   -3,  -4,  -1,  -2,  -13, -9,  -14, -16, -6,  -15, -12, -11, -5,  -7,  -10, -8,  -22, -24, -23, -21, -20, -17, -19, -18,
975:     12,  7,   9,   13,  6,   15,  4,   14,  22,  21,  19,  17,  8,   5,   16,  10,  18,  20,  11,  23,  2,   1,   0,   3,   -2,  -3,  -4,  -1,  -18, -11, -20, -23, -12, -22, -9,  -6,  -24, -21, -17, -19, -10, -13, -8,  -14, -7,  -15, -16, -5,
976:     23,  22,  21,  20,  19,  18,  17,  16,  15,  14,  13,  12,  11,  10,  9,   8,   7,   6,   5,   4,   3,   2,   1,   0,   -1,  -2,  -3,  -4,  -5,  -6,  -7,  -8,  -9,  -10, -11, -12, -13, -14, -15, -16, -17, -18, -19, -20, -21, -22, -23, -24,
977:     -24, -23, -22, -21, -20, -19, -18, -17, -16, -15, -14, -13, -12, -11, -10, -9,  -8,  -7,  -6,  -5,  -4,  -3,  -2,  -1,  0,   1,   2,   3,   4,   5,   6,   7,   8,   9,   10,  11,  12,  13,  14,  15,  16,  17,  18,  19,  20,  21,  22,  23,
978:     -13, -8,  -10, -14, -7,  -16, -5,  -15, -23, -22, -20, -18, -9,  -6,  -17, -11, -19, -21, -12, -24, -3,  -2,  -1,  -4,  1,   2,   3,   0,   17,  10,  19,  22,  11,  21,  8,   5,   23,  20,  16,  18,  9,   12,  7,   13,  6,   14,  15,  4,
979:     -18, -19, -17, -20, -21, -23, -24, -22, -8,  -10, -7,  -5,  -11, -12, -15, -6,  -16, -14, -9,  -13, -2,  -1,  -4,  -3,  2,   3,   0,   1,   12,  8,   13,  15,  5,   14,  11,  10,  4,   6,   9,   7,   21,  23,  22,  20,  19,  16,  18,  17,
980:     -5,  -16, -15, -7,  -14, -8,  -13, -10, -19, -17, -21, -24, -6,  -9,  -22, -12, -23, -20, -11, -18, -1,  -4,  -3,  -2,  3,   0,   1,   2,   23,  11,  20,  18,  10,  16,  5,   8,   17,  19,  21,  22,  14,  4,   15,  6,   13,  9,   7,   12,
981:     -16, -2,  -12, -8,  -10, -11, -15, -4,  -20, -21, -9,  -3,  -23, -17, -24, -13, -18, -1,  -7,  -6,  -19, -14, -22, -5,  4,   21,  13,  18,  5,   6,   0,   17,  12,  23,  16,  22,  2,   8,   20,  19,  3,   14,  10,  9,   7,   11,  1,   15,
982:     -20, -22, -23, -18, -24, -17, -21, -19, -10, -8,  -13, -14, -2,  -4,  -16, -3,  -15, -5,  -1,  -7,  -11, -9,  -12, -6,  5,   11,  8,   10,  6,   0,   4,   14,  2,   15,  3,   1,   13,  12,  7,   9,   18,  20,  16,  23,  17,  22,  21,  19,
983:     -10, -12, -2,  -15, -16, -4,  -8,  -11, -24, -18, -3,  -9,  -22, -19, -20, -14, -21, -6,  -5,  -1,  -17, -13, -23, -7,  6,   22,  12,  16,  0,   4,   5,   20,  13,  19,  18,  21,  8,   2,   17,  23,  10,  7,   3,   15,  14,  1,   11,  9,
984:     -12, -7,  -14, -4,  -11, -5,  -2,  -13, -6,  -3,  -19, -23, -21, -18, -9,  -8,  -1,  -17, -15, -22, -24, -16, -20, -10, 7,   17,  14,  20,  18,  15,  22,  8,   9,   0,   19,  23,  16,  21,  5,   2,   6,   10,  13,  1,   11,  4,   12,  3,
985:     -21, -17, -19, -24, -18, -22, -20, -23, -15, -16, -5,  -7,  -4,  -2,  -8,  -1,  -10, -13, -3,  -14, -12, -6,  -11, -9,  8,   10,  5,   11,  13,  2,   12,  9,   0,   7,   1,   3,   6,   4,   15,  14,  22,  19,  21,  17,  23,  18,  16,  20,
986:     -4,  -13, -5,  -12, -2,  -14, -11, -7,  -3,  -6,  -22, -17, -24, -20, -1,  -10, -9,  -23, -16, -19, -21, -15, -18, -8,  9,   19,  15,  23,  21,  14,  16,  0,   7,   8,   17,  20,  22,  18,  2,   5,   12,  1,   4,   10,  3,   13,  6,   11,
987:     -7,  -10, -8,  -5,  -13, -15, -14, -16, -17, -19, -18, -20, -1,  -3,  -23, -2,  -22, -24, -4,  -21, -6,  -11, -9,  -12, 10,  5,   11,  8,   19,  1,   17,  16,  3,   18,  0,   2,   20,  23,  22,  21,  7,   6,   9,   4,   12,  15,  14,  13,
988:     -14, -15, -16, -13, -5,  -10, -7,  -8,  -22, -23, -24, -21, -3,  -1,  -19, -4,  -17, -18, -2,  -20, -9,  -12, -6,  -11, 11,  8,   10,  5,   20,  3,   23,  21,  1,   22,  2,   0,   19,  17,  18,  16,  15,  13,  14,  12,  4,   7,   9,   6,
989:     -8,  -4,  -11, -16, -15, -12, -10, -2,  -21, -20, -6,  -1,  -19, -22, -18, -5,  -24, -3,  -14, -9,  -23, -7,  -17, -13, 12,  16,  6,   22,  8,   13,  2,   23,  4,   17,  21,  18,  0,   5,   19,  20,  1,   9,   11,  14,  15,  10,  3,   7,
990:     -15, -11, -4,  -10, -8,  -2,  -16, -12, -18, -24, -1,  -6,  -17, -23, -21, -7,  -20, -9,  -13, -3,  -22, -5,  -19, -14, 13,  18,  4,   21,  2,   12,  8,   19,  6,   20,  22,  16,  5,   0,   23,  17,  11,  15,  1,   7,   9,   3,   10,  14,
991:     -2,  -5,  -13, -11, -4,  -7,  -12, -14, -1,  -9,  -17, -22, -18, -21, -3,  -15, -6,  -19, -8,  -23, -20, -10, -24, -16, 14,  20,  7,   17,  16,  9,   21,  2,   15,  5,   23,  19,  18,  22,  0,   8,   4,   3,   12,  11,  1,   6,   13,  10,
992:     -11, -14, -7,  -2,  -12, -13, -4,  -5,  -9,  -1,  -23, -19, -20, -24, -6,  -16, -3,  -22, -10, -17, -18, -8,  -21, -15, 15,  23,  9,   19,  22,  7,   18,  5,   14,  2,   20,  17,  21,  16,  8,   0,   13,  11,  6,   3,   10,  12,  4,   1,
993:     -1,  -24, -18, -6,  -3,  -21, -9,  -20, -4,  -11, -15, -10, -5,  -14, -2,  -22, -12, -16, -19, -8,  -7,  -17, -13, -23, 16,  6,   22,  12,  9,   21,  14,  3,   18,  10,  4,   13,  7,   15,  1,   11,  17,  0,   23,  5,   2,   19,  20,  8,
994:     -23, -1,  -9,  -19, -17, -6,  -22, -3,  -7,  -14, -11, -2,  -8,  -15, -13, -18, -5,  -4,  -21, -12, -16, -20, -10, -24, 17,  14,  20,  7,   10,  19,  1,   12,  23,  4,   9,   15,  3,   11,  6,   13,  0,   16,  8,   21,  22,  5,   2,   18,
995:     -6,  -20, -21, -1,  -9,  -18, -3,  -24, -11, -4,  -8,  -16, -7,  -13, -12, -23, -2,  -10, -17, -15, -5,  -19, -14, -22, 18,  4,   21,  13,  15,  22,  7,   10,  16,  3,   6,   12,  14,  9,   11,  1,   20,  5,   19,  0,   8,   23,  17,  2,
996:     -17, -9,  -1,  -22, -23, -3,  -19, -6,  -13, -5,  -2,  -11, -10, -16, -7,  -20, -14, -12, -24, -4,  -15, -18, -8,  -21, 19,  15,  23,  9,   1,   17,  10,  6,   20,  13,  7,   14,  11,  3,   12,  4,   8,   22,  0,   18,  16,  2,   5,   21,
997:     -22, -6,  -3,  -17, -19, -1,  -23, -9,  -5,  -13, -4,  -12, -15, -8,  -14, -21, -7,  -11, -18, -2,  -10, -24, -16, -20, 20,  7,   17,  14,  3,   23,  11,  13,  19,  6,   15,  9,   10,  1,   4,   12,  5,   18,  2,   22,  21,  0,   8,   16,
998:     -3,  -18, -24, -9,  -1,  -20, -6,  -21, -2,  -12, -10, -15, -13, -7,  -4,  -17, -11, -8,  -23, -16, -14, -22, -5,  -19, 21,  13,  18,  4,   14,  16,  9,   1,   22,  11,  12,  6,   15,  7,   3,   10,  23,  2,   17,  8,   0,   20,  19,  5,
999:     -9,  -21, -20, -3,  -6,  -24, -1,  -18, -12, -2,  -16, -8,  -14, -5,  -11, -19, -4,  -15, -22, -10, -13, -23, -7,  -17, 22,  12,  16,  6,   7,   18,  15,  11,  21,  1,   13,  4,   9,   14,  10,  3,   19,  8,   20,  2,   5,   17,  23,  0,
1000:     -19, -3,  -6,  -23, -22, -9,  -17, -1,  -14, -7,  -12, -4,  -16, -10, -5,  -24, -13, -2,  -20, -11, -8,  -21, -15, -18, 23,  9,   19,  15,  11,  20,  3,   4,   17,  12,  14,  7,   1,   10,  13,  6,   2,   21,  5,   16,  18,  8,   0,   22,
1001:   };
1002:   static const PetscInt tripMult[12 * 12] = {
1003:     1,  0,  2,  3,  5,  4,  -6, -4, -5, -2, -3, -1, 0,  2,  1,  4,  3,  5,  -5, -6, -4, -3, -1, -2, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 4,  3,  5,  0,  2,  1,  -3, -1, -2, -5, -6, -4,
1004:     3,  5,  4,  1,  0,  2,  -2, -3, -1, -6, -4, -5, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -4, -6, -5, -2, -1, -3, 1,  2,  0,  5,  3,  4,
1005:     -5, -4, -6, -1, -3, -2, 2,  0,  1,  4,  5,  3,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -1, -3, -2, -5, -4, -6, 4,  5,  3,  2,  0,  1,  -2, -1, -3, -4, -6, -5, 5,  3,  4,  1,  2,  0,
1006:   };
1007:   static const PetscInt ttriMult[12 * 12] = {
1008:     0,  2,  1,  3,  5,  4,  -6, -4, -5, -3, -1, -2, 1,  0,  2,  4,  3,  5,  -5, -6, -4, -2, -3, -1, 2,  1,  0,  5,  4,  3,  -4, -5, -6, -1, -2, -3, 3,  5,  4,  0,  2,  1,  -3, -1, -2, -6, -4, -5,
1009:     4,  3,  5,  1,  0,  2,  -2, -3, -1, -5, -6, -4, 5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  -5, -4, -6, -2, -1, -3, 1,  2,  0,  4,  5,  3,
1010:     -4, -6, -5, -1, -3, -2, 2,  0,  1,  5,  3,  4,  -3, -2, -1, -6, -5, -4, 3,  4,  5,  0,  1,  2,  -2, -1, -3, -5, -4, -6, 4,  5,  3,  1,  2,  0,  -1, -3, -2, -4, -6, -5, 5,  3,  4,  2,  0,  1,
1011:   };
1012:   static const PetscInt tquadMult[16 * 16] = {
1013:     0,  3,  2,  1,  4,  7,  6,  5,  -8, -5, -6, -7, -4, -1, -2, -3, 1,  0,  3,  2,  5,  4,  7,  6,  -7, -8, -5, -6, -3, -4, -1, -2, 2,  1,  0,  3,  6,  5,  4,  7,  -6, -7, -8, -5, -2, -3, -4, -1, 3, 2, 1, 0,
1014:     7,  6,  5,  4,  -5, -6, -7, -8, -1, -2, -3, -4, 4,  7,  6,  5,  0,  3,  2,  1,  -4, -1, -2, -3, -8, -5, -6, -7, 5,  4,  7,  6,  1,  0,  3,  2,  -3, -4, -1, -2, -7, -8, -5, -6, 6,  5,  4,  7,  2, 1, 0, 3,
1015:     -2, -3, -4, -1, -6, -7, -8, -5, 7,  6,  5,  4,  3,  2,  1,  0,  -1, -2, -3, -4, -5, -6, -7, -8, -8, -7, -6, -5, -4, -3, -2, -1, 0,  1,  2,  3,  4,  5,  6,  7,  -7, -6, -5, -8, -3, -2, -1, -4, 1, 2, 3, 0,
1016:     5,  6,  7,  4,  -6, -5, -8, -7, -2, -1, -4, -3, 2,  3,  0,  1,  6,  7,  4,  5,  -5, -8, -7, -6, -1, -4, -3, -2, 3,  0,  1,  2,  7,  4,  5,  6,  -4, -3, -2, -1, -8, -7, -6, -5, 4,  5,  6,  7,  0, 1, 2, 3,
1017:     -3, -2, -1, -4, -7, -6, -5, -8, 5,  6,  7,  4,  1,  2,  3,  0,  -2, -1, -4, -3, -6, -5, -8, -7, 6,  7,  4,  5,  2,  3,  0,  1,  -1, -4, -3, -2, -5, -8, -7, -6, 7,  4,  5,  6,  3,  0,  1,  2,
1018:   };
1019:   static const PetscInt pyrMult[8 * 8] = {
1020:     0, 3, 2, 1, -4, -1, -2, -3, 1, 0, 3, 2, -3, -4, -1, -2, 2, 1, 0, 3, -2, -3, -4, -1, 3, 2, 1, 0, -1, -2, -3, -4, -4, -3, -2, -1, 0, 1, 2, 3, -3, -2, -1, -4, 1, 2, 3, 0, -2, -1, -4, -3, 2, 3, 0, 1, -1, -4, -3, -2, 3, 0, 1, 2,
1021:   };
1022:   switch (ct) {
1023:   case DM_POLYTOPE_POINT:
1024:     return 0;
1025:   case DM_POLYTOPE_SEGMENT:
1026:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1027:     return segMult[(o1 + 1) * 2 + o2 + 1];
1028:   case DM_POLYTOPE_TRIANGLE:
1029:     return triMult[(o1 + 3) * 6 + o2 + 3];
1030:   case DM_POLYTOPE_QUADRILATERAL:
1031:     return quadMult[(o1 + 4) * 8 + o2 + 4];
1032:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1033:     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1034:   case DM_POLYTOPE_TETRAHEDRON:
1035:     return tetMult[(o1 + 12) * 24 + o2 + 12];
1036:   case DM_POLYTOPE_HEXAHEDRON:
1037:     return hexMult[(o1 + 24) * 48 + o2 + 24];
1038:   case DM_POLYTOPE_TRI_PRISM:
1039:     return tripMult[(o1 + 6) * 12 + o2 + 6];
1040:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1041:     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1042:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1043:     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1044:   case DM_POLYTOPE_PYRAMID:
1045:     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1046:   default:
1047:     return 0;
1048:   }
1049: }

1051: /* This is orientation o1 acting on orientation o2^{-1} */
1052: static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1053: {
1054:   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1055:   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1056:   static const PetscInt tetInv[24]   = {-9, -11, -4, -12, -5, -7, -6, -8, -10, -3, -2, -1, 0, 2, 1, 3, 8, 10, 6, 11, 4, 9, 5, 7};
1057:   static const PetscInt hexInv[48]   = {-17, -18, -20, -19, -22, -21, -23, -24, -15, -16, -14, -13, -11, -12, -10, -9, -8, -5, -6, -7, -4, -3, -2, -1, 0, 3, 2, 1, 6, 5, 4, 9, 8, 7, 10, 11, 12, 13, 14, 15, 17, 16, 19, 18, 21, 20, 23, 22};
1058:   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1059:   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1060:   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1061:   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1062:   switch (ct) {
1063:   case DM_POLYTOPE_POINT:
1064:     return 0;
1065:   case DM_POLYTOPE_SEGMENT:
1066:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1067:     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1068:   case DM_POLYTOPE_TRIANGLE:
1069:     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1070:   case DM_POLYTOPE_QUADRILATERAL:
1071:     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1072:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1073:     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1074:   case DM_POLYTOPE_TETRAHEDRON:
1075:     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1076:   case DM_POLYTOPE_HEXAHEDRON:
1077:     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1078:   case DM_POLYTOPE_TRI_PRISM:
1079:     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1080:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1081:     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1082:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1083:     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1084:   case DM_POLYTOPE_PYRAMID:
1085:     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1086:   default:
1087:     return 0;
1088:   }
1089: }

1091: PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1092: PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1093: PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1094: PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1095: PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);

1097: #endif