Actual source code: petscdm.h

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

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

 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 DMClearNamedGlobalVectors(DM);
 68: PETSC_EXTERN PetscErrorCode DMClearNamedLocalVectors(DM);
 69: PETSC_EXTERN PetscErrorCode DMHasNamedGlobalVector(DM, const char *, PetscBool *);
 70: PETSC_EXTERN PetscErrorCode DMGetNamedGlobalVector(DM, const char *, Vec *);
 71: PETSC_EXTERN PetscErrorCode DMRestoreNamedGlobalVector(DM, const char *, Vec *);
 72: PETSC_EXTERN PetscErrorCode DMHasNamedLocalVector(DM, const char *, PetscBool *);
 73: PETSC_EXTERN PetscErrorCode DMGetNamedLocalVector(DM, const char *, Vec *);
 74: PETSC_EXTERN PetscErrorCode DMRestoreNamedLocalVector(DM, const char *, Vec *);
 75: PETSC_EXTERN PetscErrorCode DMGetLocalToGlobalMapping(DM, ISLocalToGlobalMapping *);
 76: PETSC_EXTERN PetscErrorCode DMCreateFieldIS(DM, PetscInt *, char ***, IS **);
 77: PETSC_EXTERN PetscErrorCode DMGetBlockSize(DM, PetscInt *);
 78: PETSC_EXTERN PetscErrorCode DMCreateColoring(DM, ISColoringType, ISColoring *);
 79: PETSC_EXTERN PetscErrorCode DMCreateMatrix(DM, Mat *);
 80: PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateSkip(DM, PetscBool);
 81: PETSC_EXTERN PetscErrorCode DMSetMatrixPreallocateOnly(DM, PetscBool);
 82: PETSC_EXTERN PetscErrorCode DMSetMatrixStructureOnly(DM, PetscBool);
 83: PETSC_EXTERN PetscErrorCode DMSetBlockingType(DM, DMBlockingType);
 84: PETSC_EXTERN PetscErrorCode DMGetBlockingType(DM, DMBlockingType *);
 85: PETSC_EXTERN PetscErrorCode DMCreateInterpolation(DM, DM, Mat *, Vec *);
 86: PETSC_EXTERN PetscErrorCode DMCreateRestriction(DM, DM, Mat *);
 87: PETSC_EXTERN PetscErrorCode DMCreateInjection(DM, DM, Mat *);
 88: PETSC_EXTERN PetscErrorCode DMCreateMassMatrix(DM, DM, Mat *);
 89: PETSC_EXTERN PetscErrorCode DMCreateMassMatrixLumped(DM, Vec *);
 90: PETSC_EXTERN PetscErrorCode DMGetWorkArray(DM, PetscInt, MPI_Datatype, void *);
 91: PETSC_EXTERN PetscErrorCode DMRestoreWorkArray(DM, PetscInt, MPI_Datatype, void *);
 92: PETSC_EXTERN PetscErrorCode DMRefine(DM, MPI_Comm, DM *);
 93: PETSC_EXTERN PetscErrorCode DMCoarsen(DM, MPI_Comm, DM *);
 94: PETSC_EXTERN PetscErrorCode DMGetCoarseDM(DM, DM *);
 95: PETSC_EXTERN PetscErrorCode DMSetCoarseDM(DM, DM);
 96: PETSC_EXTERN PetscErrorCode DMGetFineDM(DM, DM *);
 97: PETSC_EXTERN PetscErrorCode DMSetFineDM(DM, DM);
 98: PETSC_EXTERN PetscErrorCode DMRefineHierarchy(DM, PetscInt, DM[]);
 99: PETSC_EXTERN PetscErrorCode DMCoarsenHierarchy(DM, PetscInt, DM[]);
100: PETSC_EXTERN PetscErrorCode DMCoarsenHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
101: PETSC_EXTERN PetscErrorCode DMCoarsenHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, Vec, Mat, DM, void *), void *);
102: PETSC_EXTERN PetscErrorCode DMRefineHookAdd(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
103: PETSC_EXTERN PetscErrorCode DMRefineHookRemove(DM, PetscErrorCode (*)(DM, DM, void *), PetscErrorCode (*)(DM, Mat, DM, void *), void *);
104: PETSC_EXTERN PetscErrorCode DMRestrict(DM, Mat, Vec, Mat, DM);
105: PETSC_EXTERN PetscErrorCode DMInterpolate(DM, Mat, DM);
106: PETSC_EXTERN PetscErrorCode DMInterpolateSolution(DM, DM, Mat, Vec, Vec);
107: PETSC_EXTERN PetscErrorCode DMExtrude(DM, PetscInt, DM *);
108: PETSC_EXTERN PetscErrorCode DMSetFromOptions(DM);
109: PETSC_EXTERN PetscErrorCode DMViewFromOptions(DM, PetscObject, const char[]);

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

118: PETSC_EXTERN PetscErrorCode DMSetUp(DM);
119: PETSC_EXTERN PetscErrorCode DMCreateInterpolationScale(DM, DM, Mat, Vec *);
120: PETSC_EXTERN PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMDACreateAggregates()", ) PetscErrorCode DMCreateAggregates(DM, DM, Mat *);
121: PETSC_EXTERN PetscErrorCode DMGlobalToLocalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
122: PETSC_EXTERN PetscErrorCode DMLocalToGlobalHookAdd(DM, PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), PetscErrorCode (*)(DM, Vec, InsertMode, Vec, void *), void *);
123: PETSC_EXTERN PetscErrorCode DMGlobalToLocal(DM, Vec, InsertMode, Vec);
124: PETSC_EXTERN PetscErrorCode DMGlobalToLocalBegin(DM, Vec, InsertMode, Vec);
125: PETSC_EXTERN PetscErrorCode DMGlobalToLocalEnd(DM, Vec, InsertMode, Vec);
126: PETSC_EXTERN PetscErrorCode DMLocalToGlobal(DM, Vec, InsertMode, Vec);
127: PETSC_EXTERN PetscErrorCode DMLocalToGlobalBegin(DM, Vec, InsertMode, Vec);
128: PETSC_EXTERN PetscErrorCode DMLocalToGlobalEnd(DM, Vec, InsertMode, Vec);
129: PETSC_EXTERN PetscErrorCode DMLocalToLocalBegin(DM, Vec, InsertMode, Vec);
130: PETSC_EXTERN PetscErrorCode DMLocalToLocalEnd(DM, Vec, InsertMode, Vec);
131: PETSC_EXTERN PetscErrorCode DMConvert(DM, DMType, DM *);

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

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

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

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

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

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

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

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

224: typedef struct NLF_DAAD *NLF;

226: #define DM_FILE_CLASSID 1211221

228: /* FEM support */
229: PETSC_EXTERN PetscErrorCode DMPrintCellIndices(PetscInt, const char[], PetscInt, const PetscInt[]);
230: PETSC_EXTERN PetscErrorCode DMPrintCellVector(PetscInt, const char[], PetscInt, const PetscScalar[]);
231: PETSC_EXTERN PetscErrorCode DMPrintCellVectorReal(PetscInt, const char[], PetscInt, const PetscReal[]);
232: PETSC_EXTERN PetscErrorCode DMPrintCellMatrix(PetscInt, const char[], PetscInt, PetscInt, const PetscScalar[]);
233: PETSC_EXTERN PetscErrorCode DMPrintLocalVec(DM, const char[], PetscReal, Vec);

235: PETSC_EXTERN PetscErrorCode DMSetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
236: PETSC_EXTERN PetscErrorCode DMGetNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));
237: PETSC_EXTERN PetscErrorCode DMSetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (*)(DM, PetscInt, PetscInt, MatNullSpace *));
238: PETSC_EXTERN PetscErrorCode DMGetNearNullSpaceConstructor(DM, PetscInt, PetscErrorCode (**)(DM, PetscInt, PetscInt, MatNullSpace *));

240: PETSC_EXTERN PetscErrorCode DMGetSection(DM, PetscSection *); /* Use DMGetLocalSection() in new code (since v3.12) */
241: PETSC_EXTERN PetscErrorCode DMSetSection(DM, PetscSection);   /* Use DMSetLocalSection() in new code (since v3.12) */
242: PETSC_EXTERN PetscErrorCode DMGetLocalSection(DM, PetscSection *);
243: PETSC_EXTERN PetscErrorCode DMSetLocalSection(DM, PetscSection);
244: PETSC_EXTERN PetscErrorCode DMGetGlobalSection(DM, PetscSection *);
245: PETSC_EXTERN PetscErrorCode DMSetGlobalSection(DM, PetscSection);
246: PETSC_EXTERN PetscErrorCode DMCreateSectionPermutation(DM, IS *, PetscBT *);
247: PETSC_EXTERN PetscErrorCode DMReorderSectionGetDefault(DM, DMReorderDefaultFlag *);
248: PETSC_EXTERN PetscErrorCode DMReorderSectionSetDefault(DM, DMReorderDefaultFlag);
249: PETSC_EXTERN PetscErrorCode DMReorderSectionGetType(DM, MatOrderingType *);
250: PETSC_EXTERN PetscErrorCode DMReorderSectionSetType(DM, MatOrderingType);
251: PETSC_EXTERN PetscErrorCode DMUseTensorOrder(DM, PetscBool);
252: static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetSection()", ) PetscErrorCode DMGetDefaultSection(DM dm, PetscSection *s)
253: {
254:   return DMGetSection(dm, s);
255: }
256: static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetSection()", ) PetscErrorCode DMSetDefaultSection(DM dm, PetscSection s)
257: {
258:   return DMSetSection(dm, s);
259: }
260: static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMGetGlobalSection()", ) PetscErrorCode DMGetDefaultGlobalSection(DM dm, PetscSection *s)
261: {
262:   return DMGetGlobalSection(dm, s);
263: }
264: static inline PETSC_DEPRECATED_FUNCTION(3, 9, 0, "DMSetGlobalSection()", ) PetscErrorCode DMSetDefaultGlobalSection(DM dm, PetscSection s)
265: {
266:   return DMSetGlobalSection(dm, s);
267: }

269: PETSC_EXTERN PetscErrorCode DMGetSectionSF(DM, PetscSF *);
270: PETSC_EXTERN PetscErrorCode DMSetSectionSF(DM, PetscSF);
271: PETSC_EXTERN PetscErrorCode DMCreateSectionSF(DM, PetscSection, PetscSection);
272: static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMGetSectionSF()", ) PetscErrorCode DMGetDefaultSF(DM dm, PetscSF *s)
273: {
274:   return DMGetSectionSF(dm, s);
275: }
276: static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMSetSectionSF()", ) PetscErrorCode DMSetDefaultSF(DM dm, PetscSF s)
277: {
278:   return DMSetSectionSF(dm, s);
279: }
280: static inline PETSC_DEPRECATED_FUNCTION(3, 12, 0, "DMCreateSectionSF()", ) PetscErrorCode DMCreateDefaultSF(DM dm, PetscSection l, PetscSection g)
281: {
282:   return DMCreateSectionSF(dm, l, g);
283: }
284: PETSC_EXTERN PetscErrorCode DMGetPointSF(DM, PetscSF *);
285: PETSC_EXTERN PetscErrorCode DMSetPointSF(DM, PetscSF);
286: PETSC_EXTERN PetscErrorCode DMGetNaturalSF(DM, PetscSF *);
287: PETSC_EXTERN PetscErrorCode DMSetNaturalSF(DM, PetscSF);

289: PETSC_EXTERN PetscErrorCode DMGetDefaultConstraints(DM, PetscSection *, Mat *, Vec *);
290: PETSC_EXTERN PetscErrorCode DMSetDefaultConstraints(DM, PetscSection, Mat, Vec);

292: PETSC_EXTERN PetscErrorCode DMGetOutputDM(DM, DM *);
293: PETSC_EXTERN PetscErrorCode DMGetOutputSequenceNumber(DM, PetscInt *, PetscReal *);
294: PETSC_EXTERN PetscErrorCode DMSetOutputSequenceNumber(DM, PetscInt, PetscReal);
295: PETSC_EXTERN PetscErrorCode DMOutputSequenceLoad(DM, PetscViewer, const char *, PetscInt, PetscReal *);

297: PETSC_EXTERN PetscErrorCode DMGetNumFields(DM, PetscInt *);
298: PETSC_EXTERN PetscErrorCode DMSetNumFields(DM, PetscInt);
299: PETSC_EXTERN PetscErrorCode DMGetField(DM, PetscInt, DMLabel *, PetscObject *);
300: PETSC_EXTERN PetscErrorCode DMSetField(DM, PetscInt, DMLabel, PetscObject);
301: PETSC_EXTERN PetscErrorCode DMAddField(DM, DMLabel, PetscObject);
302: PETSC_EXTERN PetscErrorCode DMSetFieldAvoidTensor(DM, PetscInt, PetscBool);
303: PETSC_EXTERN PetscErrorCode DMGetFieldAvoidTensor(DM, PetscInt, PetscBool *);
304: PETSC_EXTERN PetscErrorCode DMClearFields(DM);
305: PETSC_EXTERN PetscErrorCode DMCopyFields(DM, DM);
306: PETSC_EXTERN PetscErrorCode DMGetAdjacency(DM, PetscInt, PetscBool *, PetscBool *);
307: PETSC_EXTERN PetscErrorCode DMSetAdjacency(DM, PetscInt, PetscBool, PetscBool);
308: PETSC_EXTERN PetscErrorCode DMGetBasicAdjacency(DM, PetscBool *, PetscBool *);
309: PETSC_EXTERN PetscErrorCode DMSetBasicAdjacency(DM, PetscBool, PetscBool);

311: PETSC_EXTERN PetscErrorCode DMGetNumDS(DM, PetscInt *);
312: PETSC_EXTERN PetscErrorCode DMGetDS(DM, PetscDS *);
313: PETSC_EXTERN PetscErrorCode DMGetCellDS(DM, PetscInt, PetscDS *, PetscDS *);
314: PETSC_EXTERN PetscErrorCode DMGetRegionDS(DM, DMLabel, IS *, PetscDS *, PetscDS *);
315: PETSC_EXTERN PetscErrorCode DMSetRegionDS(DM, DMLabel, IS, PetscDS, PetscDS);
316: PETSC_EXTERN PetscErrorCode DMGetRegionNumDS(DM, PetscInt, DMLabel *, IS *, PetscDS *, PetscDS *);
317: PETSC_EXTERN PetscErrorCode DMSetRegionNumDS(DM, PetscInt, DMLabel, IS, PetscDS, PetscDS);
318: PETSC_EXTERN PetscErrorCode DMFindRegionNum(DM, PetscDS, PetscInt *);
319: PETSC_EXTERN PetscErrorCode DMCreateFEDefault(DM, PetscInt, const char[], PetscInt, PetscFE *);
320: PETSC_EXTERN PetscErrorCode DMCreateDS(DM);
321: PETSC_EXTERN PetscErrorCode DMClearDS(DM);
322: PETSC_EXTERN PetscErrorCode DMCopyDS(DM, DM);
323: PETSC_EXTERN PetscErrorCode DMCopyDisc(DM, DM);
324: PETSC_EXTERN PetscErrorCode DMComputeExactSolution(DM, PetscReal, Vec, Vec);
325: PETSC_EXTERN PetscErrorCode DMGetNumAuxiliaryVec(DM, PetscInt *);
326: PETSC_EXTERN PetscErrorCode DMGetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec *);
327: PETSC_EXTERN PetscErrorCode DMSetAuxiliaryVec(DM, DMLabel, PetscInt, PetscInt, Vec);
328: PETSC_EXTERN PetscErrorCode DMGetAuxiliaryLabels(DM, DMLabel[], PetscInt[], PetscInt[]);
329: PETSC_EXTERN PetscErrorCode DMCopyAuxiliaryVec(DM, DM);
330: PETSC_EXTERN PetscErrorCode DMClearAuxiliaryVec(DM);

332: /*MC
333:   DMInterpolationInfo - Structure for holding information about interpolation on a mesh

335:   Synopsis:
336:     comm   - The communicator
337:     dim    - The spatial dimension of points
338:     nInput - The number of input points
339:     points - The input point coordinates
340:     cells  - The cell containing each point
341:     n      - The number of local points
342:     coords - The point coordinates
343:     dof    - The number of components to interpolate

345:   Level: intermediate

347: .seealso: [](ch_dmbase), `DM`, `DMInterpolationCreate()`, `DMInterpolationEvaluate()`, `DMInterpolationAddPoints()`
348: M*/
349: struct _DMInterpolationInfo {
350:   MPI_Comm   comm;
351:   PetscInt   dim;    /*1 The spatial dimension of points */
352:   PetscInt   nInput; /* The number of input points */
353:   PetscReal *points; /* The input point coordinates */
354:   PetscInt  *cells;  /* The cell containing each point */
355:   PetscInt   n;      /* The number of local points */
356:   Vec        coords; /* The point coordinates */
357:   PetscInt   dof;    /* The number of components to interpolate */
358: };
359: typedef struct _DMInterpolationInfo *DMInterpolationInfo;

361: PETSC_EXTERN PetscErrorCode DMInterpolationCreate(MPI_Comm, DMInterpolationInfo *);
362: PETSC_EXTERN PetscErrorCode DMInterpolationSetDim(DMInterpolationInfo, PetscInt);
363: PETSC_EXTERN PetscErrorCode DMInterpolationGetDim(DMInterpolationInfo, PetscInt *);
364: PETSC_EXTERN PetscErrorCode DMInterpolationSetDof(DMInterpolationInfo, PetscInt);
365: PETSC_EXTERN PetscErrorCode DMInterpolationGetDof(DMInterpolationInfo, PetscInt *);
366: PETSC_EXTERN PetscErrorCode DMInterpolationAddPoints(DMInterpolationInfo, PetscInt, PetscReal[]);
367: PETSC_EXTERN PetscErrorCode DMInterpolationSetUp(DMInterpolationInfo, DM, PetscBool, PetscBool);
368: PETSC_EXTERN PetscErrorCode DMInterpolationGetCoordinates(DMInterpolationInfo, Vec *);
369: PETSC_EXTERN PetscErrorCode DMInterpolationGetVector(DMInterpolationInfo, Vec *);
370: PETSC_EXTERN PetscErrorCode DMInterpolationRestoreVector(DMInterpolationInfo, Vec *);
371: PETSC_EXTERN PetscErrorCode DMInterpolationEvaluate(DMInterpolationInfo, DM, Vec, Vec);
372: PETSC_EXTERN PetscErrorCode DMInterpolationDestroy(DMInterpolationInfo *);

374: PETSC_EXTERN PetscErrorCode DMCreateLabel(DM, const char[]);
375: PETSC_EXTERN PetscErrorCode DMCreateLabelAtIndex(DM, PetscInt, const char[]);
376: PETSC_EXTERN PetscErrorCode DMGetLabelValue(DM, const char[], PetscInt, PetscInt *);
377: PETSC_EXTERN PetscErrorCode DMSetLabelValue(DM, const char[], PetscInt, PetscInt);
378: PETSC_EXTERN PetscErrorCode DMClearLabelValue(DM, const char[], PetscInt, PetscInt);
379: PETSC_EXTERN PetscErrorCode DMGetLabelSize(DM, const char[], PetscInt *);
380: PETSC_EXTERN PetscErrorCode DMGetLabelIdIS(DM, const char[], IS *);
381: PETSC_EXTERN PetscErrorCode DMGetStratumSize(DM, const char[], PetscInt, PetscInt *);
382: PETSC_EXTERN PetscErrorCode DMGetStratumIS(DM, const char[], PetscInt, IS *);
383: PETSC_EXTERN PetscErrorCode DMSetStratumIS(DM, const char[], PetscInt, IS);
384: PETSC_EXTERN PetscErrorCode DMClearLabelStratum(DM, const char[], PetscInt);
385: PETSC_EXTERN PetscErrorCode DMGetLabelOutput(DM, const char[], PetscBool *);
386: PETSC_EXTERN PetscErrorCode DMSetLabelOutput(DM, const char[], PetscBool);
387: PETSC_EXTERN PetscErrorCode DMGetFirstLabeledPoint(DM, DM, DMLabel, PetscInt, const PetscInt *, PetscInt, PetscInt *, PetscDS *);

389: /*E
390:    DMCopyLabelsMode - Determines how `DMCopyLabels()` behaves when there is a `DMLabel` in the source and destination `DM`s with the same name

392:    Values:
393: +  `DM_COPY_LABELS_REPLACE` - replace label in destination by label from source
394: .  `DM_COPY_LABELS_KEEP`    - keep destination label
395: -  `DM_COPY_LABELS_FAIL`    - generate an error

397:    Level: advanced

399: .seealso: [](ch_dmbase), `DMLabel`, `DM`, `DMCompareLabels()`, `DMRemoveLabel()`
400: E*/
401: typedef enum {
402:   DM_COPY_LABELS_REPLACE,
403:   DM_COPY_LABELS_KEEP,
404:   DM_COPY_LABELS_FAIL
405: } DMCopyLabelsMode;
406: PETSC_EXTERN const char *const DMCopyLabelsModes[];

408: PETSC_EXTERN PetscErrorCode DMGetNumLabels(DM, PetscInt *);
409: PETSC_EXTERN PetscErrorCode DMGetLabelName(DM, PetscInt, const char **);
410: PETSC_EXTERN PetscErrorCode DMHasLabel(DM, const char[], PetscBool *);
411: PETSC_EXTERN PetscErrorCode DMGetLabel(DM, const char *, DMLabel *);
412: PETSC_EXTERN PetscErrorCode DMSetLabel(DM, DMLabel);
413: PETSC_EXTERN PetscErrorCode DMGetLabelByNum(DM, PetscInt, DMLabel *);
414: PETSC_EXTERN PetscErrorCode DMAddLabel(DM, DMLabel);
415: PETSC_EXTERN PetscErrorCode DMRemoveLabel(DM, const char[], DMLabel *);
416: PETSC_EXTERN PetscErrorCode DMRemoveLabelBySelf(DM, DMLabel *, PetscBool);
417: PETSC_EXTERN PetscErrorCode DMCopyLabels(DM, DM, PetscCopyMode, PetscBool, DMCopyLabelsMode emode);
418: PETSC_EXTERN PetscErrorCode DMCompareLabels(DM, DM, PetscBool *, char **);

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

423: PETSC_EXTERN PetscErrorCode DMProjectFunction(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
424: PETSC_EXTERN PetscErrorCode DMProjectFunctionLocal(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
425: PETSC_EXTERN PetscErrorCode DMProjectFunctionLabel(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
426: PETSC_EXTERN PetscErrorCode DMProjectFunctionLabelLocal(DM, PetscReal, DMLabel, PetscInt, const PetscInt[], PetscInt, const PetscInt[], PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, InsertMode, Vec);
427: 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);
428: 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);
429: 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);
430: 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);
431: PETSC_EXTERN PetscErrorCode DMComputeL2Diff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
432: PETSC_EXTERN PetscErrorCode DMComputeL2GradientDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, const PetscReal[], PetscReal *);
433: PETSC_EXTERN PetscErrorCode DMComputeL2FieldDiff(DM, PetscReal, PetscErrorCode (**)(PetscInt, PetscReal, const PetscReal[], PetscInt, PetscScalar *, void *), void **, Vec, PetscReal *);
434: PETSC_EXTERN PetscErrorCode DMComputeError(DM, Vec, PetscReal[], Vec *);
435: PETSC_EXTERN PetscErrorCode DMHasBasisTransform(DM, PetscBool *);
436: PETSC_EXTERN PetscErrorCode DMCopyTransform(DM, DM);

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

440: PETSC_EXTERN PetscErrorCode DMMonitorSet(DM, PetscErrorCode (*)(DM, void *), void *, PetscErrorCode (*)(void **));
441: PETSC_EXTERN PetscErrorCode DMMonitorCancel(DM);
442: PETSC_EXTERN PetscErrorCode DMMonitorSetFromOptions(DM, const char[], const char[], const char[], PetscErrorCode (*)(DM, void *), PetscErrorCode (*)(DM, PetscViewerAndFormat *), PetscBool *);
443: PETSC_EXTERN PetscErrorCode DMMonitor(DM);

445: static inline PetscBool DMPolytopeTypeIsHybrid(DMPolytopeType ct)
446: {
447:   switch (ct) {
448:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
449:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
450:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
451:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
452:     return PETSC_TRUE;
453:   default:
454:     return PETSC_FALSE;
455:   }
456: }

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

484: static inline PetscInt DMPolytopeTypeGetConeSize(DMPolytopeType ct)
485: {
486:   switch (ct) {
487:   case DM_POLYTOPE_POINT:
488:     return 0;
489:   case DM_POLYTOPE_SEGMENT:
490:     return 2;
491:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
492:     return 2;
493:   case DM_POLYTOPE_TRIANGLE:
494:     return 3;
495:   case DM_POLYTOPE_QUADRILATERAL:
496:     return 4;
497:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
498:     return 4;
499:   case DM_POLYTOPE_TETRAHEDRON:
500:     return 4;
501:   case DM_POLYTOPE_HEXAHEDRON:
502:     return 6;
503:   case DM_POLYTOPE_TRI_PRISM:
504:     return 5;
505:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
506:     return 5;
507:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
508:     return 6;
509:   case DM_POLYTOPE_PYRAMID:
510:     return 5;
511:   default:
512:     return -1;
513:   }
514: }

516: static inline PetscInt DMPolytopeTypeGetNumVertices(DMPolytopeType ct)
517: {
518:   switch (ct) {
519:   case DM_POLYTOPE_POINT:
520:     return 1;
521:   case DM_POLYTOPE_SEGMENT:
522:     return 2;
523:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
524:     return 2;
525:   case DM_POLYTOPE_TRIANGLE:
526:     return 3;
527:   case DM_POLYTOPE_QUADRILATERAL:
528:     return 4;
529:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
530:     return 4;
531:   case DM_POLYTOPE_TETRAHEDRON:
532:     return 4;
533:   case DM_POLYTOPE_HEXAHEDRON:
534:     return 8;
535:   case DM_POLYTOPE_TRI_PRISM:
536:     return 6;
537:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
538:     return 6;
539:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
540:     return 8;
541:   case DM_POLYTOPE_PYRAMID:
542:     return 5;
543:   default:
544:     return -1;
545:   }
546: }

548: static inline DMPolytopeType DMPolytopeTypeSimpleShape(PetscInt dim, PetscBool simplex)
549: {
550:   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)));
551: }

553: static inline PetscInt DMPolytopeTypeGetNumArrangements(DMPolytopeType ct)
554: {
555:   switch (ct) {
556:   case DM_POLYTOPE_POINT:
557:     return 1;
558:   case DM_POLYTOPE_SEGMENT:
559:     return 2;
560:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
561:     return 2;
562:   case DM_POLYTOPE_TRIANGLE:
563:     return 6;
564:   case DM_POLYTOPE_QUADRILATERAL:
565:     return 8;
566:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
567:     return 4;
568:   case DM_POLYTOPE_TETRAHEDRON:
569:     return 24;
570:   case DM_POLYTOPE_HEXAHEDRON:
571:     return 48;
572:   case DM_POLYTOPE_TRI_PRISM:
573:     return 12;
574:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
575:     return 12;
576:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
577:     return 16;
578:   case DM_POLYTOPE_PYRAMID:
579:     return 8;
580:   default:
581:     return -1;
582:   }
583: }

585: /* An arrangement is a face order combined with an orientation for each face */
586: static inline const PetscInt *DMPolytopeTypeGetArrangement(DMPolytopeType ct, PetscInt o)
587: {
588:   static const PetscInt pntArr[1 * 2] = {0, 0};
589:   /* a: swap */
590:   static const PetscInt segArr[2 * 2 * 2] = {1, 0, 0, 0, /* -1: a */
591:                                              0, 0, 1, 0,
592:                                              /*  0: e */};
593:   /* a: swap first two
594:      b: swap last two */
595:   static const PetscInt triArr[6 * 3 * 2] = {0, -1, 2, -1, 1, -1, /* -3: b */
596:                                              2, -1, 1, -1, 0, -1, /* -2: aba */
597:                                              1, -1, 0, -1, 2, -1, /* -1: a */
598:                                              0, 0,  1, 0,  2, 0,  /*  0: identity */
599:                                              1, 0,  2, 0,  0, 0,  /*  1: ba */
600:                                              2, 0,  0, 0,  1, 0,
601:                                              /*  2: ab */};
602:   /* a: forward cyclic permutation
603:      b: swap first and last pairs */
604:   static const PetscInt quadArr[8 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -4: b */
605:                                               0, -1, 3, -1, 2, -1, 1, -1, /* -3: b a^3 = a b */
606:                                               3, -1, 2, -1, 1, -1, 0, -1, /* -2: b a^2 = a^2 b */
607:                                               2, -1, 1, -1, 0, -1, 3, -1, /* -1: b a   = a^3 b */
608:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
609:                                               1, 0,  2, 0,  3, 0,  0, 0,  /*  1: a */
610:                                               2, 0,  3, 0,  0, 0,  1, 0,  /*  2: a^2 */
611:                                               3, 0,  0, 0,  1, 0,  2, 0,
612:                                               /*  3: a^3 */};
613:   /* r: rotate 180
614:      b: swap top and bottom segments */
615:   static const PetscInt tsegArr[4 * 4 * 2] = {1, -1, 0, -1, 3, -1, 2, -1, /* -2: r b */
616:                                               0, -1, 1, -1, 3, 0,  2, 0,  /* -1: r */
617:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*  0: identity */
618:                                               1, 0,  0, 0,  2, -1, 3, -1,
619:                                               /*  1: b */};
620:   /* https://en.wikiversity.org/wiki/Symmetric_group_S4 */
621:   static const PetscInt tetArr[24 * 4 * 2] = {3, -2, 2, -3, 0, -1, 1, -1, /* -12: (1324)   p22 */
622:                                               3, -1, 1, -3, 2, -1, 0, -1, /* -11: (14)     p21 */
623:                                               3, -3, 0, -3, 1, -1, 2, -1, /* -10: (1234)   p18 */
624:                                               2, -1, 3, -1, 1, -3, 0, -2, /*  -9: (1423)   p17 */
625:                                               2, -3, 0, -1, 3, -2, 1, -3, /*  -8: (1342)   p13 */
626:                                               2, -2, 1, -2, 0, -2, 3, -2, /*  -7: (24)     p14 */
627:                                               1, -2, 0, -2, 2, -2, 3, -1, /*  -6: (34)     p6  */
628:                                               1, -1, 3, -3, 0, -3, 2, -2, /*  -5: (1243)   p10 */
629:                                               1, -3, 2, -1, 3, -1, 0, -3, /*  -4: (1432)   p9  */
630:                                               0, -3, 1, -1, 3, -3, 2, -3, /*  -3: (12)     p1  */
631:                                               0, -2, 2, -2, 1, -2, 3, -3, /*  -2: (23)     p2  */
632:                                               0, -1, 3, -2, 2, -3, 1, -2, /*  -1: (13)     p5  */
633:                                               0, 0,  1, 0,  2, 0,  3, 0,  /*   0: ()       p0  */
634:                                               0, 1,  3, 1,  1, 2,  2, 0,  /*   1: (123)    p4  */
635:                                               0, 2,  2, 1,  3, 0,  1, 2,  /*   2: (132)    p3  */
636:                                               1, 2,  0, 1,  3, 1,  2, 2,  /*   3: (12)(34) p7  */
637:                                               1, 0,  2, 0,  0, 0,  3, 1,  /*   4: (243)    p8  */
638:                                               1, 1,  3, 2,  2, 2,  0, 0,  /*   5: (143)    p11 */
639:                                               2, 1,  3, 0,  0, 2,  1, 0,  /*   6: (13)(24) p16 */
640:                                               2, 2,  1, 1,  3, 2,  0, 2,  /*   7: (142)    p15 */
641:                                               2, 0,  0, 0,  1, 0,  3, 2,  /*   8: (234)    p12 */
642:                                               3, 2,  2, 2,  1, 1,  0, 1,  /*   9: (14)(23) p23 */
643:                                               3, 0,  0, 2,  2, 1,  1, 1,  /*  10: (134)    p19 */
644:                                               3, 1,  1, 2,  0, 1,  2, 1 /*  11: (124)    p20 */};
645:   /* Each rotation determines a permutation of the four diagonals, and this defines the isomorphism with S_4 */
646:   static const PetscInt hexArr[48 * 6 * 2] = {
647:     2, -3, 3, -2, 4, -2, 5, -3, 1, -3, 0, -1, /* -24: reflect bottom and use -3 on top */
648:     4, -2, 5, -2, 0, -1, 1, -4, 3, -2, 2, -3, /* -23: reflect bottom and use -3 on top */
649:     5, -3, 4, -1, 1, -2, 0, -3, 3, -4, 2, -1, /* -22: reflect bottom and use -3 on top */
650:     3, -1, 2, -4, 4, -4, 5, -1, 0, -4, 1, -4, /* -21: reflect bottom and use -3 on top */
651:     3, -3, 2, -2, 5, -1, 4, -4, 1, -1, 0, -3, /* -20: reflect bottom and use -3 on top */
652:     4, -4, 5, -4, 1, -4, 0, -1, 2, -4, 3, -1, /* -19: reflect bottom and use -3 on top */
653:     2, -1, 3, -4, 5, -3, 4, -2, 0, -2, 1, -2, /* -18: reflect bottom and use -3 on top */
654:     5, -1, 4, -3, 0, -3, 1, -2, 2, -2, 3, -3, /* -17: reflect bottom and use -3 on top */
655:     4, -3, 5, -1, 3, -2, 2, -4, 1, -4, 0, -4, /* -16: reflect bottom and use -3 on top */
656:     5, -4, 4, -4, 3, -4, 2, -2, 0, -3, 1, -1, /* -15: reflect bottom and use -3 on top */
657:     3, -4, 2, -1, 1, -1, 0, -4, 4, -4, 5, -4, /* -14: reflect bottom and use -3 on top */
658:     2, -2, 3, -3, 0, -2, 1, -3, 4, -2, 5, -2, /* -13: reflect bottom and use -3 on top */
659:     1, -3, 0, -1, 4, -1, 5, -4, 3, -1, 2, -4, /* -12: reflect bottom and use -3 on top */
660:     1, -1, 0, -3, 5, -4, 4, -1, 2, -1, 3, -4, /* -11: reflect bottom and use -3 on top */
661:     5, -2, 4, -2, 2, -2, 3, -4, 1, -2, 0, -2, /* -10: reflect bottom and use -3 on top */
662:     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, 5, -3, /*  -9: reflect bottom and use -3 on top */
663:     4, -1, 5, -3, 2, -4, 3, -2, 0, -1, 1, -3, /*  -8: reflect bottom and use -3 on top */
664:     3, -2, 2, -3, 0, -4, 1, -1, 5, -1, 4, -3, /*  -7: reflect bottom and use -3 on top */
665:     1, -4, 0, -4, 3, -1, 2, -1, 5, -4, 4, -4, /*  -6: reflect bottom and use -3 on top */
666:     2, -4, 3, -1, 1, -3, 0, -2, 5, -3, 4, -1, /*  -5: reflect bottom and use -3 on top */
667:     0, -4, 1, -4, 4, -3, 5, -2, 2, -3, 3, -2, /*  -4: reflect bottom and use -3 on top */
668:     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, 5, -1, /*  -3: reflect bottom and use -3 on top */
669:     0, -2, 1, -2, 5, -2, 4, -3, 3, -3, 2, -2, /*  -2: reflect bottom and use -3 on top */
670:     0, -1, 1, -3, 2, -3, 3, -3, 5, -2, 4, -2, /*  -1: reflect bottom and use -3 on top */
671:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*   0: identity */
672:     0, 1,  1, 3,  5, 3,  4, 0,  2, 0,  3, 1,  /*   1: 90  rotation about z */
673:     0, 2,  1, 2,  3, 0,  2, 0,  5, 3,  4, 1,  /*   2: 180 rotation about z */
674:     0, 3,  1, 1,  4, 0,  5, 3,  3, 0,  2, 1,  /*   3: 270 rotation about z */
675:     2, 3,  3, 2,  1, 0,  0, 3,  4, 3,  5, 1,  /*   4: 90  rotation about x */
676:     1, 3,  0, 1,  3, 2,  2, 2,  4, 2,  5, 2,  /*   5: 180 rotation about x */
677:     3, 1,  2, 0,  0, 1,  1, 2,  4, 1,  5, 3,  /*   6: 270 rotation about x */
678:     4, 0,  5, 0,  2, 1,  3, 3,  1, 1,  0, 3,  /*   7: 90  rotation about y */
679:     1, 1,  0, 3,  2, 2,  3, 2,  5, 1,  4, 3,  /*   8: 180 rotation about y */
680:     5, 1,  4, 3,  2, 3,  3, 1,  0, 0,  1, 0,  /*   9: 270 rotation about y */
681:     1, 0,  0, 0,  5, 1,  4, 2,  3, 2,  2, 3,  /*  10: 180 rotation about x+y */
682:     1, 2,  0, 2,  4, 2,  5, 1,  2, 2,  3, 3,  /*  11: 180 rotation about x-y */
683:     2, 1,  3, 0,  0, 3,  1, 0,  5, 0,  4, 0,  /*  12: 180 rotation about y+z */
684:     3, 3,  2, 2,  1, 2,  0, 1,  5, 2,  4, 2,  /*  13: 180 rotation about y-z */
685:     5, 3,  4, 1,  3, 1,  2, 3,  1, 3,  0, 1,  /*  14: 180 rotation about z+x */
686:     4, 2,  5, 2,  3, 3,  2, 1,  0, 2,  1, 2,  /*  15: 180 rotation about z-x */
687:     5, 0,  4, 0,  0, 0,  1, 3,  3, 1,  2, 0,  /*  16: 120 rotation about x+y+z (v0v6) */
688:     2, 0,  3, 1,  5, 0,  4, 3,  1, 0,  0, 0,  /*  17: 240 rotation about x+y+z (v0v6) */
689:     4, 3,  5, 1,  1, 1,  0, 2,  3, 3,  2, 2,  /*  18: 120 rotation about x+y-z (v4v2) */
690:     3, 2,  2, 3,  5, 2,  4, 1,  0, 1,  1, 3,  /*  19: 240 rotation about x+y-z (v4v2) */
691:     3, 0,  2, 1,  4, 1,  5, 2,  1, 2,  0, 2,  /*  20: 120 rotation about x-y+z (v1v5) */
692:     5, 2,  4, 2,  1, 3,  0, 0,  2, 3,  3, 2,  /*  21: 240 rotation about x-y+z (v1v5) */
693:     4, 1,  5, 3,  0, 2,  1, 1,  2, 1,  3, 0,  /*  22: 120 rotation about x-y-z (v7v3) */
694:     2, 2,  3, 3,  4, 3,  5, 0,  0, 3,  1, 1,  /*  23: 240 rotation about x-y-z (v7v3) */
695:   };
696:   static const PetscInt tripArr[12 * 5 * 2] = {
697:     1, -3, 0, -1, 3, -1, 4, -1, 2, -1, /* -6: reflect bottom and top */
698:     1, -1, 0, -3, 4, -1, 2, -1, 3, -1, /* -5: reflect bottom and top */
699:     1, -2, 0, -2, 2, -1, 3, -1, 4, -1, /* -4: reflect bottom and top */
700:     0, -3, 1, -1, 3, -3, 2, -3, 4, -3, /* -3: reflect bottom and top */
701:     0, -2, 1, -2, 4, -3, 3, -3, 2, -3, /* -2: reflect bottom and top */
702:     0, -1, 1, -3, 2, -3, 4, -3, 3, -3, /* -1: reflect bottom and top */
703:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
704:     0, 1,  1, 2,  4, 0,  2, 0,  3, 0,  /*  1: 120 rotation about z */
705:     0, 2,  1, 1,  3, 0,  4, 0,  2, 0,  /*  2: 240 rotation about z */
706:     1, 1,  0, 2,  2, 2,  4, 2,  3, 2,  /*  3: 180 rotation about y of 0 */
707:     1, 0,  0, 0,  4, 2,  3, 2,  2, 2,  /*  4: 180 rotation about y of 1 */
708:     1, 2,  0, 1,  3, 2,  2, 2,  4, 2,  /*  5: 180 rotation about y of 2 */
709:   };
710:   /* a: rotate 120 about z
711:      b: swap top and bottom segments
712:      r: reflect */
713:   static const PetscInt ttriArr[12 * 5 * 2] = {
714:     1, -3, 0, -3, 2, -2, 4, -2, 3, -2, /* -6: r b a^2 */
715:     1, -2, 0, -2, 4, -2, 3, -2, 2, -2, /* -5: r b a */
716:     1, -1, 0, -1, 3, -2, 2, -2, 4, -2, /* -4: r b */
717:     0, -3, 1, -3, 2, -1, 4, -1, 3, -1, /* -3: r a^2 */
718:     0, -2, 1, -2, 4, -1, 3, -1, 2, -1, /* -2: r a */
719:     0, -1, 1, -1, 3, -1, 2, -1, 4, -1, /* -1: r */
720:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
721:     0, 1,  1, 1,  3, 0,  4, 0,  2, 0,  /*  1: a */
722:     0, 2,  1, 2,  4, 0,  2, 0,  3, 0,  /*  2: a^2 */
723:     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  /*  3: b */
724:     1, 1,  0, 1,  3, 1,  4, 1,  2, 1,  /*  4: b a */
725:     1, 2,  0, 2,  4, 1,  2, 1,  3, 1,  /*  5: b a^2 */
726:   };
727:   /* a: rotate 90 about z
728:      b: swap top and bottom segments
729:      r: reflect */
730:   static const PetscInt tquadArr[16 * 6 * 2] = {
731:     1, -4, 0, -4, 3, -2, 2, -2, 5, -2, 4, -2, /* -8: r b a^3 */
732:     1, -3, 0, -3, 2, -2, 5, -2, 4, -2, 3, -2, /* -7: r b a^2 */
733:     1, -2, 0, -2, 5, -2, 4, -2, 3, -2, 2, -2, /* -6: r b a */
734:     1, -1, 0, -1, 4, -2, 3, -2, 2, -2, 5, -2, /* -5: r b */
735:     0, -4, 1, -4, 3, -1, 2, -1, 5, -1, 4, -1, /* -4: r a^3 */
736:     0, -3, 1, -3, 2, -1, 5, -1, 4, -1, 3, -1, /* -3: r a^2 */
737:     0, -2, 1, -2, 5, -1, 4, -1, 3, -1, 2, -1, /* -2: r a */
738:     0, -1, 1, -1, 4, -1, 3, -1, 2, -1, 5, -1, /* -1: r */
739:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  5, 0,  /*  0: identity */
740:     0, 1,  1, 1,  3, 0,  4, 0,  5, 0,  2, 0,  /*  1: a */
741:     0, 2,  1, 2,  4, 0,  5, 0,  2, 0,  3, 0,  /*  2: a^2 */
742:     0, 3,  1, 3,  5, 0,  2, 0,  3, 0,  4, 0,  /*  3: a^3 */
743:     1, 0,  0, 0,  2, 1,  3, 1,  4, 1,  5, 1,  /*  4: b */
744:     1, 1,  0, 1,  3, 1,  4, 1,  5, 1,  2, 1,  /*  5: b a */
745:     1, 2,  0, 2,  4, 1,  5, 1,  2, 1,  3, 1,  /*  6: b a^2 */
746:     1, 3,  0, 3,  5, 1,  2, 1,  3, 1,  4, 1,  /*  7: b a^3 */
747:   };
748:   static const PetscInt pyrArr[8 * 5 * 2] = {
749:     0, -4, 2, -3, 1, -3, 4, -3, 3, -3, /* -4: Reflect bottom face */
750:     0, -3, 3, -3, 2, -3, 1, -3, 4, -3, /* -3: Reflect bottom face */
751:     0, -2, 4, -3, 3, -3, 2, -3, 1, -3, /* -2: Reflect bottom face */
752:     0, -1, 1, -3, 4, -3, 3, -3, 2, -3, /* -1: Reflect bottom face */
753:     0, 0,  1, 0,  2, 0,  3, 0,  4, 0,  /*  0: identity */
754:     0, 1,  4, 0,  1, 0,  2, 0,  3, 0,  /*  1:  90 rotation about z */
755:     0, 2,  3, 0,  4, 0,  1, 0,  2, 0,  /*  2: 180 rotation about z */
756:     0, 3,  2, 0,  3, 0,  4, 0,  1, 0,  /*  3: 270 rotation about z */
757:   };
758:   switch (ct) {
759:   case DM_POLYTOPE_POINT:
760:     return pntArr;
761:   case DM_POLYTOPE_SEGMENT:
762:     return &segArr[(o + 1) * 2 * 2];
763:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
764:     return &segArr[(o + 1) * 2 * 2];
765:   case DM_POLYTOPE_TRIANGLE:
766:     return &triArr[(o + 3) * 3 * 2];
767:   case DM_POLYTOPE_QUADRILATERAL:
768:     return &quadArr[(o + 4) * 4 * 2];
769:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
770:     return &tsegArr[(o + 2) * 4 * 2];
771:   case DM_POLYTOPE_TETRAHEDRON:
772:     return &tetArr[(o + 12) * 4 * 2];
773:   case DM_POLYTOPE_HEXAHEDRON:
774:     return &hexArr[(o + 24) * 6 * 2];
775:   case DM_POLYTOPE_TRI_PRISM:
776:     return &tripArr[(o + 6) * 5 * 2];
777:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
778:     return &ttriArr[(o + 6) * 5 * 2];
779:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
780:     return &tquadArr[(o + 8) * 6 * 2];
781:   case DM_POLYTOPE_PYRAMID:
782:     return &pyrArr[(o + 4) * 5 * 2];
783:   default:
784:     return PETSC_NULLPTR;
785:   }
786: }

788: /* A vertex arrangement is a vertex order */
789: static inline const PetscInt *DMPolytopeTypeGetVertexArrangement(DMPolytopeType ct, PetscInt o)
790: {
791:   static const PetscInt pntVerts[1]      = {0};
792:   static const PetscInt segVerts[2 * 2]  = {1, 0, 0, 1};
793:   static const PetscInt triVerts[6 * 3]  = {1, 0, 2, 0, 2, 1, 2, 1, 0, 0, 1, 2, 1, 2, 0, 2, 0, 1};
794:   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};
795:   static const PetscInt tsegVerts[4 * 4] = {3, 2, 1, 0, 1, 0, 3, 2, 0, 1, 2, 3, 2, 3, 0, 1};
796:   static const PetscInt tetVerts[24 * 4] = {2, 3, 1, 0, /* -12: (1324)   p22 */
797:                                             3, 1, 2, 0, /* -11: (14)     p21 */
798:                                             1, 2, 3, 0, /* -10: (1234)   p18 */
799:                                             3, 2, 0, 1, /*  -9: (1423)   p17 */
800:                                             2, 0, 3, 1, /*  -8: (1342)   p13 */
801:                                             0, 3, 2, 1, /*  -7: (24)     p14 */
802:                                             0, 1, 3, 2, /*  -6: (34)     p6  */
803:                                             1, 3, 0, 2, /*  -5: (1243)   p10 */
804:                                             3, 0, 1, 2, /*  -4: (1432    p9  */
805:                                             1, 0, 2, 3, /*  -3: (12)     p1  */
806:                                             0, 2, 1, 3, /*  -2: (23)     p2  */
807:                                             2, 1, 0, 3, /*  -1: (13)     p5  */
808:                                             0, 1, 2, 3, /*   0: ()       p0  */
809:                                             1, 2, 0, 3, /*   1: (123)    p4  */
810:                                             2, 0, 1, 3, /*   2: (132)    p3  */
811:                                             1, 0, 3, 2, /*   3: (12)(34) p7  */
812:                                             0, 3, 1, 2, /*   4: (243)    p8  */
813:                                             3, 1, 0, 2, /*   5: (143)    p11 */
814:                                             2, 3, 0, 1, /*   6: (13)(24) p16 */
815:                                             3, 0, 2, 1, /*   7: (142)    p15 */
816:                                             0, 2, 3, 1, /*   8: (234)    p12 */
817:                                             3, 2, 1, 0, /*   9: (14)(23) p23 */
818:                                             2, 1, 3, 0, /*  10: (134)    p19 */
819:                                             1, 3, 2, 0 /*  11: (124)    p20 */};
820:   static const PetscInt hexVerts[48 * 8] = {
821:     3, 0, 4, 5, 2, 6, 7, 1, /* -24: reflected 23 */
822:     3, 5, 6, 2, 0, 1, 7, 4, /* -23: reflected 22 */
823:     4, 0, 1, 7, 5, 6, 2, 3, /* -22: reflected 21 */
824:     6, 7, 1, 2, 5, 3, 0, 4, /* -21: reflected 20 */
825:     1, 2, 6, 7, 0, 4, 5, 3, /* -20: reflected 19 */
826:     6, 2, 3, 5, 7, 4, 0, 1, /* -19: reflected 18 */
827:     4, 5, 3, 0, 7, 1, 2, 6, /* -18: reflected 17 */
828:     1, 7, 4, 0, 2, 3, 5, 6, /* -17: reflected 16 */
829:     2, 3, 5, 6, 1, 7, 4, 0, /* -16: reflected 15 */
830:     7, 4, 0, 1, 6, 2, 3, 5, /* -15: reflected 14 */
831:     7, 1, 2, 6, 4, 5, 3, 0, /* -14: reflected 13 */
832:     0, 4, 5, 3, 1, 2, 6, 7, /* -13: reflected 12 */
833:     5, 4, 7, 6, 3, 2, 1, 0, /* -12: reflected 11 */
834:     7, 6, 5, 4, 1, 0, 3, 2, /* -11: reflected 10 */
835:     0, 1, 7, 4, 3, 5, 6, 2, /* -10: reflected  9 */
836:     4, 7, 6, 5, 0, 3, 2, 1, /*  -9: reflected  8 */
837:     5, 6, 2, 3, 4, 0, 1, 7, /*  -8: reflected  7 */
838:     2, 6, 7, 1, 3, 0, 4, 5, /*  -7: reflected  6 */
839:     6, 5, 4, 7, 2, 1, 0, 3, /*  -6: reflected  5 */
840:     5, 3, 0, 4, 6, 7, 1, 2, /*  -5: reflected  4 */
841:     2, 1, 0, 3, 6, 5, 4, 7, /*  -4: reflected  3 */
842:     1, 0, 3, 2, 7, 6, 5, 4, /*  -3: reflected  2 */
843:     0, 3, 2, 1, 4, 7, 6, 5, /*  -2: reflected  1 */
844:     3, 2, 1, 0, 5, 4, 7, 6, /*  -1: reflected  0 */
845:     0, 1, 2, 3, 4, 5, 6, 7, /*   0: identity */
846:     1, 2, 3, 0, 7, 4, 5, 6, /*   1: 90  rotation about z */
847:     2, 3, 0, 1, 6, 7, 4, 5, /*   2: 180 rotation about z */
848:     3, 0, 1, 2, 5, 6, 7, 4, /*   3: 270 rotation about z */
849:     4, 0, 3, 5, 7, 6, 2, 1, /*   4: 90  rotation about x */
850:     7, 4, 5, 6, 1, 2, 3, 0, /*   5: 180 rotation about x */
851:     1, 7, 6, 2, 0, 3, 5, 4, /*   6: 270 rotation about x */
852:     3, 2, 6, 5, 0, 4, 7, 1, /*   7: 90  rotation about y */
853:     5, 6, 7, 4, 3, 0, 1, 2, /*   8: 180 rotation about y */
854:     4, 7, 1, 0, 5, 3, 2, 6, /*   9: 270 rotation about y */
855:     4, 5, 6, 7, 0, 1, 2, 3, /*  10: 180 rotation about x+y */
856:     6, 7, 4, 5, 2, 3, 0, 1, /*  11: 180 rotation about x-y */
857:     3, 5, 4, 0, 2, 1, 7, 6, /*  12: 180 rotation about y+z */
858:     6, 2, 1, 7, 5, 4, 0, 3, /*  13: 180 rotation about y-z */
859:     1, 0, 4, 7, 2, 6, 5, 3, /*  14: 180 rotation about z+x */
860:     6, 5, 3, 2, 7, 1, 0, 4, /*  15: 180 rotation about z-x */
861:     0, 4, 7, 1, 3, 2, 6, 5, /*  16: 120 rotation about x+y+z (v0v6) */
862:     0, 3, 5, 4, 1, 7, 6, 2, /*  17: 240 rotation about x+y+z (v0v6) */
863:     5, 3, 2, 6, 4, 7, 1, 0, /*  18: 120 rotation about x+y-z (v4v2) */
864:     7, 6, 2, 1, 4, 0, 3, 5, /*  19: 240 rotation about x+y-z (v4v2) */
865:     2, 1, 7, 6, 3, 5, 4, 0, /*  20: 120 rotation about x-y+z (v1v5) */
866:     7, 1, 0, 4, 6, 5, 3, 2, /*  21: 240 rotation about x-y+z (v1v5) */
867:     2, 6, 5, 3, 1, 0, 4, 7, /*  22: 120 rotation about x-y-z (v7v3) */
868:     5, 4, 0, 3, 6, 2, 1, 7, /*  23: 240 rotation about x-y-z (v7v3) */
869:   };
870:   static const PetscInt tripVerts[12 * 6] = {
871:     4, 3, 5, 2, 1, 0, /* -6: reflect bottom and top */
872:     5, 4, 3, 1, 0, 2, /* -5: reflect bottom and top */
873:     3, 5, 4, 0, 2, 1, /* -4: reflect bottom and top */
874:     1, 0, 2, 5, 4, 3, /* -3: reflect bottom and top */
875:     0, 2, 1, 3, 5, 4, /* -2: reflect bottom and top */
876:     2, 1, 0, 4, 3, 5, /* -1: reflect bottom and top */
877:     0, 1, 2, 3, 4, 5, /*  0: identity */
878:     1, 2, 0, 5, 3, 4, /*  1: 120 rotation about z */
879:     2, 0, 1, 4, 5, 3, /*  2: 240 rotation about z */
880:     4, 5, 3, 2, 0, 1, /*  3: 180 rotation about y of 0 */
881:     3, 4, 5, 0, 1, 2, /*  4: 180 rotation about y of 1 */
882:     5, 3, 4, 1, 2, 0, /*  5: 180 rotation about y of 2 */
883:   };
884:   static const PetscInt ttriVerts[12 * 6] = {
885:     4, 3, 5, 1, 0, 2, /* -6: r b a^2 */
886:     3, 5, 4, 0, 2, 1, /* -5: r b a */
887:     5, 4, 3, 2, 1, 0, /* -4: r b */
888:     1, 0, 2, 4, 3, 5, /* -3: r a^2 */
889:     0, 2, 1, 3, 5, 4, /* -2: r a */
890:     2, 1, 0, 5, 4, 3, /* -1: r */
891:     0, 1, 2, 3, 4, 5, /*  0: identity */
892:     1, 2, 0, 4, 5, 3, /*  1: a */
893:     2, 0, 1, 5, 3, 4, /*  2: a^2 */
894:     3, 4, 5, 0, 1, 2, /*  3: b */
895:     4, 5, 3, 1, 2, 0, /*  4: b a */
896:     5, 3, 4, 2, 0, 1, /*  5: b a^2 */
897:   };
898:   /* a: rotate 90 about z
899:      b: swap top and bottom segments
900:      r: reflect */
901:   static const PetscInt tquadVerts[16 * 8] = {
902:     6, 5, 4, 7, 2, 1, 0, 3, /* -8: r b a^3 */
903:     5, 4, 7, 6, 1, 0, 3, 2, /* -7: r b a^2 */
904:     4, 7, 6, 5, 0, 3, 2, 1, /* -6: r b a */
905:     7, 6, 5, 4, 3, 2, 1, 0, /* -5: r b */
906:     2, 1, 0, 3, 6, 5, 4, 7, /* -4: r a^3 */
907:     1, 0, 3, 2, 5, 4, 7, 6, /* -3: r a^2 */
908:     0, 3, 2, 1, 4, 7, 6, 5, /* -2: r a */
909:     3, 2, 1, 0, 7, 6, 5, 4, /* -1: r */
910:     0, 1, 2, 3, 4, 5, 6, 7, /*  0: identity */
911:     1, 2, 3, 0, 5, 6, 7, 4, /*  1: a */
912:     2, 3, 0, 1, 6, 7, 4, 5, /*  2: a^2 */
913:     3, 0, 1, 2, 7, 4, 5, 6, /*  3: a^3 */
914:     4, 5, 6, 7, 0, 1, 2, 3, /*  4: b */
915:     5, 6, 7, 4, 1, 2, 3, 0, /*  5: b a */
916:     6, 7, 4, 5, 2, 3, 0, 1, /*  6: b a^2 */
917:     7, 4, 5, 6, 3, 0, 1, 2, /*  7: b a^3 */
918:   };
919:   static const PetscInt pyrVerts[8 * 5] = {
920:     2, 1, 0, 3, 4, /* -4: Reflect bottom face */
921:     1, 0, 3, 2, 4, /* -3: Reflect bottom face */
922:     0, 3, 2, 1, 4, /* -2: Reflect bottom face */
923:     3, 2, 1, 0, 4, /* -1: Reflect bottom face */
924:     0, 1, 2, 3, 4, /*  0: identity */
925:     1, 2, 3, 0, 4, /*  1:  90 rotation about z */
926:     2, 3, 0, 1, 4, /*  2: 180 rotation about z */
927:     3, 0, 1, 2, 4, /*  3: 270 rotation about z */
928:   };
929:   switch (ct) {
930:   case DM_POLYTOPE_POINT:
931:     return pntVerts;
932:   case DM_POLYTOPE_SEGMENT:
933:     return &segVerts[(o + 1) * 2];
934:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
935:     return &segVerts[(o + 1) * 2];
936:   case DM_POLYTOPE_TRIANGLE:
937:     return &triVerts[(o + 3) * 3];
938:   case DM_POLYTOPE_QUADRILATERAL:
939:     return &quadVerts[(o + 4) * 4];
940:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
941:     return &tsegVerts[(o + 2) * 4];
942:   case DM_POLYTOPE_TETRAHEDRON:
943:     return &tetVerts[(o + 12) * 4];
944:   case DM_POLYTOPE_HEXAHEDRON:
945:     return &hexVerts[(o + 24) * 8];
946:   case DM_POLYTOPE_TRI_PRISM:
947:     return &tripVerts[(o + 6) * 6];
948:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
949:     return &ttriVerts[(o + 6) * 6];
950:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
951:     return &tquadVerts[(o + 8) * 8];
952:   case DM_POLYTOPE_PYRAMID:
953:     return &pyrVerts[(o + 4) * 5];
954:   default:
955:     return PETSC_NULLPTR;
956:   }
957: }

959: /* This is orientation o1 acting on orientation o2 */
960: static inline PetscInt DMPolytopeTypeComposeOrientation(DMPolytopeType ct, PetscInt o1, PetscInt o2)
961: {
962:   static const PetscInt segMult[2 * 2]   = {0, -1, -1, 0};
963:   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};
964:   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,
965:                                             -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};
966:   static const PetscInt tsegMult[4 * 4]  = {0, 1, -2, -1, 1, 0, -1, -2, -2, -1, 0, 1, -1, -2, 1, 0};
967:   static const PetscInt tetMult[24 * 24] = {
968:     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,
969:     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,
970:     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,
971:     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,
972:     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,
973:     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,
974:     -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,
975:     -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,
976:     -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,
977:     -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,
978:     -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,
979:     -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,
980:   };
981:   static const PetscInt hexMult[48 * 48] = {
982:     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,
983:     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,
984:     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,
985:     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,
986:     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,
987:     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,
988:     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,
989:     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,
990:     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,
991:     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,
992:     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,
993:     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,
994:     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,
995:     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,
996:     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,
997:     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,
998:     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,
999:     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,
1000:     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,
1001:     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,
1002:     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,
1003:     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,
1004:     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,
1005:     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,
1006:     -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,
1007:     -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,
1008:     -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,
1009:     -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,
1010:     -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,
1011:     -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,
1012:     -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,
1013:     -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,
1014:     -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,
1015:     -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,
1016:     -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,
1017:     -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,
1018:     -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,
1019:     -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,
1020:     -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,
1021:     -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,
1022:     -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,
1023:     -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,
1024:     -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,
1025:     -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,
1026:     -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,
1027:     -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,
1028:     -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,
1029:     -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,
1030:   };
1031:   static const PetscInt tripMult[12 * 12] = {
1032:     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,
1033:     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,
1034:     -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,
1035:   };
1036:   static const PetscInt ttriMult[12 * 12] = {
1037:     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,
1038:     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,
1039:     -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,
1040:   };
1041:   static const PetscInt tquadMult[16 * 16] = {
1042:     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,
1043:     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,
1044:     -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,
1045:     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,
1046:     -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,
1047:   };
1048:   static const PetscInt pyrMult[8 * 8] = {
1049:     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,
1050:   };
1051:   switch (ct) {
1052:   case DM_POLYTOPE_POINT:
1053:     return 0;
1054:   case DM_POLYTOPE_SEGMENT:
1055:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1056:     return segMult[(o1 + 1) * 2 + o2 + 1];
1057:   case DM_POLYTOPE_TRIANGLE:
1058:     return triMult[(o1 + 3) * 6 + o2 + 3];
1059:   case DM_POLYTOPE_QUADRILATERAL:
1060:     return quadMult[(o1 + 4) * 8 + o2 + 4];
1061:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1062:     return tsegMult[(o1 + 2) * 4 + o2 + 2];
1063:   case DM_POLYTOPE_TETRAHEDRON:
1064:     return tetMult[(o1 + 12) * 24 + o2 + 12];
1065:   case DM_POLYTOPE_HEXAHEDRON:
1066:     return hexMult[(o1 + 24) * 48 + o2 + 24];
1067:   case DM_POLYTOPE_TRI_PRISM:
1068:     return tripMult[(o1 + 6) * 12 + o2 + 6];
1069:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1070:     return ttriMult[(o1 + 6) * 12 + o2 + 6];
1071:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1072:     return tquadMult[(o1 + 8) * 16 + o2 + 8];
1073:   case DM_POLYTOPE_PYRAMID:
1074:     return pyrMult[(o1 + 4) * 8 + o2 + 4];
1075:   default:
1076:     return 0;
1077:   }
1078: }

1080: /* This is orientation o1 acting on orientation o2^{-1} */
1081: static inline PetscInt DMPolytopeTypeComposeOrientationInv(DMPolytopeType ct, PetscInt o1, PetscInt o2)
1082: {
1083:   static const PetscInt triInv[6]    = {-3, -2, -1, 0, 2, 1};
1084:   static const PetscInt quadInv[8]   = {-4, -3, -2, -1, 0, 3, 2, 1};
1085:   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};
1086:   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};
1087:   static const PetscInt tripInv[12]  = {-5, -6, -4, -3, -2, -1, 0, 2, 1, 3, 4, 5};
1088:   static const PetscInt ttriInv[12]  = {-6, -5, -4, -3, -2, -1, 0, 2, 1, 3, 5, 4};
1089:   static const PetscInt tquadInv[16] = {-8, -7, -6, -5, -4, -3, -2, -1, 0, 3, 2, 1, 4, 7, 6, 5};
1090:   static const PetscInt pyrInv[8]    = {-4, -3, -2, -1, 0, 3, 2, 1};
1091:   switch (ct) {
1092:   case DM_POLYTOPE_POINT:
1093:     return 0;
1094:   case DM_POLYTOPE_SEGMENT:
1095:   case DM_POLYTOPE_POINT_PRISM_TENSOR:
1096:     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1097:   case DM_POLYTOPE_TRIANGLE:
1098:     return DMPolytopeTypeComposeOrientation(ct, o1, triInv[o2 + 3]);
1099:   case DM_POLYTOPE_QUADRILATERAL:
1100:     return DMPolytopeTypeComposeOrientation(ct, o1, quadInv[o2 + 4]);
1101:   case DM_POLYTOPE_SEG_PRISM_TENSOR:
1102:     return DMPolytopeTypeComposeOrientation(ct, o1, o2);
1103:   case DM_POLYTOPE_TETRAHEDRON:
1104:     return DMPolytopeTypeComposeOrientation(ct, o1, tetInv[o2 + 12]);
1105:   case DM_POLYTOPE_HEXAHEDRON:
1106:     return DMPolytopeTypeComposeOrientation(ct, o1, hexInv[o2 + 24]);
1107:   case DM_POLYTOPE_TRI_PRISM:
1108:     return DMPolytopeTypeComposeOrientation(ct, o1, tripInv[o2 + 6]);
1109:   case DM_POLYTOPE_TRI_PRISM_TENSOR:
1110:     return DMPolytopeTypeComposeOrientation(ct, o1, ttriInv[o2 + 6]);
1111:   case DM_POLYTOPE_QUAD_PRISM_TENSOR:
1112:     return DMPolytopeTypeComposeOrientation(ct, o1, tquadInv[o2 + 8]);
1113:   case DM_POLYTOPE_PYRAMID:
1114:     return DMPolytopeTypeComposeOrientation(ct, o1, pyrInv[o2 + 4]);
1115:   default:
1116:     return 0;
1117:   }
1118: }

1120: PETSC_EXTERN PetscErrorCode DMPolytopeMatchOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1121: PETSC_EXTERN PetscErrorCode DMPolytopeMatchVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *, PetscBool *);
1122: PETSC_EXTERN PetscErrorCode DMPolytopeGetOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1123: PETSC_EXTERN PetscErrorCode DMPolytopeGetVertexOrientation(DMPolytopeType, const PetscInt[], const PetscInt[], PetscInt *);
1124: PETSC_EXTERN PetscErrorCode DMPolytopeInCellTest(DMPolytopeType, const PetscReal[], PetscBool *);