Actual source code: matimpl.h
petsc-3.10.3 2018-12-18
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      2: #ifndef __MATIMPL_H

      5:  #include <petscmat.h>
      6:  #include <petscmatcoarsen.h>
      7:  #include <petsc/private/petscimpl.h>

      9: PETSC_EXTERN PetscBool MatRegisterAllCalled;
     10: PETSC_EXTERN PetscBool MatSeqAIJRegisterAllCalled;
     11: PETSC_EXTERN PetscBool MatOrderingRegisterAllCalled;
     12: PETSC_EXTERN PetscBool MatColoringRegisterAllCalled;
     13: PETSC_EXTERN PetscBool MatPartitioningRegisterAllCalled;
     14: PETSC_EXTERN PetscBool MatCoarsenRegisterAllCalled;
     15: PETSC_EXTERN PetscErrorCode MatRegisterAll(void);
     16: PETSC_EXTERN PetscErrorCode MatOrderingRegisterAll(void);
     17: PETSC_EXTERN PetscErrorCode MatColoringRegisterAll(void);
     18: PETSC_EXTERN PetscErrorCode MatPartitioningRegisterAll(void);
     19: PETSC_EXTERN PetscErrorCode MatCoarsenRegisterAll(void);
     20: PETSC_EXTERN PetscErrorCode MatSeqAIJRegisterAll(void);

     22: /*
     23:   This file defines the parts of the matrix data structure that are
     24:   shared by all matrix types.
     25: */

     27: /*
     28:     If you add entries here also add them to the MATOP enum
     29:     in include/petscmat.h and include/petsc/finclude/petscmat.h
     30: */
     31: typedef struct _MatOps *MatOps;
     32: struct _MatOps {
     33:   /* 0*/
     34:   PetscErrorCode (*setvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
     35:   PetscErrorCode (*getrow)(Mat,PetscInt,PetscInt *,PetscInt*[],PetscScalar*[]);
     36:   PetscErrorCode (*restorerow)(Mat,PetscInt,PetscInt *,PetscInt *[],PetscScalar *[]);
     37:   PetscErrorCode (*mult)(Mat,Vec,Vec);
     38:   PetscErrorCode (*multadd)(Mat,Vec,Vec,Vec);
     39:   /* 5*/
     40:   PetscErrorCode (*multtranspose)(Mat,Vec,Vec);
     41:   PetscErrorCode (*multtransposeadd)(Mat,Vec,Vec,Vec);
     42:   PetscErrorCode (*solve)(Mat,Vec,Vec);
     43:   PetscErrorCode (*solveadd)(Mat,Vec,Vec,Vec);
     44:   PetscErrorCode (*solvetranspose)(Mat,Vec,Vec);
     45:   /*10*/
     46:   PetscErrorCode (*solvetransposeadd)(Mat,Vec,Vec,Vec);
     47:   PetscErrorCode (*lufactor)(Mat,IS,IS,const MatFactorInfo*);
     48:   PetscErrorCode (*choleskyfactor)(Mat,IS,const MatFactorInfo*);
     49:   PetscErrorCode (*sor)(Mat,Vec,PetscReal,MatSORType,PetscReal,PetscInt,PetscInt,Vec);
     50:   PetscErrorCode (*transpose)(Mat,MatReuse,Mat *);
     51:   /*15*/
     52:   PetscErrorCode (*getinfo)(Mat,MatInfoType,MatInfo*);
     53:   PetscErrorCode (*equal)(Mat,Mat,PetscBool  *);
     54:   PetscErrorCode (*getdiagonal)(Mat,Vec);
     55:   PetscErrorCode (*diagonalscale)(Mat,Vec,Vec);
     56:   PetscErrorCode (*norm)(Mat,NormType,PetscReal*);
     57:   /*20*/
     58:   PetscErrorCode (*assemblybegin)(Mat,MatAssemblyType);
     59:   PetscErrorCode (*assemblyend)(Mat,MatAssemblyType);
     60:   PetscErrorCode (*setoption)(Mat,MatOption,PetscBool );
     61:   PetscErrorCode (*zeroentries)(Mat);
     62:   /*24*/
     63:   PetscErrorCode (*zerorows)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
     64:   PetscErrorCode (*lufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
     65:   PetscErrorCode (*lufactornumeric)(Mat,Mat,const MatFactorInfo*);
     66:   PetscErrorCode (*choleskyfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
     67:   PetscErrorCode (*choleskyfactornumeric)(Mat,Mat,const MatFactorInfo*);
     68:   /*29*/
     69:   PetscErrorCode (*setup)(Mat);
     70:   PetscErrorCode (*ilufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
     71:   PetscErrorCode (*iccfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
     72:   PetscErrorCode (*getdiagonalblock)(Mat,Mat*);
     73:   PetscErrorCode (*placeholder_33)(Mat);
     74:   /*34*/
     75:   PetscErrorCode (*duplicate)(Mat,MatDuplicateOption,Mat*);
     76:   PetscErrorCode (*forwardsolve)(Mat,Vec,Vec);
     77:   PetscErrorCode (*backwardsolve)(Mat,Vec,Vec);
     78:   PetscErrorCode (*ilufactor)(Mat,IS,IS,const MatFactorInfo*);
     79:   PetscErrorCode (*iccfactor)(Mat,IS,const MatFactorInfo*);
     80:   /*39*/
     81:   PetscErrorCode (*axpy)(Mat,PetscScalar,Mat,MatStructure);
     82:   PetscErrorCode (*createsubmatrices)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat *[]);
     83:   PetscErrorCode (*increaseoverlap)(Mat,PetscInt,IS[],PetscInt);
     84:   PetscErrorCode (*getvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],PetscScalar []);
     85:   PetscErrorCode (*copy)(Mat,Mat,MatStructure);
     86:   /*44*/
     87:   PetscErrorCode (*getrowmax)(Mat,Vec,PetscInt[]);
     88:   PetscErrorCode (*scale)(Mat,PetscScalar);
     89:   PetscErrorCode (*shift)(Mat,PetscScalar);
     90:   PetscErrorCode (*diagonalset)(Mat,Vec,InsertMode);
     91:   PetscErrorCode (*zerorowscolumns)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
     92:   /*49*/
     93:   PetscErrorCode (*setrandom)(Mat,PetscRandom);
     94:   PetscErrorCode (*getrowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     95:   PetscErrorCode (*restorerowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt *,const PetscInt *[],const PetscInt *[],PetscBool  *);
     96:   PetscErrorCode (*getcolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     97:   PetscErrorCode (*restorecolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     98:   /*54*/
     99:   PetscErrorCode (*fdcoloringcreate)(Mat,ISColoring,MatFDColoring);
    100:   PetscErrorCode (*coloringpatch)(Mat,PetscInt,PetscInt,ISColoringValue[],ISColoring*);
    101:   PetscErrorCode (*setunfactored)(Mat);
    102:   PetscErrorCode (*permute)(Mat,IS,IS,Mat*);
    103:   PetscErrorCode (*setvaluesblocked)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    104:   /*59*/
    105:   PetscErrorCode (*createsubmatrix)(Mat,IS,IS,MatReuse,Mat*);
    106:   PetscErrorCode (*destroy)(Mat);
    107:   PetscErrorCode (*view)(Mat,PetscViewer);
    108:   PetscErrorCode (*convertfrom)(Mat, MatType,MatReuse,Mat*);
    109:   PetscErrorCode (*matmatmult)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
    110:   /*64*/
    111:   PetscErrorCode (*matmatmultsymbolic)(Mat,Mat,Mat,PetscReal,Mat*);
    112:   PetscErrorCode (*matmatmultnumeric)(Mat,Mat,Mat,Mat);
    113:   PetscErrorCode (*setlocaltoglobalmapping)(Mat,ISLocalToGlobalMapping,ISLocalToGlobalMapping);
    114:   PetscErrorCode (*setvalueslocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    115:   PetscErrorCode (*zerorowslocal)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
    116:   /*69*/
    117:   PetscErrorCode (*getrowmaxabs)(Mat,Vec,PetscInt[]);
    118:   PetscErrorCode (*getrowminabs)(Mat,Vec,PetscInt[]);
    119:   PetscErrorCode (*convert)(Mat, MatType,MatReuse,Mat*);
    120:   PetscErrorCode (*hasoperation)(Mat,MatOperation,PetscBool*);
    121:   PetscErrorCode (*placeholder_73)(Mat,void*);
    122:   /*74*/
    123:   PetscErrorCode (*setvaluesadifor)(Mat,PetscInt,void*);
    124:   PetscErrorCode (*fdcoloringapply)(Mat,MatFDColoring,Vec,void*);
    125:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,Mat);
    126:   PetscErrorCode (*multconstrained)(Mat,Vec,Vec);
    127:   PetscErrorCode (*multtransposeconstrained)(Mat,Vec,Vec);
    128:   /*79*/
    129:   PetscErrorCode (*findzerodiagonals)(Mat,IS*);
    130:   PetscErrorCode (*mults)(Mat, Vecs, Vecs);
    131:   PetscErrorCode (*solves)(Mat, Vecs, Vecs);
    132:   PetscErrorCode (*getinertia)(Mat,PetscInt*,PetscInt*,PetscInt*);
    133:   PetscErrorCode (*load)(Mat, PetscViewer);
    134:   /*84*/
    135:   PetscErrorCode (*issymmetric)(Mat,PetscReal,PetscBool *);
    136:   PetscErrorCode (*ishermitian)(Mat,PetscReal,PetscBool *);
    137:   PetscErrorCode (*isstructurallysymmetric)(Mat,PetscBool *);
    138:   PetscErrorCode (*setvaluesblockedlocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    139:   PetscErrorCode (*getvecs)(Mat,Vec*,Vec*);
    140:   /*89*/
    141:   PetscErrorCode (*matmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    142:   PetscErrorCode (*matmultsymbolic)(Mat,Mat,PetscReal,Mat*);
    143:   PetscErrorCode (*matmultnumeric)(Mat,Mat,Mat);
    144:   PetscErrorCode (*ptap)(Mat,Mat,MatReuse,PetscReal,Mat*);
    145:   PetscErrorCode (*ptapsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
    146:   /*94*/
    147:   PetscErrorCode (*ptapnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
    148:   PetscErrorCode (*mattransposemult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    149:   PetscErrorCode (*mattransposemultsymbolic)(Mat,Mat,PetscReal,Mat*);
    150:   PetscErrorCode (*mattransposemultnumeric)(Mat,Mat,Mat);
    151:   PetscErrorCode (*placeholder_98)(Mat);
    152:   /*99*/
    153:   PetscErrorCode (*placeholder_99)(Mat);
    154:   PetscErrorCode (*placeholder_100)(Mat);
    155:   PetscErrorCode (*placeholder_101)(Mat);
    156:   PetscErrorCode (*conjugate)(Mat);                              /* complex conjugate */
    157:   PetscErrorCode (*viewnative)(Mat,PetscViewer);
    158:   /*104*/
    159:   PetscErrorCode (*setvaluesrow)(Mat,PetscInt,const PetscScalar[]);
    160:   PetscErrorCode (*realpart)(Mat);
    161:   PetscErrorCode (*imaginarypart)(Mat);
    162:   PetscErrorCode (*getrowuppertriangular)(Mat);
    163:   PetscErrorCode (*restorerowuppertriangular)(Mat);
    164:   /*109*/
    165:   PetscErrorCode (*matsolve)(Mat,Mat,Mat);
    166:   PetscErrorCode (*matsolvetranspose)(Mat,Mat,Mat);
    167:   PetscErrorCode (*getrowmin)(Mat,Vec,PetscInt[]);
    168:   PetscErrorCode (*getcolumnvector)(Mat,Vec,PetscInt);
    169:   PetscErrorCode (*missingdiagonal)(Mat,PetscBool *,PetscInt*);
    170:   /*114*/
    171:   PetscErrorCode (*getseqnonzerostructure)(Mat,Mat *);
    172:   PetscErrorCode (*create)(Mat);
    173:   PetscErrorCode (*getghosts)(Mat,PetscInt*,const PetscInt *[]);
    174:   PetscErrorCode (*getlocalsubmatrix)(Mat,IS,IS,Mat*);
    175:   PetscErrorCode (*restorelocalsubmatrix)(Mat,IS,IS,Mat*);
    176:   /*119*/
    177:   PetscErrorCode (*multdiagonalblock)(Mat,Vec,Vec);
    178:   PetscErrorCode (*hermitiantranspose)(Mat,MatReuse,Mat*);
    179:   PetscErrorCode (*multhermitiantranspose)(Mat,Vec,Vec);
    180:   PetscErrorCode (*multhermitiantransposeadd)(Mat,Vec,Vec,Vec);
    181:   PetscErrorCode (*getmultiprocblock)(Mat,MPI_Comm,MatReuse,Mat*);
    182:   /*124*/
    183:   PetscErrorCode (*findnonzerorows)(Mat,IS*);
    184:   PetscErrorCode (*getcolumnnorms)(Mat,NormType,PetscReal*);
    185:   PetscErrorCode (*invertblockdiagonal)(Mat,const PetscScalar**);
    186:   PetscErrorCode (*invertvariableblockdiagonal)(Mat,PetscInt,const PetscInt*,PetscScalar*);
    187:   PetscErrorCode (*createsubmatricesmpi)(Mat,PetscInt,const IS[], const IS[], MatReuse, Mat**);
    188:   /*129*/
    189:   PetscErrorCode (*setvaluesbatch)(Mat,PetscInt,PetscInt,PetscInt*,const PetscScalar*);
    190:   PetscErrorCode (*transposematmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    191:   PetscErrorCode (*transposematmultsymbolic)(Mat,Mat,PetscReal,Mat*);
    192:   PetscErrorCode (*transposematmultnumeric)(Mat,Mat,Mat);
    193:   PetscErrorCode (*transposecoloringcreate)(Mat,ISColoring,MatTransposeColoring);
    194:   /*134*/
    195:   PetscErrorCode (*transcoloringapplysptoden)(MatTransposeColoring,Mat,Mat);
    196:   PetscErrorCode (*transcoloringapplydentosp)(MatTransposeColoring,Mat,Mat);
    197:   PetscErrorCode (*rart)(Mat,Mat,MatReuse,PetscReal,Mat*);
    198:   PetscErrorCode (*rartsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
    199:   PetscErrorCode (*rartnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
    200:   /*139*/
    201:   PetscErrorCode (*setblocksizes)(Mat,PetscInt,PetscInt);
    202:   PetscErrorCode (*aypx)(Mat,PetscScalar,Mat,MatStructure);
    203:   PetscErrorCode (*residual)(Mat,Vec,Vec,Vec);
    204:   PetscErrorCode (*fdcoloringsetup)(Mat,ISColoring,MatFDColoring);
    205:   PetscErrorCode (*findoffblockdiagonalentries)(Mat,IS*);
    206:   /*144*/
    207:   PetscErrorCode (*creatempimatconcatenateseqmat)(MPI_Comm,Mat,PetscInt,MatReuse,Mat*);
    208:   PetscErrorCode (*destroysubmatrices)(PetscInt,Mat*[]);
    209:   PetscErrorCode (*mattransposesolve)(Mat,Mat,Mat);
    210: };
    211: /*
    212:     If you add MatOps entries above also add them to the MATOP enum
    213:     in include/petscmat.h and include/petsc/finclude/petscmat.h
    214: */

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

    220: typedef struct _p_MatBaseName* MatBaseName;
    221: struct _p_MatBaseName {
    222:   char        *bname,*sname,*mname;
    223:   MatBaseName next;
    224: };

    226: PETSC_EXTERN MatBaseName MatBaseNameList;

    228: /*
    229:    Utility private matrix routines
    230: */
    231: PETSC_INTERN PetscErrorCode MatFindNonzeroRowsOrCols_Basic(Mat,PetscBool,PetscReal,IS*);
    232: PETSC_INTERN PetscErrorCode MatConvert_Basic(Mat,MatType,MatReuse,Mat*);
    233: PETSC_INTERN PetscErrorCode MatCopy_Basic(Mat,Mat,MatStructure);
    234: PETSC_INTERN PetscErrorCode MatDiagonalSet_Default(Mat,Vec,InsertMode);

    236: #if defined(PETSC_USE_DEBUG)
    237: #  define MatCheckPreallocated(A,arg) do {                              \
    238:     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); \
    239:   } while (0)
    240: #else
    241: #  define MatCheckPreallocated(A,arg) do {} while (0)
    242: #endif

    244: /*
    245:   The stash is used to temporarily store inserted matrix values that
    246:   belong to another processor. During the assembly phase the stashed
    247:   values are moved to the correct processor and
    248: */

    250: typedef struct _MatStashSpace *PetscMatStashSpace;

    252: struct _MatStashSpace {
    253:   PetscMatStashSpace next;
    254:   PetscScalar        *space_head,*val;
    255:   PetscInt           *idx,*idy;
    256:   PetscInt           total_space_size;
    257:   PetscInt           local_used;
    258:   PetscInt           local_remaining;
    259: };

    261: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceGet(PetscInt,PetscInt,PetscMatStashSpace *);
    262: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceContiguous(PetscInt,PetscMatStashSpace *,PetscScalar *,PetscInt *,PetscInt *);
    263: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceDestroy(PetscMatStashSpace*);

    265: typedef struct {
    266:   PetscInt    count;
    267: } MatStashHeader;

    269: typedef struct {
    270:   void        *buffer;          /* Of type blocktype, dynamically constructed  */
    271:   PetscInt    count;
    272:   char        pending;
    273: } MatStashFrame;

    275: typedef struct _MatStash MatStash;
    276: struct _MatStash {
    277:   PetscInt      nmax;                   /* maximum stash size */
    278:   PetscInt      umax;                   /* user specified max-size */
    279:   PetscInt      oldnmax;                /* the nmax value used previously */
    280:   PetscInt      n;                      /* stash size */
    281:   PetscInt      bs;                     /* block size of the stash */
    282:   PetscInt      reallocs;               /* preserve the no of mallocs invoked */
    283:   PetscMatStashSpace space_head,space;  /* linked list to hold stashed global row/column numbers and matrix values */

    285:   PetscErrorCode (*ScatterBegin)(Mat,MatStash*,PetscInt*);
    286:   PetscErrorCode (*ScatterGetMesg)(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    287:   PetscErrorCode (*ScatterEnd)(MatStash*);
    288:   PetscErrorCode (*ScatterDestroy)(MatStash*);

    290:   /* The following variables are used for communication */
    291:   MPI_Comm      comm;
    292:   PetscMPIInt   size,rank;
    293:   PetscMPIInt   tag1,tag2;
    294:   MPI_Request   *send_waits;            /* array of send requests */
    295:   MPI_Request   *recv_waits;            /* array of receive requests */
    296:   MPI_Status    *send_status;           /* array of send status */
    297:   PetscInt      nsends,nrecvs;          /* numbers of sends and receives */
    298:   PetscScalar   *svalues;               /* sending data */
    299:   PetscInt      *sindices;
    300:   PetscScalar   **rvalues;              /* receiving data (values) */
    301:   PetscInt      **rindices;             /* receiving data (indices) */
    302:   PetscInt      nprocessed;             /* number of messages already processed */
    303:   PetscMPIInt   *flg_v;                 /* indicates what messages have arrived so far and from whom */
    304:   PetscBool     reproduce;
    305:   PetscInt      reproduce_count;

    307:   /* The following variables are used for BTS communication */
    308:   PetscBool      subset_off_proc; /* Subsequent assemblies will set a subset (perhaps equal) of off-process entries set on first assembly */
    309:   PetscBool      use_status;      /* Use MPI_Status to determine number of items in each message */
    310:   PetscMPIInt    nsendranks;
    311:   PetscMPIInt    nrecvranks;
    312:   PetscMPIInt    *sendranks;
    313:   PetscMPIInt    *recvranks;
    314:   MatStashHeader *sendhdr,*recvhdr;
    315:   MatStashFrame  *sendframes;   /* pointers to the main messages */
    316:   MatStashFrame  *recvframes;
    317:   MatStashFrame  *recvframe_active;
    318:   PetscInt       recvframe_i;     /* index of block within active frame */
    319:   PetscMPIInt    recvframe_count; /* Count actually sent for current frame */
    320:   PetscInt       recvcount;       /* Number of receives processed so far */
    321:   PetscMPIInt    *some_indices;   /* From last call to MPI_Waitsome */
    322:   MPI_Status     *some_statuses;  /* Statuses from last call to MPI_Waitsome */
    323:   PetscMPIInt    some_count;      /* Number of requests completed in last call to MPI_Waitsome */
    324:   PetscMPIInt    some_i;          /* Index of request currently being processed */
    325:   MPI_Request    *sendreqs;
    326:   MPI_Request    *recvreqs;
    327:   PetscSegBuffer segsendblocks;
    328:   PetscSegBuffer segrecvframe;
    329:   PetscSegBuffer segrecvblocks;
    330:   MPI_Datatype   blocktype;
    331:   size_t         blocktype_size;
    332:   InsertMode     *insertmode;   /* Pointer to check mat->insertmode and set upon message arrival in case no local values have been set. */
    333: };

    335: PETSC_INTERN PetscErrorCode MatStashCreate_Private(MPI_Comm,PetscInt,MatStash*);
    336: PETSC_INTERN PetscErrorCode MatStashDestroy_Private(MatStash*);
    337: PETSC_INTERN PetscErrorCode MatStashScatterEnd_Private(MatStash*);
    338: PETSC_INTERN PetscErrorCode MatStashSetInitialSize_Private(MatStash*,PetscInt);
    339: PETSC_INTERN PetscErrorCode MatStashGetInfo_Private(MatStash*,PetscInt*,PetscInt*);
    340: PETSC_INTERN PetscErrorCode MatStashValuesRow_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscBool );
    341: PETSC_INTERN PetscErrorCode MatStashValuesCol_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscBool );
    342: PETSC_INTERN PetscErrorCode MatStashValuesRowBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    343: PETSC_INTERN PetscErrorCode MatStashValuesColBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    344: PETSC_INTERN PetscErrorCode MatStashScatterBegin_Private(Mat,MatStash*,PetscInt*);
    345: PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Private(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    346: PETSC_INTERN PetscErrorCode MatGetInfo_External(Mat,MatInfoType,MatInfo*);

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

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

    364: typedef struct { /* used by MatCreateRedundantMatrix() for reusing matredundant */
    365:   PetscInt     nzlocal,nsends,nrecvs;
    366:   PetscMPIInt  *send_rank,*recv_rank;
    367:   PetscInt     *sbuf_nz,*rbuf_nz,*sbuf_j,**rbuf_j;
    368:   PetscScalar  *sbuf_a,**rbuf_a;
    369:   MPI_Comm     subcomm;   /* when user does not provide a subcomm */
    370:   IS           isrow,iscol;
    371:   Mat          *matseq;
    372: } Mat_Redundant;

    374: struct _p_Mat {
    375:   PETSCHEADER(struct _MatOps);
    376:   PetscLayout            rmap,cmap;
    377:   void                   *data;            /* implementation-specific data */
    378:   MatFactorType          factortype;       /* MAT_FACTOR_LU, ILU, CHOLESKY or ICC */
    379:   PetscBool              assembled;        /* is the matrix assembled? */
    380:   PetscBool              was_assembled;    /* new values inserted into assembled mat */
    381:   PetscInt               num_ass;          /* number of times matrix has been assembled */
    382:   PetscObjectState       nonzerostate;     /* each time new nonzeros locations are introduced into the matrix this is updated */
    383:   MatInfo                info;             /* matrix information */
    384:   InsertMode             insertmode;       /* have values been inserted in matrix or added? */
    385:   MatStash               stash,bstash;     /* used for assembling off-proc mat emements */
    386:   MatNullSpace           nullsp;           /* null space (operator is singular) */
    387:   MatNullSpace           transnullsp;      /* null space of transpose of operator */
    388:   MatNullSpace           nearnullsp;       /* near null space to be used by multigrid methods */
    389:   PetscInt               congruentlayouts; /* are the rows and columns layouts congruent? */
    390:   PetscBool              preallocated;
    391:   MatStencilInfo         stencil;          /* information for structured grid */
    392:   PetscBool              symmetric,hermitian,structurally_symmetric,spd;
    393:   PetscBool              symmetric_set,hermitian_set,structurally_symmetric_set,spd_set; /* if true, then corresponding flag is correct*/
    394:   PetscBool              symmetric_eternal;
    395:   PetscBool              nooffprocentries,nooffproczerorows;
    396:   PetscBool              subsetoffprocentries;
    397:   PetscBool              submat_singleis; /* for efficient PCSetUP_ASM() */
    398:   PetscBool              structure_only;
    399: #if defined(PETSC_HAVE_VIENNACL) || defined(PETSC_HAVE_VECCUDA)
    400:   PetscOffloadFlag       valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
    401: #endif
    402:   void                   *spptr;          /* pointer for special library like SuperLU */
    403:   char                   *solvertype;
    404:   PetscBool              checksymmetryonassembly,checknullspaceonassembly;
    405:   PetscReal              checksymmetrytol;
    406:   Mat                    schur;             /* Schur complement matrix */
    407:   MatFactorSchurStatus   schur_status;      /* status of the Schur complement matrix */
    408:   Mat_Redundant          *redundant;        /* used by MatCreateRedundantMatrix() */
    409:   PetscBool              erroriffailure;    /* Generate an error if detected (for example a zero pivot) instead of returning */
    410:   MatFactorError         factorerrortype;               /* type of error in factorization */
    411:   PetscReal              factorerror_zeropivot_value;   /* If numerical zero pivot was detected this is the computed value */
    412:   PetscInt               factorerror_zeropivot_row;     /* Row where zero pivot was detected */
    413:   PetscInt               nblocks,*bsizes;   /* support for MatSetVariableBlockSizes() */
    414:   char                   *defaultvectype;
    415: };

    417: PETSC_INTERN PetscErrorCode MatAXPY_Basic(Mat,PetscScalar,Mat,MatStructure);
    418: PETSC_INTERN PetscErrorCode MatAXPY_BasicWithPreallocation(Mat,Mat,PetscScalar,Mat,MatStructure);

    420: /*
    421:     Utility for MatFactor (Schur complement)
    422: */
    423: PETSC_INTERN PetscErrorCode MatFactorFactorizeSchurComplement_Private(Mat);
    424: PETSC_INTERN PetscErrorCode MatFactorInvertSchurComplement_Private(Mat);
    425: PETSC_INTERN PetscErrorCode MatFactorUpdateSchurStatus_Private(Mat);
    426: PETSC_INTERN PetscErrorCode MatFactorSetUpInPlaceSchur_Private(Mat);

    428: /*
    429:     Utility for MatZeroRows
    430: */
    431: PETSC_INTERN PetscErrorCode MatZeroRowsMapLocal_Private(Mat,PetscInt,const PetscInt*,PetscInt*,PetscInt**);

    433: /*
    434:     Object for partitioning graphs
    435: */

    437: typedef struct _MatPartitioningOps *MatPartitioningOps;
    438: struct _MatPartitioningOps {
    439:   PetscErrorCode (*apply)(MatPartitioning,IS*);
    440:   PetscErrorCode (*applynd)(MatPartitioning,IS*);
    441:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatPartitioning);
    442:   PetscErrorCode (*destroy)(MatPartitioning);
    443:   PetscErrorCode (*view)(MatPartitioning,PetscViewer);
    444: };

    446: struct _p_MatPartitioning {
    447:   PETSCHEADER(struct _MatPartitioningOps);
    448:   Mat         adj;
    449:   PetscInt    *vertex_weights;
    450:   PetscReal   *part_weights;
    451:   PetscInt    n;                                 /* number of partitions */
    452:   void        *data;
    453:   PetscInt    setupcalled;
    454: };

    456: /* needed for parallel nested dissection by ParMetis and PTSCOTCH */
    457: PETSC_INTERN PetscErrorCode MatPartitioningSizesToSep_Private(PetscInt,PetscInt[],PetscInt[],PetscInt[]);

    459: /*
    460:     Object for coarsen graphs
    461: */
    462: typedef struct _MatCoarsenOps *MatCoarsenOps;
    463: struct _MatCoarsenOps {
    464:   PetscErrorCode (*apply)(MatCoarsen);
    465:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatCoarsen);
    466:   PetscErrorCode (*destroy)(MatCoarsen);
    467:   PetscErrorCode (*view)(MatCoarsen,PetscViewer);
    468: };

    470: struct _p_MatCoarsen {
    471:   PETSCHEADER(struct _MatCoarsenOps);
    472:   Mat              graph;
    473:   PetscInt         setupcalled;
    474:   void             *subctx;
    475:   /* */
    476:   PetscBool        strict_aggs;
    477:   IS               perm;
    478:   PetscCoarsenData *agg_lists;
    479: };

    481: /*
    482:     MatFDColoring is used to compute Jacobian matrices efficiently
    483:   via coloring. The data structure is explained below in an example.

    485:    Color =   0    1     0    2   |   2      3       0
    486:    ---------------------------------------------------
    487:             00   01              |          05
    488:             10   11              |   14     15               Processor  0
    489:                        22    23  |          25
    490:                        32    33  |
    491:    ===================================================
    492:                                  |   44     45     46
    493:             50                   |          55               Processor 1
    494:                                  |   64            66
    495:    ---------------------------------------------------

    497:     ncolors = 4;

    499:     ncolumns      = {2,1,1,0}
    500:     columns       = {{0,2},{1},{3},{}}
    501:     nrows         = {4,2,3,3}
    502:     rows          = {{0,1,2,3},{0,1},{1,2,3},{0,1,2}}
    503:     vwscale       = {dx(0),dx(1),dx(2),dx(3)}               MPI Vec
    504:     vscale        = {dx(0),dx(1),dx(2),dx(3),dx(4),dx(5)}   Seq Vec

    506:     ncolumns      = {1,0,1,1}
    507:     columns       = {{6},{},{4},{5}}
    508:     nrows         = {3,0,2,2}
    509:     rows          = {{0,1,2},{},{1,2},{1,2}}
    510:     vwscale       = {dx(4),dx(5),dx(6)}              MPI Vec
    511:     vscale        = {dx(0),dx(4),dx(5),dx(6)}        Seq Vec

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

    516: */
    517: typedef struct {
    518:   PetscInt     row;
    519:   PetscInt     col;
    520:   PetscScalar  *valaddr;   /* address of value */
    521: } MatEntry;

    523: typedef struct {
    524:   PetscInt     row;
    525:   PetscScalar  *valaddr;   /* address of value */
    526: } MatEntry2;

    528: struct  _p_MatFDColoring{
    529:   PETSCHEADER(int);
    530:   PetscInt       M,N,m;            /* total rows, columns; local rows */
    531:   PetscInt       rstart;           /* first row owned by local processor */
    532:   PetscInt       ncolors;          /* number of colors */
    533:   PetscInt       *ncolumns;        /* number of local columns for a color */
    534:   PetscInt       **columns;        /* lists the local columns of each color (using global column numbering) */
    535:   PetscInt       *nrows;           /* number of local rows for each color */
    536:   MatEntry       *matentry;        /* holds (row, column, address of value) for Jacobian matrix entry */
    537:   MatEntry2      *matentry2;       /* holds (row, address of value) for Jacobian matrix entry */
    538:   PetscScalar    *dy;              /* store a block of F(x+dx)-F(x) when J is in BAIJ format */
    539:   PetscReal      error_rel;        /* square root of relative error in computing function */
    540:   PetscReal      umin;             /* minimum allowable u'dx value */
    541:   Vec            w1,w2,w3;         /* work vectors used in computing Jacobian */
    542:   PetscBool      fset;             /* indicates that the initial function value F(X) is set */
    543:   PetscErrorCode (*f)(void);       /* function that defines Jacobian */
    544:   void           *fctx;            /* optional user-defined context for use by the function f */
    545:   Vec            vscale;           /* holds FD scaling, i.e. 1/dx for each perturbed column */
    546:   PetscInt       currentcolor;     /* color for which function evaluation is being done now */
    547:   const char     *htype;           /* "wp" or "ds" */
    548:   ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_LOCAL */
    549:   PetscInt       brows,bcols;      /* number of block rows or columns for speedup inserting the dense matrix into sparse Jacobian */
    550:   PetscBool      setupcalled;      /* true if setup has been called */
    551:   PetscBool      viewed;           /* true if the -mat_fd_coloring_view has been triggered already */
    552:   void           (*ftn_func_pointer)(void),*ftn_func_cntx; /* serve the same purpose as *fortran_func_pointers in PETSc objects */
    553: };

    555: typedef struct _MatColoringOps *MatColoringOps;
    556: struct _MatColoringOps {
    557:   PetscErrorCode (*destroy)(MatColoring);
    558:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatColoring);
    559:   PetscErrorCode (*view)(MatColoring,PetscViewer);
    560:   PetscErrorCode (*apply)(MatColoring,ISColoring*);
    561:   PetscErrorCode (*weights)(MatColoring,PetscReal**,PetscInt**);
    562: };

    564: struct _p_MatColoring {
    565:   PETSCHEADER(struct _MatColoringOps);
    566:   Mat                   mat;
    567:   PetscInt              dist;             /* distance of the coloring */
    568:   PetscInt              maxcolors;        /* the maximum number of colors returned, maxcolors=1 for MIS */
    569:   void                  *data;            /* inner context */
    570:   PetscBool             valid;            /* check to see if what is produced is a valid coloring */
    571:   MatColoringWeightType weight_type;      /* type of weight computation to be performed */
    572:   PetscReal             *user_weights;    /* custom weights and permutation */
    573:   PetscInt              *user_lperm;
    574:   PetscBool             valid_iscoloring; /* check to see if matcoloring is produced a valid iscoloring */
    575: };

    577: struct  _p_MatTransposeColoring{
    578:   PETSCHEADER(int);
    579:   PetscInt       M,N,m;            /* total rows, columns; local rows */
    580:   PetscInt       rstart;           /* first row owned by local processor */
    581:   PetscInt       ncolors;          /* number of colors */
    582:   PetscInt       *ncolumns;        /* number of local columns for a color */
    583:   PetscInt       *nrows;           /* number of local rows for each color */
    584:   PetscInt       currentcolor;     /* color for which function evaluation is being done now */
    585:   ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_LOCAL */

    587:   PetscInt       *colorforrow,*colorforcol;  /* pointer to rows and columns */
    588:   PetscInt       *rows;                      /* lists the local rows for each color (using the local row numbering) */
    589:   PetscInt       *den2sp;                    /* maps (row,color) in the dense matrix to index of sparse matrix array a->a */
    590:   PetscInt       *columns;                   /* lists the local columns of each color (using global column numbering) */
    591:   PetscInt       brows;                      /* number of rows for efficient implementation of MatTransColoringApplyDenToSp() */
    592:   PetscInt       *lstart;                    /* array used for loop over row blocks of Csparse */
    593: };

    595: /*
    596:    Null space context for preconditioner/operators
    597: */
    598: struct _p_MatNullSpace {
    599:   PETSCHEADER(int);
    600:   PetscBool      has_cnst;
    601:   PetscInt       n;
    602:   Vec*           vecs;
    603:   PetscScalar*   alpha;                 /* for projections */
    604:   PetscErrorCode (*remove)(MatNullSpace,Vec,void*);  /* for user provided removal function */
    605:   void*          rmctx;                 /* context for remove() function */
    606: };

    608: /*
    609:    Checking zero pivot for LU, ILU preconditioners.
    610: */
    611: typedef struct {
    612:   PetscInt       nshift,nshift_max;
    613:   PetscReal      shift_amount,shift_lo,shift_hi,shift_top,shift_fraction;
    614:   PetscBool      newshift;
    615:   PetscReal      rs;  /* active row sum of abs(offdiagonals) */
    616:   PetscScalar    pv;  /* pivot of the active row */
    617: } FactorShiftCtx;

    619: /*
    620:  Used by MatCreateSubMatrices_MPIXAIJ_Local()
    621: */
    622:  #include <petscctable.h>
    623: typedef struct { /* used by MatCreateSubMatrices_MPIAIJ_SingleIS_Local() and MatCreateSubMatrices_MPIAIJ_Local */
    624:   PetscInt   id;   /* index of submats, only submats[0] is responsible for deleting some arrays below */
    625:   PetscInt   nrqs,nrqr;
    626:   PetscInt   **rbuf1,**rbuf2,**rbuf3,**sbuf1,**sbuf2;
    627:   PetscInt   **ptr;
    628:   PetscInt   *tmp;
    629:   PetscInt   *ctr;
    630:   PetscInt   *pa; /* proc array */
    631:   PetscInt   *req_size,*req_source1,*req_source2;
    632:   PetscBool  allcolumns,allrows;
    633:   PetscBool  singleis;
    634:   PetscInt   *row2proc; /* row to proc map */
    635:   PetscInt   nstages;
    636: #if defined(PETSC_USE_CTABLE)
    637:   PetscTable cmap,rmap;
    638:   PetscInt   *cmap_loc,*rmap_loc;
    639: #else
    640:   PetscInt   *cmap,*rmap;
    641: #endif

    643:   PetscErrorCode (*destroy)(Mat);
    644: } Mat_SubSppt;

    646: PETSC_EXTERN PetscErrorCode MatFactorDumpMatrix(Mat);
    647: PETSC_INTERN PetscErrorCode MatShift_Basic(Mat,PetscScalar);
    648: PETSC_INTERN PetscErrorCode MatSetBlockSizes_Default(Mat,PetscInt,PetscInt);

    650: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_nz(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    651: {
    652:   PetscReal _rs   = sctx->rs;
    653:   PetscReal _zero = info->zeropivot*_rs;

    656:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    657:     /* force |diag| > zeropivot*rs */
    658:     if (!sctx->nshift) sctx->shift_amount = info->shiftamount;
    659:     else sctx->shift_amount *= 2.0;
    660:     sctx->newshift = PETSC_TRUE;
    661:     (sctx->nshift)++;
    662:   } else {
    663:     sctx->newshift = PETSC_FALSE;
    664:   }
    665:   return(0);
    666: }

    668: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_pd(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    669: {
    670:   PetscReal _rs   = sctx->rs;
    671:   PetscReal _zero = info->zeropivot*_rs;

    674:   if (PetscRealPart(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    675:     /* force matfactor to be diagonally dominant */
    676:     if (sctx->nshift == sctx->nshift_max) {
    677:       sctx->shift_fraction = sctx->shift_hi;
    678:     } else {
    679:       sctx->shift_lo = sctx->shift_fraction;
    680:       sctx->shift_fraction = (sctx->shift_hi+sctx->shift_lo)/2.;
    681:     }
    682:     sctx->shift_amount = sctx->shift_fraction * sctx->shift_top;
    683:     sctx->nshift++;
    684:     sctx->newshift = PETSC_TRUE;
    685:   } else {
    686:     sctx->newshift = PETSC_FALSE;
    687:   }
    688:   return(0);
    689: }

    691: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_inblocks(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    692: {
    693:   PetscReal _zero = info->zeropivot;

    696:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    697:     sctx->pv          += info->shiftamount;
    698:     sctx->shift_amount = 0.0;
    699:     sctx->nshift++;
    700:   }
    701:   sctx->newshift = PETSC_FALSE;
    702:   return(0);
    703: }

    705: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_none(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    706: {
    707:   PetscReal      _zero = info->zeropivot;

    711:   sctx->newshift = PETSC_FALSE;
    712:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)) {
    713:     if (!mat->erroriffailure) {
    714:       PetscInfo3(mat,"Detected zero pivot in factorization in row %D value %g tolerance %g\n",row,(double)PetscAbsScalar(sctx->pv),(double)_zero);
    715:       fact->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    716:       fact->factorerror_zeropivot_value = PetscAbsScalar(sctx->pv);
    717:       fact->factorerror_zeropivot_row   = row;
    718:     } else SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot row %D value %g tolerance %g\n",row,(double)PetscAbsScalar(sctx->pv),(double)_zero);
    719:   }
    720:   return(0);
    721: }

    723: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    724: {

    728:   if (info->shifttype == (PetscReal) MAT_SHIFT_NONZERO){
    729:     MatPivotCheck_nz(mat,info,sctx,row);
    730:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE){
    731:     MatPivotCheck_pd(mat,info,sctx,row);
    732:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_INBLOCKS){
    733:     MatPivotCheck_inblocks(mat,info,sctx,row);
    734:   } else {
    735:     MatPivotCheck_none(fact,mat,info,sctx,row);
    736:   }
    737:   return(0);
    738: }

    740: /*
    741:   Create and initialize a linked list
    742:   Input Parameters:
    743:     idx_start - starting index of the list
    744:     lnk_max   - max value of lnk indicating the end of the list
    745:     nlnk      - max length of the list
    746:   Output Parameters:
    747:     lnk       - list initialized
    748:     bt        - PetscBT (bitarray) with all bits set to false
    749:     lnk_empty - flg indicating the list is empty
    750: */
    751: #define PetscLLCreate(idx_start,lnk_max,nlnk,lnk,bt) \
    752:   (PetscMalloc1(nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,0))

    754: #define PetscLLCreate_new(idx_start,lnk_max,nlnk,lnk,bt,lnk_empty)\
    755:   (PetscMalloc1(nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk_empty = PETSC_TRUE,0) ||(lnk[idx_start] = lnk_max,0))

    757: /*
    758:   Add an index set into a sorted linked list
    759:   Input Parameters:
    760:     nidx      - number of input indices
    761:     indices   - integer array
    762:     idx_start - starting index of the list
    763:     lnk       - linked list(an integer array) that is created
    764:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    765:   output Parameters:
    766:     nlnk      - number of newly added indices
    767:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    768:     bt        - updated PetscBT (bitarray)
    769: */
    770: #define PetscLLAdd(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    771: {\
    772:   PetscInt _k,_entry,_location,_lnkdata;\
    773:   nlnk     = 0;\
    774:   _lnkdata = idx_start;\
    775:   for (_k=0; _k<nidx; _k++){\
    776:     _entry = indices[_k];\
    777:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    778:       /* search for insertion location */\
    779:       /* start from the beginning if _entry < previous _entry */\
    780:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    781:       do {\
    782:         _location = _lnkdata;\
    783:         _lnkdata  = lnk[_location];\
    784:       } while (_entry > _lnkdata);\
    785:       /* insertion location is found, add entry into lnk */\
    786:       lnk[_location] = _entry;\
    787:       lnk[_entry]    = _lnkdata;\
    788:       nlnk++;\
    789:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    790:     }\
    791:   }\
    792: }

    794: /*
    795:   Add a permuted index set into a sorted linked list
    796:   Input Parameters:
    797:     nidx      - number of input indices
    798:     indices   - integer array
    799:     perm      - permutation of indices
    800:     idx_start - starting index of the list
    801:     lnk       - linked list(an integer array) that is created
    802:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    803:   output Parameters:
    804:     nlnk      - number of newly added indices
    805:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    806:     bt        - updated PetscBT (bitarray)
    807: */
    808: #define PetscLLAddPerm(nidx,indices,perm,idx_start,nlnk,lnk,bt) 0;\
    809: {\
    810:   PetscInt _k,_entry,_location,_lnkdata;\
    811:   nlnk     = 0;\
    812:   _lnkdata = idx_start;\
    813:   for (_k=0; _k<nidx; _k++){\
    814:     _entry = perm[indices[_k]];\
    815:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    816:       /* search for insertion location */\
    817:       /* start from the beginning if _entry < previous _entry */\
    818:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    819:       do {\
    820:         _location = _lnkdata;\
    821:         _lnkdata  = lnk[_location];\
    822:       } while (_entry > _lnkdata);\
    823:       /* insertion location is found, add entry into lnk */\
    824:       lnk[_location] = _entry;\
    825:       lnk[_entry]    = _lnkdata;\
    826:       nlnk++;\
    827:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    828:     }\
    829:   }\
    830: }

    832: /*
    833:   Add a SORTED ascending index set into a sorted linked list - same as PetscLLAdd() bus skip 'if (_k && _entry < _lnkdata) _lnkdata  = idx_start;'
    834:   Input Parameters:
    835:     nidx      - number of input indices
    836:     indices   - sorted integer array
    837:     idx_start - starting index of the list
    838:     lnk       - linked list(an integer array) that is created
    839:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    840:   output Parameters:
    841:     nlnk      - number of newly added indices
    842:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    843:     bt        - updated PetscBT (bitarray)
    844: */
    845: #define PetscLLAddSorted(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    846: {\
    847:   PetscInt _k,_entry,_location,_lnkdata;\
    848:   nlnk      = 0;\
    849:   _lnkdata  = idx_start;\
    850:   for (_k=0; _k<nidx; _k++){\
    851:     _entry = indices[_k];\
    852:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    853:       /* search for insertion location */\
    854:       do {\
    855:         _location = _lnkdata;\
    856:         _lnkdata  = lnk[_location];\
    857:       } while (_entry > _lnkdata);\
    858:       /* insertion location is found, add entry into lnk */\
    859:       lnk[_location] = _entry;\
    860:       lnk[_entry]    = _lnkdata;\
    861:       nlnk++;\
    862:       _lnkdata = _entry; /* next search starts from here */\
    863:     }\
    864:   }\
    865: }

    867: #define PetscLLAddSorted_new(nidx,indices,idx_start,lnk_empty,nlnk,lnk,bt) 0; \
    868: {\
    869:   PetscInt _k,_entry,_location,_lnkdata;\
    870:   if (lnk_empty){\
    871:     _lnkdata  = idx_start;                      \
    872:     for (_k=0; _k<nidx; _k++){                  \
    873:       _entry = indices[_k];                             \
    874:       PetscBTSet(bt,_entry);  /* mark the new entry */          \
    875:           _location = _lnkdata;                                 \
    876:           _lnkdata  = lnk[_location];                           \
    877:         /* insertion location is found, add entry into lnk */   \
    878:         lnk[_location] = _entry;                                \
    879:         lnk[_entry]    = _lnkdata;                              \
    880:         _lnkdata = _entry; /* next search starts from here */   \
    881:     }                                                           \
    882:     /*\
    883:     lnk[indices[nidx-1]] = lnk[idx_start];\
    884:     lnk[idx_start]       = indices[0];\
    885:     PetscBTSet(bt,indices[0]);  \
    886:     for (_k=1; _k<nidx; _k++){                  \
    887:       PetscBTSet(bt,indices[_k]);                                          \
    888:       lnk[indices[_k-1]] = indices[_k];                                  \
    889:     }                                                           \
    890:      */\
    891:     nlnk      = nidx;\
    892:     lnk_empty = PETSC_FALSE;\
    893:   } else {\
    894:     nlnk      = 0;                              \
    895:     _lnkdata  = idx_start;                      \
    896:     for (_k=0; _k<nidx; _k++){                  \
    897:       _entry = indices[_k];                             \
    898:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */       \
    899:         /* search for insertion location */                     \
    900:         do {                                                    \
    901:           _location = _lnkdata;                                 \
    902:           _lnkdata  = lnk[_location];                           \
    903:         } while (_entry > _lnkdata);                            \
    904:         /* insertion location is found, add entry into lnk */   \
    905:         lnk[_location] = _entry;                                \
    906:         lnk[_entry]    = _lnkdata;                              \
    907:         nlnk++;                                                 \
    908:         _lnkdata = _entry; /* next search starts from here */   \
    909:       }                                                         \
    910:     }                                                           \
    911:   }                                                             \
    912: }

    914: /*
    915:   Add a SORTED index set into a sorted linked list used for LUFactorSymbolic()
    916:   Same as PetscLLAddSorted() with an additional operation:
    917:        count the number of input indices that are no larger than 'diag'
    918:   Input Parameters:
    919:     indices   - sorted integer array
    920:     idx_start - starting index of the list, index of pivot row
    921:     lnk       - linked list(an integer array) that is created
    922:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    923:     diag      - index of the active row in LUFactorSymbolic
    924:     nzbd      - number of input indices with indices <= idx_start
    925:     im        - im[idx_start] is initialized as num of nonzero entries in row=idx_start
    926:   output Parameters:
    927:     nlnk      - number of newly added indices
    928:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    929:     bt        - updated PetscBT (bitarray)
    930:     im        - im[idx_start]: unchanged if diag is not an entry
    931:                              : num of entries with indices <= diag if diag is an entry
    932: */
    933: #define PetscLLAddSortedLU(indices,idx_start,nlnk,lnk,bt,diag,nzbd,im) 0;\
    934: {\
    935:   PetscInt _k,_entry,_location,_lnkdata,_nidx;\
    936:   nlnk     = 0;\
    937:   _lnkdata = idx_start;\
    938:   _nidx = im[idx_start] - nzbd; /* num of entries with idx_start < index <= diag */\
    939:   for (_k=0; _k<_nidx; _k++){\
    940:     _entry = indices[_k];\
    941:     nzbd++;\
    942:     if ( _entry== diag) im[idx_start] = nzbd;\
    943:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    944:       /* search for insertion location */\
    945:       do {\
    946:         _location = _lnkdata;\
    947:         _lnkdata  = lnk[_location];\
    948:       } while (_entry > _lnkdata);\
    949:       /* insertion location is found, add entry into lnk */\
    950:       lnk[_location] = _entry;\
    951:       lnk[_entry]    = _lnkdata;\
    952:       nlnk++;\
    953:       _lnkdata = _entry; /* next search starts from here */\
    954:     }\
    955:   }\
    956: }

    958: /*
    959:   Copy data on the list into an array, then initialize the list
    960:   Input Parameters:
    961:     idx_start - starting index of the list
    962:     lnk_max   - max value of lnk indicating the end of the list
    963:     nlnk      - number of data on the list to be copied
    964:     lnk       - linked list
    965:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    966:   output Parameters:
    967:     indices   - array that contains the copied data
    968:     lnk       - linked list that is cleaned and initialize
    969:     bt        - PetscBT (bitarray) with all bits set to false
    970: */
    971: #define PetscLLClean(idx_start,lnk_max,nlnk,lnk,indices,bt) 0;\
    972: {\
    973:   PetscInt _j,_idx=idx_start;\
    974:   for (_j=0; _j<nlnk; _j++){\
    975:     _idx = lnk[_idx];\
    976:     indices[_j] = _idx;\
    977:     PetscBTClear(bt,_idx);\
    978:   }\
    979:   lnk[idx_start] = lnk_max;\
    980: }
    981: /*
    982:   Free memories used by the list
    983: */
    984: #define PetscLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    986: /* Routines below are used for incomplete matrix factorization */
    987: /*
    988:   Create and initialize a linked list and its levels
    989:   Input Parameters:
    990:     idx_start - starting index of the list
    991:     lnk_max   - max value of lnk indicating the end of the list
    992:     nlnk      - max length of the list
    993:   Output Parameters:
    994:     lnk       - list initialized
    995:     lnk_lvl   - array of size nlnk for storing levels of lnk
    996:     bt        - PetscBT (bitarray) with all bits set to false
    997: */
    998: #define PetscIncompleteLLCreate(idx_start,lnk_max,nlnk,lnk,lnk_lvl,bt)\
    999:   (PetscIntMultError(2,nlnk,NULL) || PetscMalloc1(2*nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,lnk_lvl = lnk + nlnk,0))

    1001: /*
    1002:   Initialize a sorted linked list used for ILU and ICC
    1003:   Input Parameters:
    1004:     nidx      - number of input idx
    1005:     idx       - integer array used for storing column indices
    1006:     idx_start - starting index of the list
    1007:     perm      - indices of an IS
    1008:     lnk       - linked list(an integer array) that is created
    1009:     lnklvl    - levels of lnk
    1010:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1011:   output Parameters:
    1012:     nlnk     - number of newly added idx
    1013:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1014:     lnklvl   - levels of lnk
    1015:     bt       - updated PetscBT (bitarray)
    1016: */
    1017: #define PetscIncompleteLLInit(nidx,idx,idx_start,perm,nlnk,lnk,lnklvl,bt) 0;\
    1018: {\
    1019:   PetscInt _k,_entry,_location,_lnkdata;\
    1020:   nlnk     = 0;\
    1021:   _lnkdata = idx_start;\
    1022:   for (_k=0; _k<nidx; _k++){\
    1023:     _entry = perm[idx[_k]];\
    1024:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1025:       /* search for insertion location */\
    1026:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1027:       do {\
    1028:         _location = _lnkdata;\
    1029:         _lnkdata  = lnk[_location];\
    1030:       } while (_entry > _lnkdata);\
    1031:       /* insertion location is found, add entry into lnk */\
    1032:       lnk[_location]  = _entry;\
    1033:       lnk[_entry]     = _lnkdata;\
    1034:       lnklvl[_entry] = 0;\
    1035:       nlnk++;\
    1036:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1037:     }\
    1038:   }\
    1039: }

    1041: /*
    1042:   Add a SORTED index set into a sorted linked list for ILU
    1043:   Input Parameters:
    1044:     nidx      - number of input indices
    1045:     idx       - sorted integer array used for storing column indices
    1046:     level     - level of fill, e.g., ICC(level)
    1047:     idxlvl    - level of idx
    1048:     idx_start - starting index of the list
    1049:     lnk       - linked list(an integer array) that is created
    1050:     lnklvl    - levels of lnk
    1051:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1052:     prow      - the row number of idx
    1053:   output Parameters:
    1054:     nlnk     - number of newly added idx
    1055:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1056:     lnklvl   - levels of lnk
    1057:     bt       - updated PetscBT (bitarray)

    1059:   Note: the level of factor(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(i,prow)+lvl(prow,j)+1)
    1060:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1061: */
    1062: #define PetscILULLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,lnklvl_prow) 0;\
    1063: {\
    1064:   PetscInt _k,_entry,_location,_lnkdata,_incrlev,_lnklvl_prow=lnklvl[prow];\
    1065:   nlnk     = 0;\
    1066:   _lnkdata = idx_start;\
    1067:   for (_k=0; _k<nidx; _k++){\
    1068:     _incrlev = idxlvl[_k] + _lnklvl_prow + 1;\
    1069:     if (_incrlev > level) continue;\
    1070:     _entry = idx[_k];\
    1071:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1072:       /* search for insertion location */\
    1073:       do {\
    1074:         _location = _lnkdata;\
    1075:         _lnkdata  = lnk[_location];\
    1076:       } while (_entry > _lnkdata);\
    1077:       /* insertion location is found, add entry into lnk */\
    1078:       lnk[_location]  = _entry;\
    1079:       lnk[_entry]     = _lnkdata;\
    1080:       lnklvl[_entry] = _incrlev;\
    1081:       nlnk++;\
    1082:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1083:     } else { /* existing entry: update lnklvl */\
    1084:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1085:     }\
    1086:   }\
    1087: }

    1089: /*
    1090:   Add a index set into a sorted linked list
    1091:   Input Parameters:
    1092:     nidx      - number of input idx
    1093:     idx   - integer array used for storing column indices
    1094:     level     - level of fill, e.g., ICC(level)
    1095:     idxlvl - level of idx
    1096:     idx_start - starting index of the list
    1097:     lnk       - linked list(an integer array) that is created
    1098:     lnklvl   - levels of lnk
    1099:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1100:   output Parameters:
    1101:     nlnk      - number of newly added idx
    1102:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1103:     lnklvl   - levels of lnk
    1104:     bt        - updated PetscBT (bitarray)
    1105: */
    1106: #define PetscIncompleteLLAdd(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1107: {\
    1108:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1109:   nlnk     = 0;\
    1110:   _lnkdata = idx_start;\
    1111:   for (_k=0; _k<nidx; _k++){\
    1112:     _incrlev = idxlvl[_k] + 1;\
    1113:     if (_incrlev > level) continue;\
    1114:     _entry = idx[_k];\
    1115:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1116:       /* search for insertion location */\
    1117:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1118:       do {\
    1119:         _location = _lnkdata;\
    1120:         _lnkdata  = lnk[_location];\
    1121:       } while (_entry > _lnkdata);\
    1122:       /* insertion location is found, add entry into lnk */\
    1123:       lnk[_location]  = _entry;\
    1124:       lnk[_entry]     = _lnkdata;\
    1125:       lnklvl[_entry] = _incrlev;\
    1126:       nlnk++;\
    1127:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1128:     } else { /* existing entry: update lnklvl */\
    1129:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1130:     }\
    1131:   }\
    1132: }

    1134: /*
    1135:   Add a SORTED index set into a sorted linked list
    1136:   Input Parameters:
    1137:     nidx      - number of input indices
    1138:     idx   - sorted integer array used for storing column indices
    1139:     level     - level of fill, e.g., ICC(level)
    1140:     idxlvl - level of idx
    1141:     idx_start - starting index of the list
    1142:     lnk       - linked list(an integer array) that is created
    1143:     lnklvl    - levels of lnk
    1144:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1145:   output Parameters:
    1146:     nlnk      - number of newly added idx
    1147:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1148:     lnklvl    - levels of lnk
    1149:     bt        - updated PetscBT (bitarray)
    1150: */
    1151: #define PetscIncompleteLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1152: {\
    1153:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1154:   nlnk = 0;\
    1155:   _lnkdata = idx_start;\
    1156:   for (_k=0; _k<nidx; _k++){\
    1157:     _incrlev = idxlvl[_k] + 1;\
    1158:     if (_incrlev > level) continue;\
    1159:     _entry = idx[_k];\
    1160:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1161:       /* search for insertion location */\
    1162:       do {\
    1163:         _location = _lnkdata;\
    1164:         _lnkdata  = lnk[_location];\
    1165:       } while (_entry > _lnkdata);\
    1166:       /* insertion location is found, add entry into lnk */\
    1167:       lnk[_location] = _entry;\
    1168:       lnk[_entry]    = _lnkdata;\
    1169:       lnklvl[_entry] = _incrlev;\
    1170:       nlnk++;\
    1171:       _lnkdata = _entry; /* next search starts from here */\
    1172:     } else { /* existing entry: update lnklvl */\
    1173:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1174:     }\
    1175:   }\
    1176: }

    1178: /*
    1179:   Add a SORTED index set into a sorted linked list for ICC
    1180:   Input Parameters:
    1181:     nidx      - number of input indices
    1182:     idx       - sorted integer array used for storing column indices
    1183:     level     - level of fill, e.g., ICC(level)
    1184:     idxlvl    - level of idx
    1185:     idx_start - starting index of the list
    1186:     lnk       - linked list(an integer array) that is created
    1187:     lnklvl    - levels of lnk
    1188:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1189:     idxlvl_prow - idxlvl[prow], where prow is the row number of the idx
    1190:   output Parameters:
    1191:     nlnk   - number of newly added indices
    1192:     lnk    - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1193:     lnklvl - levels of lnk
    1194:     bt     - updated PetscBT (bitarray)
    1195:   Note: the level of U(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(prow,i)+lvl(prow,j)+1)
    1196:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1197: */
    1198: #define PetscICCLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,idxlvl_prow) 0;\
    1199: {\
    1200:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1201:   nlnk = 0;\
    1202:   _lnkdata = idx_start;\
    1203:   for (_k=0; _k<nidx; _k++){\
    1204:     _incrlev = idxlvl[_k] + idxlvl_prow + 1;\
    1205:     if (_incrlev > level) continue;\
    1206:     _entry = idx[_k];\
    1207:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1208:       /* search for insertion location */\
    1209:       do {\
    1210:         _location = _lnkdata;\
    1211:         _lnkdata  = lnk[_location];\
    1212:       } while (_entry > _lnkdata);\
    1213:       /* insertion location is found, add entry into lnk */\
    1214:       lnk[_location] = _entry;\
    1215:       lnk[_entry]    = _lnkdata;\
    1216:       lnklvl[_entry] = _incrlev;\
    1217:       nlnk++;\
    1218:       _lnkdata = _entry; /* next search starts from here */\
    1219:     } else { /* existing entry: update lnklvl */\
    1220:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1221:     }\
    1222:   }\
    1223: }

    1225: /*
    1226:   Copy data on the list into an array, then initialize the list
    1227:   Input Parameters:
    1228:     idx_start - starting index of the list
    1229:     lnk_max   - max value of lnk indicating the end of the list
    1230:     nlnk      - number of data on the list to be copied
    1231:     lnk       - linked list
    1232:     lnklvl    - level of lnk
    1233:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1234:   output Parameters:
    1235:     indices - array that contains the copied data
    1236:     lnk     - linked list that is cleaned and initialize
    1237:     lnklvl  - level of lnk that is reinitialized
    1238:     bt      - PetscBT (bitarray) with all bits set to false
    1239: */
    1240: #define PetscIncompleteLLClean(idx_start,lnk_max,nlnk,lnk,lnklvl,indices,indiceslvl,bt) 0;\
    1241: {\
    1242:   PetscInt _j,_idx=idx_start;\
    1243:   for (_j=0; _j<nlnk; _j++){\
    1244:     _idx = lnk[_idx];\
    1245:     *(indices+_j) = _idx;\
    1246:     *(indiceslvl+_j) = lnklvl[_idx];\
    1247:     lnklvl[_idx] = -1;\
    1248:     PetscBTClear(bt,_idx);\
    1249:   }\
    1250:   lnk[idx_start] = lnk_max;\
    1251: }
    1252: /*
    1253:   Free memories used by the list
    1254: */
    1255: #define PetscIncompleteLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    1257: #define MatCheckSameLocalSize(A,ar1,B,ar2) \
    1259:   if ((A->rmap->n != B->rmap->n) || (A->cmap->n != B->cmap->n)) SETERRQ6(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Incompatible matrix local sizes: parameter # %d (%D x %D) != parameter # %d (%D x %D)",ar1,A->rmap->n,A->cmap->n,ar2,B->rmap->n,B->cmap->n);
    1260:
    1261: #define MatCheckSameSize(A,ar1,B,ar2) \
    1262:   if ((A->rmap->N != B->rmap->N) || (A->cmap->N != B->cmap->N)) SETERRQ6(PetscObjectComm((PetscObject)A),PETSC_ERR_ARG_INCOMP,"Incompatible matrix global sizes: parameter # %d (%D x %D) != parameter # %d (%D x %D)",ar1,A->rmap->N,A->cmap->N,ar2,B->rmap->N,B->cmap->N);\
    1263:   MatCheckSameLocalSize(A,ar1,B,ar2);
    1264:
    1265: #define VecCheckMatCompatible(M,x,ar1,b,ar2)                               \
    1266:   if (M->cmap->N != x->map->N) SETERRQ3(PetscObjectComm((PetscObject)M),PETSC_ERR_ARG_SIZ,"Vector global length incompatible with matrix: parameter # %d global size %D != matrix column global size %D",ar1,x->map->N,M->cmap->N);\
    1267:   if (M->rmap->N != b->map->N) SETERRQ3(PetscObjectComm((PetscObject)M),PETSC_ERR_ARG_SIZ,"Vector global length incompatible with matrix: parameter # %d global size %D != matrix row global size %D",ar2,b->map->N,M->rmap->N);

    1269: /* -------------------------------------------------------------------------------------------------------*/
    1270:  #include <petscbt.h>
    1271: /*
    1272:   Create and initialize a condensed linked list -
    1273:     same as PetscLLCreate(), but uses a scalable array 'lnk' with size of max number of entries, not O(N).
    1274:     Barry suggested this approach (Dec. 6, 2011):
    1275:       I've thought of an alternative way of representing a linked list that is efficient but doesn't have the O(N) scaling issue
    1276:       (it may be faster than the O(N) even sequentially due to less crazy memory access).

    1278:       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
    1279:       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
    1280:       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
    1281:       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.
    1282:       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
    1283:       to each other so memory access is much better than using the big array.

    1285:   Example:
    1286:      nlnk_max=5, lnk_max=36:
    1287:      Initial list: [0, 0 | 36, 2 | 0, 0 | 0, 0 | 0, 0 | 0, 0 | 0, 0]
    1288:      here, head_node has index 2 with value lnk[2]=lnk_max=36,
    1289:            0-th entry is used to store the number of entries in the list,
    1290:      The initial lnk represents head -> tail(marked by 36) with number of entries = lnk[0]=0.

    1292:      Now adding a sorted set {2,4}, the list becomes
    1293:      [2, 0 | 36, 4 |2, 6 | 4, 2 | 0, 0 | 0, 0 | 0, 0 ]
    1294:      represents head -> 2 -> 4 -> tail with number of entries = lnk[0]=2.

    1296:      Then adding a sorted set {0,3,35}, the list
    1297:      [5, 0 | 36, 8 | 2, 10 | 4, 12 | 0, 4 | 3, 6 | 35, 2 ]
    1298:      represents head -> 0 -> 2 -> 3 -> 4 -> 35 -> tail with number of entries = lnk[0]=5.

    1300:   Input Parameters:
    1301:     nlnk_max  - max length of the list
    1302:     lnk_max   - max value of the entries
    1303:   Output Parameters:
    1304:     lnk       - list created and initialized
    1305:     bt        - PetscBT (bitarray) with all bits set to false. Note: bt has size lnk_max, not nln_max!
    1306: */
    1307: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate(PetscInt nlnk_max,PetscInt lnk_max,PetscInt **lnk,PetscBT *bt)
    1308: {
    1310:   PetscInt       *llnk,lsize = 0;

    1313:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1314:   PetscMalloc1(lsize,lnk);
    1315:   PetscBTCreate(lnk_max,bt);
    1316:   llnk = *lnk;
    1317:   llnk[0] = 0;         /* number of entries on the list */
    1318:   llnk[2] = lnk_max;   /* value in the head node */
    1319:   llnk[3] = 2;         /* next for the head node */
    1320:   return(0);
    1321: }

    1323: /*
    1324:   Add a SORTED ascending index set into a sorted linked list. See PetscLLCondensedCreate() for detailed description.
    1325:   Input Parameters:
    1326:     nidx      - number of input indices
    1327:     indices   - sorted integer array
    1328:     lnk       - condensed linked list(an integer array) that is created
    1329:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1330:   output Parameters:
    1331:     lnk       - the sorted(increasing order) linked list containing previous and newly added non-redundate indices
    1332:     bt        - updated PetscBT (bitarray)
    1333: */
    1334: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted(PetscInt nidx,const PetscInt indices[],PetscInt lnk[],PetscBT bt)
    1335: {
    1336:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;

    1339:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1340:   _location = 2; /* head */
    1341:     for (_k=0; _k<nidx; _k++){
    1342:       _entry = indices[_k];
    1343:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */
    1344:         /* search for insertion location */
    1345:         do {
    1346:           _next     = _location + 1; /* link from previous node to next node */
    1347:           _location = lnk[_next];    /* idx of next node */
    1348:           _lnkdata  = lnk[_location];/* value of next node */
    1349:         } while (_entry > _lnkdata);
    1350:         /* insertion location is found, add entry into lnk */
    1351:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1352:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1353:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1354:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1355:         _location       = _newnode;      /* next search starts from the new node */
    1356:         _nlnk++;
    1357:       }   \
    1358:     }\
    1359:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1360:   return(0);
    1361: }

    1363: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean(PetscInt lnk_max,PetscInt nidx,PetscInt *indices,PetscInt lnk[],PetscBT bt)
    1364: {
    1366:   PetscInt       _k,_next,_nlnk;

    1369:   _next = lnk[3];       /* head node */
    1370:   _nlnk = lnk[0];       /* num of entries on the list */
    1371:   for (_k=0; _k<_nlnk; _k++){
    1372:     indices[_k] = lnk[_next];
    1373:     _next       = lnk[_next + 1];
    1374:     PetscBTClear(bt,indices[_k]);
    1375:   }
    1376:   lnk[0] = 0;          /* num of entries on the list */
    1377:   lnk[2] = lnk_max;    /* initialize head node */
    1378:   lnk[3] = 2;          /* head node */
    1379:   return(0);
    1380: }

    1382: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView(PetscInt *lnk)
    1383: {
    1385:   PetscInt       k;

    1388:   PetscPrintf(PETSC_COMM_SELF,"LLCondensed of size %D, (val,  next)\n",lnk[0]);
    1389:   for (k=2; k< lnk[0]+2; k++){
    1390:     PetscPrintf(PETSC_COMM_SELF," %D: (%D, %D)\n",2*k,lnk[2*k],lnk[2*k+1]);
    1391:   }
    1392:   return(0);
    1393: }

    1395: /*
    1396:   Free memories used by the list
    1397: */
    1398: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy(PetscInt *lnk,PetscBT bt)
    1399: {

    1403:   PetscFree(lnk);
    1404:   PetscBTDestroy(&bt);
    1405:   return(0);
    1406: }

    1408: /* -------------------------------------------------------------------------------------------------------*/
    1409: /*
    1410:  Same as PetscLLCondensedCreate(), but does not use non-scalable O(lnk_max) bitarray
    1411:   Input Parameters:
    1412:     nlnk_max  - max length of the list
    1413:   Output Parameters:
    1414:     lnk       - list created and initialized
    1415: */
    1416: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_Scalable(PetscInt nlnk_max,PetscInt **lnk)
    1417: {
    1419:   PetscInt       *llnk,lsize = 0;

    1422:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1423:   PetscMalloc1(lsize,lnk);
    1424:   llnk = *lnk;
    1425:   llnk[0] = 0;               /* number of entries on the list */
    1426:   llnk[2] = PETSC_MAX_INT;   /* value in the head node */
    1427:   llnk[3] = 2;               /* next for the head node */
    1428:   return(0);
    1429: }

    1431: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedExpand_Scalable(PetscInt nlnk_max,PetscInt **lnk)
    1432: {
    1434:   PetscInt       lsize = 0;

    1437:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1438:   PetscRealloc(lsize*sizeof(PetscInt),lnk);
    1439:   return(0);
    1440: }

    1442: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_Scalable(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1443: {
    1444:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;
    1445:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1446:   _location = 2; /* head */ \
    1447:     for (_k=0; _k<nidx; _k++){
    1448:       _entry = indices[_k];
    1449:       /* search for insertion location */
    1450:       do {
    1451:         _next     = _location + 1; /* link from previous node to next node */
    1452:         _location = lnk[_next];    /* idx of next node */
    1453:         _lnkdata  = lnk[_location];/* value of next node */
    1454:       } while (_entry > _lnkdata);
    1455:       if (_entry < _lnkdata) {
    1456:         /* insertion location is found, add entry into lnk */
    1457:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1458:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1459:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1460:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1461:         _location       = _newnode;      /* next search starts from the new node */
    1462:         _nlnk++;
    1463:       }
    1464:     }
    1465:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1466:   return 0;
    1467: }

    1469: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_Scalable(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1470: {
    1471:   PetscInt _k,_next,_nlnk;
    1472:   _next = lnk[3];       /* head node */
    1473:   _nlnk = lnk[0];
    1474:   for (_k=0; _k<_nlnk; _k++){
    1475:     indices[_k] = lnk[_next];
    1476:     _next       = lnk[_next + 1];
    1477:   }
    1478:   lnk[0] = 0;          /* num of entries on the list */
    1479:   lnk[3] = 2;          /* head node */
    1480:   return 0;
    1481: }

    1483: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_Scalable(PetscInt *lnk)
    1484: {
    1485:   return PetscFree(lnk);
    1486: }

    1488: /* -------------------------------------------------------------------------------------------------------*/
    1489: /*
    1490:       lnk[0]   number of links
    1491:       lnk[1]   number of entries
    1492:       lnk[3n]  value
    1493:       lnk[3n+1] len
    1494:       lnk[3n+2] link to next value

    1496:       The next three are always the first link

    1498:       lnk[3]    PETSC_MIN_INT+1
    1499:       lnk[4]    1
    1500:       lnk[5]    link to first real entry

    1502:       The next three are always the last link

    1504:       lnk[6]    PETSC_MAX_INT - 1
    1505:       lnk[7]    1
    1506:       lnk[8]    next valid link (this is the same as lnk[0] but without the decreases)
    1507: */

    1509: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_fast(PetscInt nlnk_max,PetscInt **lnk)
    1510: {
    1512:   PetscInt       *llnk,lsize = 0;

    1515:   PetscIntMultError(3,nlnk_max+3,&lsize);
    1516:   PetscMalloc1(lsize,lnk);
    1517:   llnk = *lnk;
    1518:   llnk[0] = 0;   /* nlnk: number of entries on the list */
    1519:   llnk[1] = 0;          /* number of integer entries represented in list */
    1520:   llnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1521:   llnk[4] = 1;           /* count for the first node */
    1522:   llnk[5] = 6;         /* next for the first node */
    1523:   llnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1524:   llnk[7] = 1;           /* count for the last node */
    1525:   llnk[8] = 0;         /* next valid node to be used */
    1526:   return(0);
    1527: }

    1529: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_fast(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1530: {
    1531:   PetscInt k,entry,prev,next;
    1532:   prev      = 3;      /* first value */
    1533:   next      = lnk[prev+2];
    1534:   for (k=0; k<nidx; k++){
    1535:     entry = indices[k];
    1536:     /* search for insertion location */
    1537:     while (entry >= lnk[next]) {
    1538:       prev = next;
    1539:       next = lnk[next+2];
    1540:     }
    1541:     /* entry is in range of previous list */
    1542:     if (entry < lnk[prev]+lnk[prev+1]) continue;
    1543:     lnk[1]++;
    1544:     /* entry is right after previous list */
    1545:     if (entry == lnk[prev]+lnk[prev+1]) {
    1546:       lnk[prev+1]++;
    1547:       if (lnk[next] == entry+1) { /* combine two contiguous strings */
    1548:         lnk[prev+1] += lnk[next+1];
    1549:         lnk[prev+2]  = lnk[next+2];
    1550:         next         = lnk[next+2];
    1551:         lnk[0]--;
    1552:       }
    1553:       continue;
    1554:     }
    1555:     /* entry is right before next list */
    1556:     if (entry == lnk[next]-1) {
    1557:       lnk[next]--;
    1558:       lnk[next+1]++;
    1559:       prev = next;
    1560:       next = lnk[prev+2];
    1561:       continue;
    1562:     }
    1563:     /*  add entry into lnk */
    1564:     lnk[prev+2]    = 3*((lnk[8]++)+3);      /* connect previous node to the new node */
    1565:     prev           = lnk[prev+2];
    1566:     lnk[prev]      = entry;        /* set value of the new node */
    1567:     lnk[prev+1]    = 1;             /* number of values in contiguous string is one to start */
    1568:     lnk[prev+2]    = next;          /* connect new node to next node */
    1569:     lnk[0]++;
    1570:   }
    1571:   return 0;
    1572: }

    1574: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_fast(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1575: {
    1576:   PetscInt _k,_next,_nlnk,cnt,j;
    1577:   _next = lnk[5];       /* first node */
    1578:   _nlnk = lnk[0];
    1579:   cnt   = 0;
    1580:   for (_k=0; _k<_nlnk; _k++){
    1581:     for (j=0; j<lnk[_next+1]; j++) {
    1582:       indices[cnt++] = lnk[_next] + j;
    1583:     }
    1584:     _next       = lnk[_next + 2];
    1585:   }
    1586:   lnk[0] = 0;   /* nlnk: number of links */
    1587:   lnk[1] = 0;          /* number of integer entries represented in list */
    1588:   lnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1589:   lnk[4] = 1;           /* count for the first node */
    1590:   lnk[5] = 6;         /* next for the first node */
    1591:   lnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1592:   lnk[7] = 1;           /* count for the last node */
    1593:   lnk[8] = 0;         /* next valid location to make link */
    1594:   return 0;
    1595: }

    1597: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView_fast(PetscInt *lnk)
    1598: {
    1599:   PetscInt k,next,nlnk;
    1600:   next = lnk[5];       /* first node */
    1601:   nlnk = lnk[0];
    1602:   for (k=0; k<nlnk; k++){
    1603: #if 0                           /* Debugging code */
    1604:     printf("%d value %d len %d next %d\n",next,lnk[next],lnk[next+1],lnk[next+2]);
    1605: #endif
    1606:     next = lnk[next + 2];
    1607:   }
    1608:   return 0;
    1609: }

    1611: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_fast(PetscInt *lnk)
    1612: {
    1613:   return PetscFree(lnk);
    1614: }

    1616: /* this is extern because it is used in MatFDColoringUseDM() which is in the DM library */
    1617: PETSC_EXTERN PetscErrorCode MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,void*);

    1619: PETSC_EXTERN PetscLogEvent MAT_Mult;
    1620: PETSC_EXTERN PetscLogEvent MAT_MultMatrixFree;
    1621: PETSC_EXTERN PetscLogEvent MAT_Mults;
    1622: PETSC_EXTERN PetscLogEvent MAT_MultConstrained;
    1623: PETSC_EXTERN PetscLogEvent MAT_MultAdd;
    1624: PETSC_EXTERN PetscLogEvent MAT_MultTranspose;
    1625: PETSC_EXTERN PetscLogEvent MAT_MultTransposeConstrained;
    1626: PETSC_EXTERN PetscLogEvent MAT_MultTransposeAdd;
    1627: PETSC_EXTERN PetscLogEvent MAT_Solve;
    1628: PETSC_EXTERN PetscLogEvent MAT_Solves;
    1629: PETSC_EXTERN PetscLogEvent MAT_SolveAdd;
    1630: PETSC_EXTERN PetscLogEvent MAT_SolveTranspose;
    1631: PETSC_EXTERN PetscLogEvent MAT_SolveTransposeAdd;
    1632: PETSC_EXTERN PetscLogEvent MAT_SOR;
    1633: PETSC_EXTERN PetscLogEvent MAT_ForwardSolve;
    1634: PETSC_EXTERN PetscLogEvent MAT_BackwardSolve;
    1635: PETSC_EXTERN PetscLogEvent MAT_LUFactor;
    1636: PETSC_EXTERN PetscLogEvent MAT_LUFactorSymbolic;
    1637: PETSC_EXTERN PetscLogEvent MAT_LUFactorNumeric;
    1638: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactor;
    1639: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactorSymbolic;
    1640: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactorNumeric;
    1641: PETSC_EXTERN PetscLogEvent MAT_ILUFactor;
    1642: PETSC_EXTERN PetscLogEvent MAT_ILUFactorSymbolic;
    1643: PETSC_EXTERN PetscLogEvent MAT_ICCFactorSymbolic;
    1644: PETSC_EXTERN PetscLogEvent MAT_Copy;
    1645: PETSC_EXTERN PetscLogEvent MAT_Convert;
    1646: PETSC_EXTERN PetscLogEvent MAT_Scale;
    1647: PETSC_EXTERN PetscLogEvent MAT_AssemblyBegin;
    1648: PETSC_EXTERN PetscLogEvent MAT_AssemblyEnd;
    1649: PETSC_EXTERN PetscLogEvent MAT_SetValues;
    1650: PETSC_EXTERN PetscLogEvent MAT_GetValues;
    1651: PETSC_EXTERN PetscLogEvent MAT_GetRow;
    1652: PETSC_EXTERN PetscLogEvent MAT_GetRowIJ;
    1653: PETSC_EXTERN PetscLogEvent MAT_CreateSubMats;
    1654: PETSC_EXTERN PetscLogEvent MAT_GetColoring;
    1655: PETSC_EXTERN PetscLogEvent MAT_GetOrdering;
    1656: PETSC_EXTERN PetscLogEvent MAT_RedundantMat;
    1657: PETSC_EXTERN PetscLogEvent MAT_IncreaseOverlap;
    1658: PETSC_EXTERN PetscLogEvent MAT_Partitioning;
    1659: PETSC_EXTERN PetscLogEvent MAT_PartitioningND;
    1660: PETSC_EXTERN PetscLogEvent MAT_Coarsen;
    1661: PETSC_EXTERN PetscLogEvent MAT_ZeroEntries;
    1662: PETSC_EXTERN PetscLogEvent MAT_Load;
    1663: PETSC_EXTERN PetscLogEvent MAT_View;
    1664: PETSC_EXTERN PetscLogEvent MAT_AXPY;
    1665: PETSC_EXTERN PetscLogEvent MAT_FDColoringCreate;
    1666: PETSC_EXTERN PetscLogEvent MAT_TransposeColoringCreate;
    1667: PETSC_EXTERN PetscLogEvent MAT_FDColoringSetUp;
    1668: PETSC_EXTERN PetscLogEvent MAT_FDColoringApply;
    1669: PETSC_EXTERN PetscLogEvent MAT_Transpose;
    1670: PETSC_EXTERN PetscLogEvent MAT_FDColoringFunction;
    1671: PETSC_EXTERN PetscLogEvent MAT_CreateSubMat;
    1672: PETSC_EXTERN PetscLogEvent MAT_MatMult;
    1673: PETSC_EXTERN PetscLogEvent MAT_MatSolve;
    1674: PETSC_EXTERN PetscLogEvent MAT_MatTrSolve;
    1675: PETSC_EXTERN PetscLogEvent MAT_MatMultSymbolic;
    1676: PETSC_EXTERN PetscLogEvent MAT_MatMultNumeric;
    1677: PETSC_EXTERN PetscLogEvent MAT_Getlocalmatcondensed;
    1678: PETSC_EXTERN PetscLogEvent MAT_GetBrowsOfAcols;
    1679: PETSC_EXTERN PetscLogEvent MAT_GetBrowsOfAocols;
    1680: PETSC_EXTERN PetscLogEvent MAT_PtAP;
    1681: PETSC_EXTERN PetscLogEvent MAT_PtAPSymbolic;
    1682: PETSC_EXTERN PetscLogEvent MAT_PtAPNumeric;
    1683: PETSC_EXTERN PetscLogEvent MAT_Seqstompinum;
    1684: PETSC_EXTERN PetscLogEvent MAT_Seqstompisym;
    1685: PETSC_EXTERN PetscLogEvent MAT_Seqstompi;
    1686: PETSC_EXTERN PetscLogEvent MAT_Getlocalmat;
    1687: PETSC_EXTERN PetscLogEvent MAT_RARt;
    1688: PETSC_EXTERN PetscLogEvent MAT_RARtSymbolic;
    1689: PETSC_EXTERN PetscLogEvent MAT_RARtNumeric;
    1690: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMult;
    1691: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMultSymbolic;
    1692: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMultNumeric;
    1693: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMult;
    1694: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMultSymbolic;
    1695: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMultNumeric;
    1696: PETSC_EXTERN PetscLogEvent MAT_MatMatMult;
    1697: PETSC_EXTERN PetscLogEvent MAT_MatMatMultSymbolic;
    1698: PETSC_EXTERN PetscLogEvent MAT_MatMatMultNumeric;
    1699: PETSC_EXTERN PetscLogEvent MAT_Applypapt;
    1700: PETSC_EXTERN PetscLogEvent MAT_Applypapt_symbolic;
    1701: PETSC_EXTERN PetscLogEvent MAT_Applypapt_numeric;
    1702: PETSC_EXTERN PetscLogEvent MAT_Getsymtranspose;
    1703: PETSC_EXTERN PetscLogEvent MAT_Transpose_SeqAIJ;
    1704: PETSC_EXTERN PetscLogEvent MAT_Getsymtransreduced;
    1705: PETSC_EXTERN PetscLogEvent MAT_GetSequentialNonzeroStructure;
    1706: PETSC_EXTERN PetscLogEvent MATMFFD_Mult;
    1707: PETSC_EXTERN PetscLogEvent MAT_GetMultiProcBlock;
    1708: PETSC_EXTERN PetscLogEvent MAT_CUSPARSECopyToGPU;
    1709: PETSC_EXTERN PetscLogEvent MAT_SetValuesBatch;
    1710: PETSC_EXTERN PetscLogEvent MAT_ViennaCLCopyToGPU;
    1711: PETSC_EXTERN PetscLogEvent MAT_Merge;
    1712: PETSC_EXTERN PetscLogEvent MAT_Residual;
    1713: PETSC_EXTERN PetscLogEvent MAT_SetRandom;
    1714: PETSC_EXTERN PetscLogEvent MATCOLORING_Apply;
    1715: PETSC_EXTERN PetscLogEvent MATCOLORING_Comm;
    1716: PETSC_EXTERN PetscLogEvent MATCOLORING_Local;
    1717: PETSC_EXTERN PetscLogEvent MATCOLORING_ISCreate;
    1718: PETSC_EXTERN PetscLogEvent MATCOLORING_SetUp;
    1719: PETSC_EXTERN PetscLogEvent MATCOLORING_Weights;

    1721: #endif