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petsc / include / petsc-private / matimpl.h

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#ifndef __MATIMPL_H
#define __MATIMPL_H

#include <petscmat.h>
#include <petsc-private/petscimpl.h>

/*
  This file defines the parts of the matrix data structure that are
  shared by all matrix types.
*/

/*
    If you add entries here also add them to the MATOP enum
    in include/petscmat.h and include/finclude/petscmat.h
*/
typedef struct _MatOps *MatOps;
struct _MatOps {
  /* 0*/
  PetscErrorCode (*setvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
  PetscErrorCode (*getrow)(Mat,PetscInt,PetscInt *,PetscInt*[],PetscScalar*[]);
  PetscErrorCode (*restorerow)(Mat,PetscInt,PetscInt *,PetscInt *[],PetscScalar *[]);
  PetscErrorCode (*mult)(Mat,Vec,Vec);
  PetscErrorCode (*multadd)(Mat,Vec,Vec,Vec);
  /* 5*/
  PetscErrorCode (*multtranspose)(Mat,Vec,Vec);
  PetscErrorCode (*multtransposeadd)(Mat,Vec,Vec,Vec);
  PetscErrorCode (*solve)(Mat,Vec,Vec);
  PetscErrorCode (*solveadd)(Mat,Vec,Vec,Vec);
  PetscErrorCode (*solvetranspose)(Mat,Vec,Vec);
  /*10*/
  PetscErrorCode (*solvetransposeadd)(Mat,Vec,Vec,Vec);
  PetscErrorCode (*lufactor)(Mat,IS,IS,const MatFactorInfo*);
  PetscErrorCode (*choleskyfactor)(Mat,IS,const MatFactorInfo*);
  PetscErrorCode (*sor)(Mat,Vec,PetscReal,MatSORType,PetscReal,PetscInt,PetscInt,Vec);
  PetscErrorCode (*transpose)(Mat,MatReuse,Mat *);
  /*15*/
  PetscErrorCode (*getinfo)(Mat,MatInfoType,MatInfo*);
  PetscErrorCode (*equal)(Mat,Mat,PetscBool  *);
  PetscErrorCode (*getdiagonal)(Mat,Vec);
  PetscErrorCode (*diagonalscale)(Mat,Vec,Vec);
  PetscErrorCode (*norm)(Mat,NormType,PetscReal*);
  /*20*/
  PetscErrorCode (*assemblybegin)(Mat,MatAssemblyType);
  PetscErrorCode (*assemblyend)(Mat,MatAssemblyType);
  PetscErrorCode (*setoption)(Mat,MatOption,PetscBool );
  PetscErrorCode (*zeroentries)(Mat);
  /*24*/
  PetscErrorCode (*zerorows)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
  PetscErrorCode (*lufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
  PetscErrorCode (*lufactornumeric)(Mat,Mat,const MatFactorInfo*);
  PetscErrorCode (*choleskyfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
  PetscErrorCode (*choleskyfactornumeric)(Mat,Mat,const MatFactorInfo*);
  /*29*/
  PetscErrorCode (*setup)(Mat);
  PetscErrorCode (*ilufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
  PetscErrorCode (*iccfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
  PetscErrorCode (*placeholder_32)(Mat);
  PetscErrorCode (*placeholder_33)(Mat);
  /*34*/
  PetscErrorCode (*duplicate)(Mat,MatDuplicateOption,Mat*);
  PetscErrorCode (*forwardsolve)(Mat,Vec,Vec);
  PetscErrorCode (*backwardsolve)(Mat,Vec,Vec);
  PetscErrorCode (*ilufactor)(Mat,IS,IS,const MatFactorInfo*);
  PetscErrorCode (*iccfactor)(Mat,IS,const MatFactorInfo*);
  /*39*/
  PetscErrorCode (*axpy)(Mat,PetscScalar,Mat,MatStructure);
  PetscErrorCode (*getsubmatrices)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat *[]);
  PetscErrorCode (*increaseoverlap)(Mat,PetscInt,IS[],PetscInt);
  PetscErrorCode (*getvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],PetscScalar []);
  PetscErrorCode (*copy)(Mat,Mat,MatStructure);
  /*44*/
  PetscErrorCode (*getrowmax)(Mat,Vec,PetscInt[]);
  PetscErrorCode (*scale)(Mat,PetscScalar);
  PetscErrorCode (*shift)(Mat,PetscScalar);
  PetscErrorCode (*diagonalset)(Mat,Vec,InsertMode);
  PetscErrorCode (*zerorowscolumns)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
  /*49*/
  PetscErrorCode (*setrandom)(Mat,PetscRandom);
  PetscErrorCode (*getrowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
  PetscErrorCode (*restorerowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt *,const PetscInt *[],const PetscInt *[],PetscBool  *);
  PetscErrorCode (*getcolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
  PetscErrorCode (*restorecolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
  /*54*/
  PetscErrorCode (*fdcoloringcreate)(Mat,ISColoring,MatFDColoring);
  PetscErrorCode (*coloringpatch)(Mat,PetscInt,PetscInt,ISColoringValue[],ISColoring*);
  PetscErrorCode (*setunfactored)(Mat);
  PetscErrorCode (*permute)(Mat,IS,IS,Mat*);
  PetscErrorCode (*setvaluesblocked)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
  /*59*/
  PetscErrorCode (*getsubmatrix)(Mat,IS,IS,MatReuse,Mat*);
  PetscErrorCode (*destroy)(Mat);
  PetscErrorCode (*view)(Mat,PetscViewer);
  PetscErrorCode (*convertfrom)(Mat, MatType,MatReuse,Mat*);
  PetscErrorCode (*matmatmult)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
  /*64*/
  PetscErrorCode (*matmatmultsymbolic)(Mat,Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*matmatmultnumeric)(Mat,Mat,Mat,Mat);
  PetscErrorCode (*setlocaltoglobalmapping)(Mat,ISLocalToGlobalMapping,ISLocalToGlobalMapping);
  PetscErrorCode (*setvalueslocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
  PetscErrorCode (*zerorowslocal)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
  /*69*/
  PetscErrorCode (*getrowmaxabs)(Mat,Vec,PetscInt[]);
  PetscErrorCode (*getrowminabs)(Mat,Vec,PetscInt[]);
  PetscErrorCode (*convert)(Mat, MatType,MatReuse,Mat*);
  PetscErrorCode (*setcoloring)(Mat,ISColoring);
  PetscErrorCode (*placeholder_73)(Mat,void*);
  /*74*/
  PetscErrorCode (*setvaluesadifor)(Mat,PetscInt,void*);
  PetscErrorCode (*fdcoloringapply)(Mat,MatFDColoring,Vec,MatStructure*,void*);
  PetscErrorCode (*setfromoptions)(Mat);
  PetscErrorCode (*multconstrained)(Mat,Vec,Vec);
  PetscErrorCode (*multtransposeconstrained)(Mat,Vec,Vec);
  /*79*/
  PetscErrorCode (*findzerodiagonals)(Mat,IS*);
  PetscErrorCode (*mults)(Mat, Vecs, Vecs);
  PetscErrorCode (*solves)(Mat, Vecs, Vecs);
  PetscErrorCode (*getinertia)(Mat,PetscInt*,PetscInt*,PetscInt*);
  PetscErrorCode (*load)(Mat, PetscViewer);
  /*84*/
  PetscErrorCode (*issymmetric)(Mat,PetscReal,PetscBool *);
  PetscErrorCode (*ishermitian)(Mat,PetscReal,PetscBool *);
  PetscErrorCode (*isstructurallysymmetric)(Mat,PetscBool *);
  PetscErrorCode (*setvaluesblockedlocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
  PetscErrorCode (*getvecs)(Mat,Vec*,Vec*);
  /*89*/
  PetscErrorCode (*matmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*matmultsymbolic)(Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*matmultnumeric)(Mat,Mat,Mat);
  PetscErrorCode (*ptap)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*ptapsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
  /*94*/
  PetscErrorCode (*ptapnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
  PetscErrorCode (*mattransposemult)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*mattransposemultsymbolic)(Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*mattransposemultnumeric)(Mat,Mat,Mat);
  PetscErrorCode (*placeholder_98)(Mat);
  /*99*/
  PetscErrorCode (*placeholder_99)(Mat);
  PetscErrorCode (*placeholder_100)(Mat);
  PetscErrorCode (*placeholder_101)(Mat);
  PetscErrorCode (*conjugate)(Mat);                              /* complex conjugate */
  PetscErrorCode (*placeholder_103)(void);
  /*104*/
  PetscErrorCode (*setvaluesrow)(Mat,PetscInt,const PetscScalar[]);
  PetscErrorCode (*realpart)(Mat);
  PetscErrorCode (*imaginarypart)(Mat);
  PetscErrorCode (*getrowuppertriangular)(Mat);
  PetscErrorCode (*restorerowuppertriangular)(Mat);
  /*109*/
  PetscErrorCode (*matsolve)(Mat,Mat,Mat);
  PetscErrorCode (*getredundantmatrix)(Mat,PetscInt,MPI_Comm,MatReuse,Mat*);
  PetscErrorCode (*getrowmin)(Mat,Vec,PetscInt[]);
  PetscErrorCode (*getcolumnvector)(Mat,Vec,PetscInt);
  PetscErrorCode (*missingdiagonal)(Mat,PetscBool *,PetscInt*);
  /*114*/
  PetscErrorCode (*getseqnonzerostructure)(Mat,Mat *);
  PetscErrorCode (*create)(Mat);
  PetscErrorCode (*getghosts)(Mat,PetscInt*,const PetscInt *[]);
  PetscErrorCode (*getlocalsubmatrix)(Mat,IS,IS,Mat*);
  PetscErrorCode (*restorelocalsubmatrix)(Mat,IS,IS,Mat*);
  /*119*/
  PetscErrorCode (*multdiagonalblock)(Mat,Vec,Vec);
  PetscErrorCode (*hermitiantranspose)(Mat,MatReuse,Mat*);
  PetscErrorCode (*multhermitiantranspose)(Mat,Vec,Vec);
  PetscErrorCode (*multhermitiantransposeadd)(Mat,Vec,Vec,Vec);
  PetscErrorCode (*getmultiprocblock)(Mat,MPI_Comm,MatReuse,Mat*);
  /*124*/
  PetscErrorCode (*findnonzerorows)(Mat,IS*);
  PetscErrorCode (*getcolumnnorms)(Mat,NormType,PetscReal*);
  PetscErrorCode (*invertblockdiagonal)(Mat,const PetscScalar**);
  PetscErrorCode (*placeholder_127)(Mat,Vec,Vec,Vec);
  PetscErrorCode (*getsubmatricesparallel)(Mat,PetscInt,const IS[], const IS[], MatReuse, Mat**);
  /*129*/
  PetscErrorCode (*setvaluesbatch)(Mat,PetscInt,PetscInt,PetscInt*,const PetscScalar*);
  PetscErrorCode (*transposematmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*transposematmultsymbolic)(Mat,Mat,PetscReal,Mat*);
  PetscErrorCode (*transposematmultnumeric)(Mat,Mat,Mat);
  PetscErrorCode (*transposecoloringcreate)(Mat,ISColoring,MatTransposeColoring);
  /*134*/
  PetscErrorCode (*transcoloringapplysptoden)(MatTransposeColoring,Mat,Mat);
  PetscErrorCode (*transcoloringapplydentosp)(MatTransposeColoring,Mat,Mat);
  PetscErrorCode (*rart)(Mat,Mat,MatReuse,PetscReal,Mat*);
  PetscErrorCode (*rartsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
  PetscErrorCode (*rartnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
  /*139*/
  PetscErrorCode (*setblocksizes)(Mat,PetscInt,PetscInt);
  PetscErrorCode (*aypx)(Mat,PetscScalar,Mat,MatStructure);
  PetscErrorCode (*residual)(Mat,Vec,Vec,Vec);
};
/*
    If you add MatOps entries above also add them to the MATOP enum
    in include/petscmat.h and include/finclude/petscmat.h
*/

#include <petscsys.h>
PETSC_EXTERN PetscErrorCode MatRegisterOp(MPI_Comm, const char[], PetscVoidFunction, const char[], PetscInt, ...);
PETSC_EXTERN PetscErrorCode MatQueryOp(MPI_Comm, PetscVoidFunction*, const char[], PetscInt, ...);

typedef struct _p_MatBaseName* MatBaseName;
struct _p_MatBaseName {
  char        *bname,*sname,*mname;
  MatBaseName next;
};

PETSC_EXTERN MatBaseName MatBaseNameList;

/*
   Utility private matrix routines
*/
PETSC_INTERN PetscErrorCode MatConvert_Basic(Mat, MatType,MatReuse,Mat*);
PETSC_INTERN PetscErrorCode MatCopy_Basic(Mat,Mat,MatStructure);
PETSC_INTERN PetscErrorCode MatHeaderMerge(Mat,Mat);
PETSC_EXTERN PetscErrorCode MatHeaderReplace(Mat,Mat);
PETSC_INTERN PetscErrorCode MatAXPYGetxtoy_Private(PetscInt,PetscInt*,PetscInt*,PetscInt*, PetscInt*,PetscInt*,PetscInt*, PetscInt**);
PETSC_INTERN PetscErrorCode MatDiagonalSet_Default(Mat,Vec,InsertMode);

#if defined(PETSC_USE_DEBUG)
#  define MatCheckPreallocated(A,arg) do {                              \
    if (PetscUnlikely(!(A)->preallocated)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Must call MatXXXSetPreallocation() or MatSetUp() on argument %D \"%s\" before %s()",(arg),#A,PETSC_FUNCTION_NAME); \
  } while (0)
#else
#  define MatCheckPreallocated(A,arg) do {} while (0)
#endif

/*
  The stash is used to temporarily store inserted matrix values that
  belong to another processor. During the assembly phase the stashed
  values are moved to the correct processor and
*/

typedef struct _MatStashSpace *PetscMatStashSpace;

struct _MatStashSpace {
  PetscMatStashSpace next;
  PetscScalar        *space_head,*val;
  PetscInt           *idx,*idy;
  PetscInt           total_space_size;
  PetscInt           local_used;
  PetscInt           local_remaining;
};

PETSC_EXTERN PetscErrorCode PetscMatStashSpaceGet(PetscInt,PetscInt,PetscMatStashSpace *);
PETSC_EXTERN PetscErrorCode PetscMatStashSpaceContiguous(PetscInt,PetscMatStashSpace *,PetscScalar *,PetscInt *,PetscInt *);
PETSC_EXTERN PetscErrorCode PetscMatStashSpaceDestroy(PetscMatStashSpace*);

typedef struct {
  PetscInt      nmax;                   /* maximum stash size */
  PetscInt      umax;                   /* user specified max-size */
  PetscInt      oldnmax;                /* the nmax value used previously */
  PetscInt      n;                      /* stash size */
  PetscInt      bs;                     /* block size of the stash */
  PetscInt      reallocs;               /* preserve the no of mallocs invoked */
  PetscMatStashSpace space_head,space;  /* linked list to hold stashed global row/column numbers and matrix values */
  /* The following variables are used for communication */
  MPI_Comm      comm;
  PetscMPIInt   size,rank;
  PetscMPIInt   tag1,tag2;
  MPI_Request   *send_waits;            /* array of send requests */
  MPI_Request   *recv_waits;            /* array of receive requests */
  MPI_Status    *send_status;           /* array of send status */
  PetscInt      nsends,nrecvs;          /* numbers of sends and receives */
  PetscScalar   *svalues;               /* sending data */
  PetscInt      *sindices;
  PetscScalar   **rvalues;              /* receiving data (values) */
  PetscInt      **rindices;             /* receiving data (indices) */
  PetscInt      nprocessed;             /* number of messages already processed */
  PetscMPIInt   *flg_v;                 /* indicates what messages have arrived so far and from whom */
  PetscBool     reproduce;
  PetscInt      reproduce_count;
} MatStash;

PETSC_INTERN PetscErrorCode MatStashCreate_Private(MPI_Comm,PetscInt,MatStash*);
PETSC_INTERN PetscErrorCode MatStashDestroy_Private(MatStash*);
PETSC_INTERN PetscErrorCode MatStashScatterEnd_Private(MatStash*);
PETSC_INTERN PetscErrorCode MatStashSetInitialSize_Private(MatStash*,PetscInt);
PETSC_INTERN PetscErrorCode MatStashGetInfo_Private(MatStash*,PetscInt*,PetscInt*);
PETSC_INTERN PetscErrorCode MatStashValuesRow_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscBool );
PETSC_INTERN PetscErrorCode MatStashValuesCol_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscBool );
PETSC_INTERN PetscErrorCode MatStashValuesRowBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
PETSC_INTERN PetscErrorCode MatStashValuesColBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
PETSC_INTERN PetscErrorCode MatStashScatterBegin_Private(Mat,MatStash*,PetscInt*);
PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Private(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);

typedef struct {
  PetscInt   dim;
  PetscInt   dims[4];
  PetscInt   starts[4];
  PetscBool  noc;        /* this is a single component problem, hence user will not set MatStencil.c */
} MatStencilInfo;

/* Info about using compressed row format */
typedef struct {
  PetscBool  use;                           /* indicates compressed rows have been checked and will be used */
  PetscInt   nrows;                         /* number of non-zero rows */
  PetscInt   *i;                            /* compressed row pointer  */
  PetscInt   *rindex;                       /* compressed row index               */
} Mat_CompressedRow;
PETSC_EXTERN PetscErrorCode MatCheckCompressedRow(Mat,PetscInt,Mat_CompressedRow*,PetscInt*,PetscInt,PetscReal);

struct _p_Mat {
  PETSCHEADER(struct _MatOps);
  PetscLayout            rmap,cmap;
  void                   *data;            /* implementation-specific data */
  MatFactorType          factortype;       /* MAT_FACTOR_LU, ILU, CHOLESKY or ICC */
  PetscBool              assembled;        /* is the matrix assembled? */
  PetscBool              was_assembled;    /* new values inserted into assembled mat */
  PetscInt               num_ass;          /* number of times matrix has been assembled */
  PetscBool              same_nonzero;     /* matrix has same nonzero pattern as previous */
  MatInfo                info;             /* matrix information */
  InsertMode             insertmode;       /* have values been inserted in matrix or added? */
  MatStash               stash,bstash;     /* used for assembling off-proc mat emements */
  MatNullSpace           nullsp;           /* null space (operator is singular) */
  MatNullSpace           nearnullsp;       /* near null space to be used by multigrid methods */
  PetscBool              preallocated;
  MatStencilInfo         stencil;          /* information for structured grid */
  PetscBool              symmetric,hermitian,structurally_symmetric,spd;
  PetscBool              symmetric_set,hermitian_set,structurally_symmetric_set,spd_set; /* if true, then corresponding flag is correct*/
  PetscBool              symmetric_eternal;
  PetscBool              nooffprocentries,nooffproczerorows;
#if defined(PETSC_HAVE_CUSP)
  PetscCUSPFlag          valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
#endif
#if defined(PETSC_HAVE_VIENNACL)
  PetscViennaCLFlag          valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
#endif
  void                   *spptr;          /* pointer for special library like SuperLU */
  MatSolverPackage       solvertype;
  PetscViewer            viewonassembly;         /* the following are set in MatSetFromOptions() and used in MatAssemblyEnd() */
  PetscViewerFormat      viewformatonassembly;
  PetscBool              checksymmetryonassembly,checknullspaceonassembly;
  PetscReal              checksymmetrytol;
  };

PETSC_INTERN PetscErrorCode MatAXPY_Basic(Mat,PetscScalar,Mat,MatStructure);
PETSC_INTERN PetscErrorCode MatAXPY_BasicWithPreallocation(Mat,Mat,PetscScalar,Mat,MatStructure);
/*
    Object for partitioning graphs
*/

typedef struct _MatPartitioningOps *MatPartitioningOps;
struct _MatPartitioningOps {
  PetscErrorCode (*apply)(MatPartitioning,IS*);
  PetscErrorCode (*setfromoptions)(MatPartitioning);
  PetscErrorCode (*destroy)(MatPartitioning);
  PetscErrorCode (*view)(MatPartitioning,PetscViewer);
};

struct _p_MatPartitioning {
  PETSCHEADER(struct _MatPartitioningOps);
  Mat         adj;
  PetscInt    *vertex_weights;
  PetscReal   *part_weights;
  PetscInt    n;                                 /* number of partitions */
  void        *data;
  PetscInt    setupcalled;
};

/*
    Object for coarsen graphs
*/
typedef struct _MatCoarsenOps *MatCoarsenOps;
struct _MatCoarsenOps {
  PetscErrorCode (*apply)(MatCoarsen);
  PetscErrorCode (*setfromoptions)(MatCoarsen);
  PetscErrorCode (*destroy)(MatCoarsen);
  PetscErrorCode (*view)(MatCoarsen,PetscViewer);
};

struct _p_MatCoarsen {
  PETSCHEADER(struct _MatCoarsenOps);
  Mat         graph;
  PetscInt    verbose;
  PetscInt    setupcalled;
  void        *subctx;
  /* */
  PetscBool strict_aggs;
  IS perm;
  PetscCoarsenData *agg_lists;
};

PETSC_EXTERN PetscErrorCode PetscCDCreate(PetscInt,PetscCoarsenData**);
PETSC_EXTERN PetscErrorCode PetscCDDestroy(PetscCoarsenData*);
PETSC_EXTERN PetscErrorCode PetscLLNSetID(PetscCDIntNd*,PetscInt);
PETSC_EXTERN PetscErrorCode PetscLLNGetID(const PetscCDIntNd*,PetscInt*);
PETSC_EXTERN PetscErrorCode PetscCDAppendID(PetscCoarsenData*,PetscInt,PetscInt);
PETSC_EXTERN PetscErrorCode PetscCDAppendRemove(PetscCoarsenData*,PetscInt,PetscInt);
PETSC_EXTERN PetscErrorCode PetscCDAppendNode(PetscCoarsenData*,PetscInt,PetscCDIntNd*);
PETSC_EXTERN PetscErrorCode PetscCDRemoveNextNode(PetscCoarsenData*,PetscInt,PetscCDIntNd*);
PETSC_EXTERN PetscErrorCode PetscCDRemoveAllAt(PetscCoarsenData*,PetscInt);
PETSC_EXTERN PetscErrorCode PetscCDSizeAt(const PetscCoarsenData*,PetscInt,PetscInt*);
PETSC_EXTERN PetscErrorCode PetscCDEmptyAt(const PetscCoarsenData*,PetscInt,PetscBool*);
PETSC_EXTERN PetscErrorCode PetscCDSetChuckSize(PetscCoarsenData*,PetscInt);
PETSC_EXTERN PetscErrorCode PetscCDPrint(const PetscCoarsenData*,MPI_Comm);
PETSC_EXTERN PetscErrorCode PetscCDGetMIS(PetscCoarsenData*,IS*);
PETSC_EXTERN PetscErrorCode PetscCDGetMat(const PetscCoarsenData*,Mat*);
PETSC_EXTERN PetscErrorCode PetscCDSetMat(PetscCoarsenData*,Mat);

typedef PetscCDIntNd *PetscCDPos;
PETSC_EXTERN PetscErrorCode PetscCDGetHeadPos(const PetscCoarsenData*,PetscInt,PetscCDPos*);
PETSC_EXTERN PetscErrorCode PetscCDGetNextPos(const PetscCoarsenData*,PetscInt,PetscCDPos*);
PETSC_EXTERN PetscErrorCode PetscCDGetASMBlocks(const PetscCoarsenData*,const PetscInt,PetscInt*,IS**);
/* PetscErrorCode PetscCDSetRemovedIS( PetscCoarsenData *ail, MPI_Comm, const PetscInt, PetscInt[] ); */
/* PetscErrorCode PetscCDGetRemovedIS( PetscCoarsenData *ail, IS * ); */

/*
    MatFDColoring is used to compute Jacobian matrices efficiently
  via coloring. The data structure is explained below in an example.

   Color =   0    1     0    2   |   2      3       0
   ---------------------------------------------------
            00   01              |          05
            10   11              |   14     15               Processor  0
                       22    23  |          25
                       32    33  |
   ===================================================
                                 |   44     45     46
            50                   |          55               Processor 1
                                 |   64            66
   ---------------------------------------------------

    ncolors = 4;

    ncolumns      = {2,1,1,0}
    columns       = {{0,2},{1},{3},{}}
    nrows         = {4,2,3,3}
    rows          = {{0,1,2,3},{0,1},{1,2,3},{0,1,2}}
    columnsforrow = {{0,0,2,2},{1,1},{4,3,3},{5,5,5}}
    vscaleforrow  = {{,,,},{,},{,,},{,,}}
    vwscale       = {dx(0),dx(1),dx(2),dx(3)}               MPI Vec
    vscale        = {dx(0),dx(1),dx(2),dx(3),dx(4),dx(5)}   Seq Vec

    ncolumns      = {1,0,1,1}
    columns       = {{6},{},{4},{5}}
    nrows         = {3,0,2,2}
    rows          = {{0,1,2},{},{1,2},{1,2}}
    columnsforrow = {{6,0,6},{},{4,4},{5,5}}
    vscaleforrow =  {{,,},{},{,},{,}}
    vwscale       = {dx(4),dx(5),dx(6)}              MPI Vec
    vscale        = {dx(0),dx(4),dx(5),dx(6)}        Seq Vec

    See the routine MatFDColoringApply() for how this data is used
    to compute the Jacobian.

*/

struct  _p_MatFDColoring{
  PETSCHEADER(int);
  PetscInt       M,N,m;            /* total rows, columns; local rows */
  PetscInt       rstart;           /* first row owned by local processor */
  PetscInt       ncolors;          /* number of colors */
  PetscInt       *ncolumns;        /* number of local columns for a color */
  PetscInt       **columns;        /* lists the local columns of each color (using global column numbering) */
  PetscInt       *nrows;           /* number of local rows for each color */
  PetscInt       **rows;           /* lists the local rows for each color (using the local row numbering) */
  PetscInt       **columnsforrow;  /* lists the corresponding columns for those rows (using the global column) */
  PetscReal      error_rel;        /* square root of relative error in computing function */
  PetscReal      umin;             /* minimum allowable u'dx value */
  Vec            w1,w2,w3;         /* work vectors used in computing Jacobian */
  PetscBool      fset;             /* indicates that the initial function value F(X) is set */
  PetscErrorCode (*f)(void);       /* function that defines Jacobian */
  void           *fctx;            /* optional user-defined context for use by the function f */
  PetscInt       **vscaleforrow;   /* location in vscale for each columnsforrow[] entry */
  Vec            vscale;           /* holds FD scaling, i.e. 1/dx for each perturbed column */
  PetscInt       currentcolor;     /* color for which function evaluation is being done now */
  const char     *htype;            /* "wp" or "ds" */
  ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_GHOSTED */

  void           *ftn_func_pointer,*ftn_func_cntx; /* serve the same purpose as *fortran_func_pointers in PETSc objects */
};

typedef struct _MatColoringOps *MatColoringOps;
struct _MatColoringOps {
  PetscErrorCode (*destroy)(MatColoring);
  PetscErrorCode (*setfromoptions)(MatColoring);
  PetscErrorCode (*view)(MatColoring,PetscViewer);
  PetscErrorCode (*apply)(MatColoring,ISColoring*);
};

struct _p_MatColoring {
  PETSCHEADER(struct _MatColoringOps);
  Mat        mat;
  PetscInt   dist;      /* distance of the coloring */
  PetscInt   maxcolors; /* the maximum number of colors returned, maxcolors=1 for MIS */
  void       *data;     /* inner context */
  PetscBool  valid;     /* check to see if what is produced is a valid coloring */
};

struct  _p_MatTransposeColoring{
  PETSCHEADER(int);
  PetscInt       M,N,m;            /* total rows, columns; local rows */
  PetscInt       rstart;           /* first row owned by local processor */
  PetscInt       ncolors;          /* number of colors */
  PetscInt       *ncolumns;        /* number of local columns for a color */
  PetscInt       *nrows;           /* number of local rows for each color */
  PetscInt       currentcolor;     /* color for which function evaluation is being done now */
  ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_GHOSTED */

  PetscInt       *colorforrow,*colorforcol;  /* pointer to rows and columns */
  PetscInt       *rows;                      /* lists the local rows for each color (using the local row numbering) */
  PetscInt       *den2sp;                    /* maps (row,color) in the dense matrix to index of sparse matrix array a->a */
  PetscInt       *columns;                   /* lists the local columns of each color (using global column numbering) */
  PetscInt       brows;                      /* number of rows for efficient implementation of MatTransColoringApplyDenToSp() */
  PetscInt       *lstart;                    /* array used for loop over row blocks of Csparse */
};

/*
   Null space context for preconditioner/operators
*/
struct _p_MatNullSpace {
  PETSCHEADER(int);
  PetscBool      has_cnst;
  PetscInt       n;
  Vec*           vecs;
  PetscScalar*   alpha;                 /* for projections */
  PetscErrorCode (*remove)(MatNullSpace,Vec,void*);  /* for user provided removal function */
  void*          rmctx;                 /* context for remove() function */
};

/*
   Checking zero pivot for LU, ILU preconditioners.
*/
typedef struct {
  PetscInt       nshift,nshift_max;
  PetscReal      shift_amount,shift_lo,shift_hi,shift_top,shift_fraction;
  PetscBool      newshift;
  PetscReal      rs;  /* active row sum of abs(offdiagonals) */
  PetscScalar    pv;  /* pivot of the active row */
} FactorShiftCtx;

PETSC_EXTERN PetscErrorCode MatFactorDumpMatrix(Mat);

#undef __FUNCT__
#define __FUNCT__ "MatPivotCheck_nz"
PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_nz(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
{
  PetscReal _rs   = sctx->rs;
  PetscReal _zero = info->zeropivot*_rs;

  PetscFunctionBegin;
  if (PetscAbsScalar(sctx->pv) <= _zero){
    /* force |diag| > zeropivot*rs */
    if (!sctx->nshift) sctx->shift_amount = info->shiftamount;
    else sctx->shift_amount *= 2.0;
    sctx->newshift = PETSC_TRUE;
    (sctx->nshift)++;
  } else {
    sctx->newshift = PETSC_FALSE;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPivotCheck_pd"
PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_pd(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
{
  PetscReal _rs   = sctx->rs;
  PetscReal _zero = info->zeropivot*_rs;

  PetscFunctionBegin;
  if (PetscRealPart(sctx->pv) <= _zero){
    /* force matfactor to be diagonally dominant */
    if (sctx->nshift == sctx->nshift_max) {
      sctx->shift_fraction = sctx->shift_hi;
    } else {
      sctx->shift_lo = sctx->shift_fraction;
      sctx->shift_fraction = (sctx->shift_hi+sctx->shift_lo)/2.;
    }
    sctx->shift_amount = sctx->shift_fraction * sctx->shift_top;
    sctx->nshift++;
    sctx->newshift = PETSC_TRUE;
  } else {
    sctx->newshift = PETSC_FALSE;
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPivotCheck_inblocks"
PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_inblocks(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
{
  PetscReal _zero = info->zeropivot;

  PetscFunctionBegin;
  if (PetscAbsScalar(sctx->pv) <= _zero){
    sctx->pv          += info->shiftamount;
    sctx->shift_amount = 0.0;
    sctx->nshift++;
  }
  sctx->newshift = PETSC_FALSE;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPivotCheck_none"
PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_none(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
{
  PetscReal _zero = info->zeropivot;

  PetscFunctionBegin;
  sctx->newshift = PETSC_FALSE;
  if (PetscAbsScalar(sctx->pv) <= _zero) {
    PetscErrorCode ierr;
    PetscBool      flg = PETSC_FALSE;

    ierr = PetscOptionsGetBool(NULL,"-mat_dump",&flg,NULL);CHKERRQ(ierr);
    if (flg) {
      ierr = MatView(mat,PETSC_VIEWER_BINARY_(PetscObjectComm((PetscObject)mat)));CHKERRQ(ierr);
    }
    SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot row %D value %G tolerance %G",row,PetscAbsScalar(sctx->pv),_zero);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatPivotCheck"
PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  if (info->shifttype == (PetscReal) MAT_SHIFT_NONZERO){
    ierr = MatPivotCheck_nz(mat,info,sctx,row);CHKERRQ(ierr);
  } else if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE){
    ierr = MatPivotCheck_pd(mat,info,sctx,row);CHKERRQ(ierr);
  } else if (info->shifttype == (PetscReal) MAT_SHIFT_INBLOCKS){
    ierr = MatPivotCheck_inblocks(mat,info,sctx,row);CHKERRQ(ierr);
  } else {
    ierr = MatPivotCheck_none(mat,info,sctx,row);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/*
  Create and initialize a linked list
  Input Parameters:
    idx_start - starting index of the list
    lnk_max   - max value of lnk indicating the end of the list
    nlnk      - max length of the list
  Output Parameters:
    lnk       - list initialized
    bt        - PetscBT (bitarray) with all bits set to false
    lnk_empty - flg indicating the list is empty
*/
#define PetscLLCreate(idx_start,lnk_max,nlnk,lnk,bt) \
  (PetscMalloc(nlnk*sizeof(PetscInt),&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,0))

#define PetscLLCreate_new(idx_start,lnk_max,nlnk,lnk,bt,lnk_empty)\
  (PetscMalloc(nlnk*sizeof(PetscInt),&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk_empty = PETSC_TRUE,0) ||(lnk[idx_start] = lnk_max,0))

/*
  Add an index set into a sorted linked list
  Input Parameters:
    nidx      - number of input indices
    indices   - interger array
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk      - number of newly added indices
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    bt        - updated PetscBT (bitarray)
*/
#define PetscLLAdd(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata;\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _entry = indices[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      /* start from the beginning if _entry < previous _entry */\
      if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    }\
  }\
}

/*
  Add a permuted index set into a sorted linked list
  Input Parameters:
    nidx      - number of input indices
    indices   - interger array
    perm      - permutation of indices
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk      - number of newly added indices
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    bt        - updated PetscBT (bitarray)
*/
#define PetscLLAddPerm(nidx,indices,perm,idx_start,nlnk,lnk,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata;\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _entry = perm[indices[_k]];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      /* start from the beginning if _entry < previous _entry */\
      if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    }\
  }\
}

/*
  Add a SORTED ascending index set into a sorted linked list - same as PetscLLAdd() bus skip 'if (_k && _entry < _lnkdata) _lnkdata  = idx_start;'
  Input Parameters:
    nidx      - number of input indices
    indices   - sorted interger array
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk      - number of newly added indices
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    bt        - updated PetscBT (bitarray)
*/
#define PetscLLAddSorted(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata;\
  nlnk      = 0;\
  _lnkdata  = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _entry = indices[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here */\
    }\
  }\
}

#define PetscLLAddSorted_new(nidx,indices,idx_start,lnk_empty,nlnk,lnk,bt) 0; \
{\
  PetscInt _k,_entry,_location,_lnkdata;\
  if (lnk_empty){\
    _lnkdata  = idx_start;                      \
    for (_k=0; _k<nidx; _k++){                  \
      _entry = indices[_k];                             \
      PetscBTSet(bt,_entry);  /* mark the new entry */          \
          _location = _lnkdata;                                 \
          _lnkdata  = lnk[_location];                           \
        /* insertion location is found, add entry into lnk */   \
        lnk[_location] = _entry;                                \
        lnk[_entry]    = _lnkdata;                              \
        _lnkdata = _entry; /* next search starts from here */   \
    }                                                           \
    /*\
    lnk[indices[nidx-1]] = lnk[idx_start];\
    lnk[idx_start]       = indices[0];\
    PetscBTSet(bt,indices[0]);  \
    for (_k=1; _k<nidx; _k++){                  \
      PetscBTSet(bt,indices[_k]);                                          \
      lnk[indices[_k-1]] = indices[_k];                                  \
    }                                                           \
     */\
    nlnk      = nidx;\
    lnk_empty = PETSC_FALSE;\
  } else {\
    nlnk      = 0;                              \
    _lnkdata  = idx_start;                      \
    for (_k=0; _k<nidx; _k++){                  \
      _entry = indices[_k];                             \
      if (!PetscBTLookupSet(bt,_entry)){  /* new entry */       \
        /* search for insertion location */                     \
        do {                                                    \
          _location = _lnkdata;                                 \
          _lnkdata  = lnk[_location];                           \
        } while (_entry > _lnkdata);                            \
        /* insertion location is found, add entry into lnk */   \
        lnk[_location] = _entry;                                \
        lnk[_entry]    = _lnkdata;                              \
        nlnk++;                                                 \
        _lnkdata = _entry; /* next search starts from here */   \
      }                                                         \
    }                                                           \
  }                                                             \
}

/*
  Add a SORTED index set into a sorted linked list used for LUFactorSymbolic()
  Same as PetscLLAddSorted() with an additional operation:
       count the number of input indices that are no larger than 'diag'
  Input Parameters:
    indices   - sorted interger array
    idx_start - starting index of the list, index of pivot row
    lnk       - linked list(an integer array) that is created
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    diag      - index of the active row in LUFactorSymbolic
    nzbd      - number of input indices with indices <= idx_start
    im        - im[idx_start] is initialized as num of nonzero entries in row=idx_start
  output Parameters:
    nlnk      - number of newly added indices
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    bt        - updated PetscBT (bitarray)
    im        - im[idx_start]: unchanged if diag is not an entry
                             : num of entries with indices <= diag if diag is an entry
*/
#define PetscLLAddSortedLU(indices,idx_start,nlnk,lnk,bt,diag,nzbd,im) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata,_nidx;\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  _nidx = im[idx_start] - nzbd; /* num of entries with idx_start < index <= diag */\
  for (_k=0; _k<_nidx; _k++){\
    _entry = indices[_k];\
    nzbd++;\
    if ( _entry== diag) im[idx_start] = nzbd;\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here */\
    }\
  }\
}

/*
  Copy data on the list into an array, then initialize the list
  Input Parameters:
    idx_start - starting index of the list
    lnk_max   - max value of lnk indicating the end of the list
    nlnk      - number of data on the list to be copied
    lnk       - linked list
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    indices   - array that contains the copied data
    lnk       - linked list that is cleaned and initialize
    bt        - PetscBT (bitarray) with all bits set to false
*/
#define PetscLLClean(idx_start,lnk_max,nlnk,lnk,indices,bt) 0;\
{\
  PetscInt _j,_idx=idx_start;\
  for (_j=0; _j<nlnk; _j++){\
    _idx = lnk[_idx];\
    indices[_j] = _idx;\
    ierr = PetscBTClear(bt,_idx);CHKERRQ(ierr);\
  }\
  lnk[idx_start] = lnk_max;\
}
/*
  Free memories used by the list
*/
#define PetscLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

/* Routines below are used for incomplete matrix factorization */
/*
  Create and initialize a linked list and its levels
  Input Parameters:
    idx_start - starting index of the list
    lnk_max   - max value of lnk indicating the end of the list
    nlnk      - max length of the list
  Output Parameters:
    lnk       - list initialized
    lnk_lvl   - array of size nlnk for storing levels of lnk
    bt        - PetscBT (bitarray) with all bits set to false
*/
#define PetscIncompleteLLCreate(idx_start,lnk_max,nlnk,lnk,lnk_lvl,bt)\
  (PetscMalloc(2*nlnk*sizeof(PetscInt),&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,lnk_lvl = lnk + nlnk,0))

/*
  Initialize a sorted linked list used for ILU and ICC
  Input Parameters:
    nidx      - number of input idx
    idx       - interger array used for storing column indices
    idx_start - starting index of the list
    perm      - indices of an IS
    lnk       - linked list(an integer array) that is created
    lnklvl    - levels of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk     - number of newly added idx
    lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    lnklvl   - levels of lnk
    bt       - updated PetscBT (bitarray)
*/
#define PetscIncompleteLLInit(nidx,idx,idx_start,perm,nlnk,lnk,lnklvl,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata;\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _entry = perm[idx[_k]];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location]  = _entry;\
      lnk[_entry]     = _lnkdata;\
      lnklvl[_entry] = 0;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    }\
  }\
}

/*
  Add a SORTED index set into a sorted linked list for ILU
  Input Parameters:
    nidx      - number of input indices
    idx       - sorted interger array used for storing column indices
    level     - level of fill, e.g., ICC(level)
    idxlvl    - level of idx
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    lnklvl    - levels of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    prow      - the row number of idx
  output Parameters:
    nlnk     - number of newly added idx
    lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    lnklvl   - levels of lnk
    bt       - updated PetscBT (bitarray)

  Note: the level of factor(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(i,prow)+lvl(prow,j)+1)
        where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
*/
#define PetscILULLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,lnklvl_prow) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata,_incrlev,_lnklvl_prow=lnklvl[prow];\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _incrlev = idxlvl[_k] + _lnklvl_prow + 1;\
    if (_incrlev > level) continue;\
    _entry = idx[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location]  = _entry;\
      lnk[_entry]     = _lnkdata;\
      lnklvl[_entry] = _incrlev;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    } else { /* existing entry: update lnklvl */\
      if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    }\
  }\
}

/*
  Add a index set into a sorted linked list
  Input Parameters:
    nidx      - number of input idx
    idx   - interger array used for storing column indices
    level     - level of fill, e.g., ICC(level)
    idxlvl - level of idx
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    lnklvl   - levels of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk      - number of newly added idx
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    lnklvl   - levels of lnk
    bt        - updated PetscBT (bitarray)
*/
#define PetscIncompleteLLAdd(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
  nlnk     = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _incrlev = idxlvl[_k] + 1;\
    if (_incrlev > level) continue;\
    _entry = idx[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location]  = _entry;\
      lnk[_entry]     = _lnkdata;\
      lnklvl[_entry] = _incrlev;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    } else { /* existing entry: update lnklvl */\
      if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    }\
  }\
}

/*
  Add a SORTED index set into a sorted linked list
  Input Parameters:
    nidx      - number of input indices
    idx   - sorted interger array used for storing column indices
    level     - level of fill, e.g., ICC(level)
    idxlvl - level of idx
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    lnklvl    - levels of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    nlnk      - number of newly added idx
    lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    lnklvl    - levels of lnk
    bt        - updated PetscBT (bitarray)
*/
#define PetscIncompleteLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
  nlnk = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _incrlev = idxlvl[_k] + 1;\
    if (_incrlev > level) continue;\
    _entry = idx[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      lnklvl[_entry] = _incrlev;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here */\
    } else { /* existing entry: update lnklvl */\
      if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    }\
  }\
}

/*
  Add a SORTED index set into a sorted linked list for ICC
  Input Parameters:
    nidx      - number of input indices
    idx       - sorted interger array used for storing column indices
    level     - level of fill, e.g., ICC(level)
    idxlvl    - level of idx
    idx_start - starting index of the list
    lnk       - linked list(an integer array) that is created
    lnklvl    - levels of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    idxlvl_prow - idxlvl[prow], where prow is the row number of the idx
  output Parameters:
    nlnk   - number of newly added indices
    lnk    - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    lnklvl - levels of lnk
    bt     - updated PetscBT (bitarray)
  Note: the level of U(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(prow,i)+lvl(prow,j)+1)
        where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
*/
#define PetscICCLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,idxlvl_prow) 0;\
{\
  PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
  nlnk = 0;\
  _lnkdata = idx_start;\
  for (_k=0; _k<nidx; _k++){\
    _incrlev = idxlvl[_k] + idxlvl_prow + 1;\
    if (_incrlev > level) continue;\
    _entry = idx[_k];\
    if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
      /* search for insertion location */\
      do {\
        _location = _lnkdata;\
        _lnkdata  = lnk[_location];\
      } while (_entry > _lnkdata);\
      /* insertion location is found, add entry into lnk */\
      lnk[_location] = _entry;\
      lnk[_entry]    = _lnkdata;\
      lnklvl[_entry] = _incrlev;\
      nlnk++;\
      _lnkdata = _entry; /* next search starts from here */\
    } else { /* existing entry: update lnklvl */\
      if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    }\
  }\
}

/*
  Copy data on the list into an array, then initialize the list
  Input Parameters:
    idx_start - starting index of the list
    lnk_max   - max value of lnk indicating the end of the list
    nlnk      - number of data on the list to be copied
    lnk       - linked list
    lnklvl    - level of lnk
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    indices - array that contains the copied data
    lnk     - linked list that is cleaned and initialize
    lnklvl  - level of lnk that is reinitialized
    bt      - PetscBT (bitarray) with all bits set to false
*/
#define PetscIncompleteLLClean(idx_start,lnk_max,nlnk,lnk,lnklvl,indices,indiceslvl,bt) 0;\
{\
  PetscInt _j,_idx=idx_start;\
  for (_j=0; _j<nlnk; _j++){\
    _idx = lnk[_idx];\
    *(indices+_j) = _idx;\
    *(indiceslvl+_j) = lnklvl[_idx];\
    lnklvl[_idx] = -1;\
    ierr = PetscBTClear(bt,_idx);CHKERRQ(ierr);\
  }\
  lnk[idx_start] = lnk_max;\
}
/*
  Free memories used by the list
*/
#define PetscIncompleteLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

/* -------------------------------------------------------------------------------------------------------*/
#include <petscbt.h>
#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedCreate"
/*
  Create and initialize a condensed linked list -
    same as PetscLLCreate(), but uses a scalable array 'lnk' with size of max number of entries, not O(N).
    Barry suggested this approach (Dec. 6, 2011):
      I've thought of an alternative way of representing a linked list that is efficient but doesn't have the O(N) scaling issue
      (it may be faster than the O(N) even sequentially due to less crazy memory access).

      Instead of having some like  a  2  -> 4 -> 11 ->  22  list that uses slot 2  4 11 and 22 in a big array use a small array with two slots
      for each entry for example  [ 2 1 | 4 3 | 22 -1 | 11 2]   so the first number (of the pair) is the value while the second tells you where
      in the list the next entry is. Inserting a new link means just append another pair at the end. For example say we want to insert 13 into the
      list it would then become [2 1 | 4 3 | 22 -1 | 11 4 | 13 2 ] you just add a pair at the end and fix the point for the one that points to it.
      That is 11 use to point to the 2 slot, after the change 11 points to the 4th slot which has the value 13. Note that values are always next
      to each other so memory access is much better than using the big array.

  Example:
     nlnk_max=5, lnk_max=36:
     Initial list: [0, 0 | 36, 2 | 0, 0 | 0, 0 | 0, 0 | 0, 0 | 0, 0]
     here, head_node has index 2 with value lnk[2]=lnk_max=36,
           0-th entry is used to store the number of entries in the list,
     The initial lnk represents head -> tail(marked by 36) with number of entries = lnk[0]=0.

     Now adding a sorted set {2,4}, the list becomes
     [2, 0 | 36, 4 |2, 6 | 4, 2 | 0, 0 | 0, 0 | 0, 0 ]
     represents head -> 2 -> 4 -> tail with number of entries = lnk[0]=2.

     Then adding a sorted set {0,3,35}, the list
     [5, 0 | 36, 8 | 2, 10 | 4, 12 | 0, 4 | 3, 6 | 35, 2 ]
     represents head -> 0 -> 2 -> 3 -> 4 -> 35 -> tail with number of entries = lnk[0]=5.

  Input Parameters:
    nlnk_max  - max length of the list
    lnk_max   - max value of the entries
  Output Parameters:
    lnk       - list created and initialized
    bt        - PetscBT (bitarray) with all bits set to false. Note: bt has size lnk_max, not nln_max!
*/
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate(PetscInt nlnk_max,PetscInt lnk_max,PetscInt **lnk,PetscBT *bt)
{
  PetscErrorCode ierr;
  PetscInt       *llnk;

  PetscFunctionBegin;
  ierr = PetscMalloc(2*(nlnk_max+2)*sizeof(PetscInt),lnk);CHKERRQ(ierr);
  ierr = PetscBTCreate(lnk_max,bt);CHKERRQ(ierr);
  llnk = *lnk;
  llnk[0] = 0;         /* number of entries on the list */
  llnk[2] = lnk_max;   /* value in the head node */
  llnk[3] = 2;         /* next for the head node */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedAddSorted"
/*
  Add a SORTED ascending index set into a sorted linked list. See PetscLLCondensedCreate() for detailed description.
  Input Parameters:
    nidx      - number of input indices
    indices   - sorted interger array
    lnk       - condensed linked list(an integer array) that is created
    bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
  output Parameters:
    lnk       - the sorted(increasing order) linked list containing previous and newly added non-redundate indices
    bt        - updated PetscBT (bitarray)
*/
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted(PetscInt nidx,const PetscInt indices[],PetscInt lnk[],PetscBT bt)
{
  PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;

  PetscFunctionBegin;
  _nlnk     = lnk[0]; /* num of entries on the input lnk */
  _location = 2; /* head */
    for (_k=0; _k<nidx; _k++){
      _entry = indices[_k];
      if (!PetscBTLookupSet(bt,_entry)){  /* new entry */
        /* search for insertion location */
        do {
          _next     = _location + 1; /* link from previous node to next node */
          _location = lnk[_next];    /* idx of next node */
          _lnkdata  = lnk[_location];/* value of next node */
        } while (_entry > _lnkdata);
        /* insertion location is found, add entry into lnk */
        _newnode        = 2*(_nlnk+2);   /* index for this new node */
        lnk[_next]      = _newnode;      /* connect previous node to the new node */
        lnk[_newnode]   = _entry;        /* set value of the new node */
        lnk[_newnode+1] = _location;     /* connect new node to next node */
        _location       = _newnode;      /* next search starts from the new node */
        _nlnk++;
      }   \
    }\
  lnk[0]   = _nlnk;   /* number of entries in the list */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedClean"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean(PetscInt lnk_max,PetscInt nidx,PetscInt *indices,PetscInt lnk[],PetscBT bt)
{
  PetscErrorCode ierr;
  PetscInt       _k,_next,_nlnk;

  PetscFunctionBegin;
  _next = lnk[3];       /* head node */
  _nlnk = lnk[0];       /* num of entries on the list */
  for (_k=0; _k<_nlnk; _k++){
    indices[_k] = lnk[_next];
    _next       = lnk[_next + 1];
    ierr = PetscBTClear(bt,indices[_k]);CHKERRQ(ierr);
  }
  lnk[0] = 0;          /* num of entries on the list */
  lnk[2] = lnk_max;    /* initialize head node */
  lnk[3] = 2;          /* head node */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedView"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView(PetscInt *lnk)
{
  PetscErrorCode ierr;
  PetscInt       k;

  PetscFunctionBegin;
  ierr = PetscPrintf(PETSC_COMM_SELF,"LLCondensed of size %d, (val,  next)\n",lnk[0]);CHKERRQ(ierr);
  for (k=2; k< lnk[0]+2; k++){
    ierr = PetscPrintf(PETSC_COMM_SELF," %D: (%D, %D)\n",2*k,lnk[2*k],lnk[2*k+1]);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedDestroy"
/*
  Free memories used by the list
*/
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy(PetscInt *lnk,PetscBT bt)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscFree(lnk);CHKERRQ(ierr);
  ierr = PetscBTDestroy(&bt);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedCreate_Scalable"
/*
 Same as PetscLLCondensedCreate(), but does not use non-scalable O(lnk_max) bitarray
  Input Parameters:
    nlnk_max  - max length of the list
  Output Parameters:
    lnk       - list created and initialized
*/
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_Scalable(PetscInt nlnk_max,PetscInt **lnk)
{
  PetscErrorCode ierr;
  PetscInt       *llnk;

  PetscFunctionBegin;
  ierr = PetscMalloc(2*(nlnk_max+2)*sizeof(PetscInt),lnk);CHKERRQ(ierr);
  llnk = *lnk;
  llnk[0] = 0;               /* number of entries on the list */
  llnk[2] = PETSC_MAX_INT;   /* value in the head node */
  llnk[3] = 2;               /* next for the head node */
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedAddSorted_Scalable"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_Scalable(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
{
  PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;
  _nlnk     = lnk[0]; /* num of entries on the input lnk */
  _location = 2; /* head */ \
    for (_k=0; _k<nidx; _k++){
      _entry = indices[_k];
      /* search for insertion location */
      do {
        _next     = _location + 1; /* link from previous node to next node */
        _location = lnk[_next];    /* idx of next node */
        _lnkdata  = lnk[_location];/* value of next node */
      } while (_entry > _lnkdata);
      if (_entry < _lnkdata) {
        /* insertion location is found, add entry into lnk */
        _newnode        = 2*(_nlnk+2);   /* index for this new node */
        lnk[_next]      = _newnode;      /* connect previous node to the new node */
        lnk[_newnode]   = _entry;        /* set value of the new node */
        lnk[_newnode+1] = _location;     /* connect new node to next node */
        _location       = _newnode;      /* next search starts from the new node */
        _nlnk++;
      }
    }
  lnk[0]   = _nlnk;   /* number of entries in the list */
  return 0;
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedClean_Scalable"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_Scalable(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
{
  PetscInt _k,_next,_nlnk;
  _next = lnk[3];       /* head node */
  _nlnk = lnk[0];
  for (_k=0; _k<_nlnk; _k++){
    indices[_k] = lnk[_next];
    _next       = lnk[_next + 1];
  }
  lnk[0] = 0;          /* num of entries on the list */
  lnk[3] = 2;          /* head node */
  return 0;
}

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedDestroy_Scalable"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_Scalable(PetscInt *lnk)
{
  return PetscFree(lnk);
}

/* -------------------------------------------------------------------------------------------------------*/
/*
      lnk[0]   number of links
      lnk[1]   number of entries
      lnk[3n]  value
      lnk[3n+1] len
      lnk[3n+2] link to next value

      The next three are always the first link

      lnk[3]    PETSC_MIN_INT+1
      lnk[4]    1
      lnk[5]    link to first real entry

      The next three are always the last link

      lnk[6]    PETSC_MAX_INT - 1
      lnk[7]    1
      lnk[8]    next valid link (this is the same as lnk[0] but without the decreases)
*/

#undef __FUNCT__
#define __FUNCT__ "PetscLLCondensedCreate_fast"
PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_fast(PetscInt nlnk_max,PetscInt **lnk)
{
  PetscErrorCode ierr;
  PetscInt       *llnk;

  PetscFunctionBegin;
  ierr = PetscMalloc(3*(nlnk_max+3)*sizeof(PetscInt),lnk);CHKERRQ(ierr);
  llnk = *lnk;
  llnk[0] = 0;   /* nlnk: number of entries on the list */
  llnk[1] = 0;          /* number of integer entries represented in list */
  llnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
  llnk[4] = 1;           /* count for the first node */
  llnk[5] = 6;         /* next for the first node */
  llnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
  llnk[7] = 1;           /* count for the last node */
  llnk[8] = 0;         /* next valid node to be used */
  PetscFunctionReturn(0);
}

PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_fast(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
{
  PetscInt k,entry,prev,next;
  prev      = 3;      /* first value */
  next      = lnk[prev+2];
  for (k=0; k<nidx; k++){
    entry = indices[k];
    /* search for insertion location */
    while (entry >= lnk[next]) {
      prev = next;
      next = lnk[next+2];
    }
    /* entry is in range of previous list */
    if (entry < lnk[prev]+lnk[prev+1]) continue;
    lnk[1]++;
    /* entry is right after previous list */
    if (entry == lnk[prev]+lnk[prev+1]) {
      lnk[prev+1]++;
      if (lnk[next] == entry+1) { /* combine two contiquous strings */
        lnk[prev+1] += lnk[next+1];
        lnk[prev+2]  = lnk[next+2];
        next         = lnk[next+2];
        lnk[0]--;
      }
      continue;
    }
    /* entry is right before next list */
    if (entry == lnk[next]-1) {
      lnk[next]--;
      lnk[next+1]++;
      prev = next;
      next = lnk[prev+2];
      continue;
    }
    /*  add entry into lnk */
    lnk[prev+2]    = 3*((lnk[8]++)+3);      /* connect previous node to the new node */
    prev           = lnk[prev+2];
    lnk[prev]      = entry;        /* set value of the new node */
    lnk[prev+1]    = 1;             /* number of values in contiquous string is one to start */
    lnk[prev+2]    = next;          /* connect new node to next node */
    lnk[0]++;
  }
  return 0;
}

PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_fast(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
{
  PetscInt _k,_next,_nlnk,cnt,j;
  _next = lnk[5];       /* first node */
  _nlnk = lnk[0];
  cnt   = 0;
  for (_k=0; _k<_nlnk; _k++){
    for (j=0; j<lnk[_next+1]; j++) {
      indices[cnt++] = lnk[_next] + j;
    }
    _next       = lnk[_next + 2];
  }
  lnk[0] = 0;   /* nlnk: number of links */
  lnk[1] = 0;          /* number of integer entries represented in list */
  lnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
  lnk[4] = 1;           /* count for the first node */
  lnk[5] = 6;         /* next for the first node */
  lnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
  lnk[7] = 1;           /* count for the last node */
  lnk[8] = 0;         /* next valid location to make link */
  return 0;
}

PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView_fast(PetscInt *lnk)
{
  PetscInt k,next,nlnk;
  next = lnk[5];       /* first node */
  nlnk = lnk[0];
  for (k=0; k<nlnk; k++){
#if 0                           /* Debugging code */
    printf("%d value %d len %d next %d\n",next,lnk[next],lnk[next+1],lnk[next+2]);
#endif
    next = lnk[next + 2];
  }
  return 0;
}

PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_fast(PetscInt *lnk)
{
  return PetscFree(lnk);
}

PETSC_EXTERN PetscLogEvent MAT_Mult, MAT_MultMatrixFree, MAT_Mults, MAT_MultConstrained, MAT_MultAdd, MAT_MultTranspose;
PETSC_EXTERN PetscLogEvent MAT_MultTransposeConstrained, MAT_MultTransposeAdd, MAT_Solve, MAT_Solves, MAT_SolveAdd, MAT_SolveTranspose;
PETSC_EXTERN PetscLogEvent MAT_SolveTransposeAdd, MAT_SOR, MAT_ForwardSolve, MAT_BackwardSolve, MAT_LUFactor, MAT_LUFactorSymbolic;
PETSC_EXTERN PetscLogEvent MAT_LUFactorNumeric, MAT_CholeskyFactor, MAT_CholeskyFactorSymbolic, MAT_CholeskyFactorNumeric, MAT_ILUFactor;
PETSC_EXTERN PetscLogEvent MAT_ILUFactorSymbolic, MAT_ICCFactorSymbolic, MAT_Copy, MAT_Convert, MAT_Scale, MAT_AssemblyBegin;
PETSC_EXTERN PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_GetSubMatrices, MAT_GetColoring, MAT_GetOrdering, MAT_GetRedundantMatrix;
PETSC_EXTERN PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate, MAT_TransposeColoringCreate;
PETSC_EXTERN PetscLogEvent MAT_FDColoringApply, MAT_Transpose, MAT_FDColoringFunction;
PETSC_EXTERN PetscLogEvent MAT_MatMult, MAT_MatSolve,MAT_MatMultSymbolic, MAT_MatMultNumeric,MAT_Getlocalmatcondensed,MAT_GetBrowsOfAcols,MAT_GetBrowsOfAocols;
PETSC_EXTERN PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric,MAT_Seqstompinum,MAT_Seqstompisym,MAT_Seqstompi,MAT_Getlocalmat;
PETSC_EXTERN PetscLogEvent MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
PETSC_EXTERN PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
PETSC_EXTERN PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
PETSC_EXTERN PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
PETSC_EXTERN PetscLogEvent MAT_Applypapt, MAT_Applypapt_symbolic, MAT_Applypapt_numeric;
PETSC_EXTERN PetscLogEvent MAT_Getsymtranspose, MAT_Transpose_SeqAIJ, MAT_Getsymtransreduced,MAT_GetSequentialNonzeroStructure;

PETSC_EXTERN PetscLogEvent MATMFFD_Mult;
PETSC_EXTERN PetscLogEvent MAT_GetMultiProcBlock;
PETSC_EXTERN PetscLogEvent MAT_CUSPCopyToGPU, MAT_CUSPARSECopyToGPU, MAT_SetValuesBatch, MAT_SetValuesBatchI, MAT_SetValuesBatchII, MAT_SetValuesBatchIII, MAT_SetValuesBatchIV;
PETSC_EXTERN PetscLogEvent MAT_ViennaCLCopyToGPU;
PETSC_EXTERN PetscLogEvent MAT_Merge,MAT_Residual;
PETSC_EXTERN PetscLogEvent Mat_Coloring_Apply,Mat_Coloring_Comm,Mat_Coloring_Local,Mat_Coloring_ISCreate,Mat_Coloring_SetUp;

#endif