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/usr/lib/petscdir/3.1/include/petscao.h is in libpetsc3.1-dev 3.1.dfsg-11ubuntu1.

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/* 
  An application ordering is mapping between an application-centric
  ordering (the ordering that is "natural" for the application) and 
  the parallel ordering that PETSc uses.
*/
#if !defined(__PETSCAO_H)
#define __PETSCAO_H
#include "petscis.h"
#include "petscmat.h"
PETSC_EXTERN_CXX_BEGIN

typedef enum {AO_BASIC=0, AO_ADVANCED=1, AO_MAPPING=2} AOType;

/*S
     AO - Abstract PETSc object that manages mapping between different global numbering

   Level: intermediate

  Concepts: global numbering

.seealso:  AOCreateBasic(), AOCreateBasicIS(), AOPetscToApplication(), AOView(), AOApplicationToPetsc()
S*/
typedef struct _p_AO* AO;

/* Logging support */
extern PetscCookie PETSCDM_DLLEXPORT AO_COOKIE;

EXTERN PetscErrorCode PETSCDM_DLLEXPORT DMInitializePackage(const char[]);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOCreateBasic(MPI_Comm,PetscInt,const PetscInt[],const PetscInt[],AO*);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOCreateBasicIS(IS,IS,AO*);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOCreateMapping(MPI_Comm,PetscInt,const PetscInt[],const PetscInt[],AO*);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOCreateMappingIS(IS,IS,AO*);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOView(AO,PetscViewer);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AODestroy(AO);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AORegister(const char [], const char [], const char [], PetscErrorCode (*)(AO));
#if defined(PETSC_USE_DYNAMIC_LIBRARIES)
#define AORegisterDynamic(a,b,c,d) AORegister(a,b,c,0)
#else
#define AORegisterDynamic(a,b,c,d) AORegister(a,b,c,d)
#endif

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOPetscToApplication(AO,PetscInt,PetscInt[]);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOApplicationToPetsc(AO,PetscInt,PetscInt[]);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOPetscToApplicationIS(AO,IS);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOApplicationToPetscIS(AO,IS);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOPetscToApplicationPermuteInt(AO, PetscInt, PetscInt[]);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOApplicationToPetscPermuteInt(AO, PetscInt, PetscInt[]);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOPetscToApplicationPermuteReal(AO, PetscInt, PetscReal[]);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOApplicationToPetscPermuteReal(AO, PetscInt, PetscReal[]);

EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOMappingHasApplicationIndex(AO, PetscInt, PetscTruth *);
EXTERN PetscErrorCode PETSCDM_DLLEXPORT AOMappingHasPetscIndex(AO, PetscInt, PetscTruth *);

/* ----------------------------------------------------*/
PETSC_EXTERN_CXX_END
#endif