Actual source code: matimpl.h
petsc-3.15.0 2021-03-30
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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 src/mat/f90-mod/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 (*setinf)(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 (*placeholder_63)(void);
    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)(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 (*placeholder_89)(void);
    142:   PetscErrorCode (*matmultsymbolic)(Mat,Mat,PetscReal,Mat);
    143:   PetscErrorCode (*matmultnumeric)(Mat,Mat,Mat);
    144:   PetscErrorCode (*placeholder_92)(void);
    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 (*placeholder_95)(void);
    149:   PetscErrorCode (*mattransposemultsymbolic)(Mat,Mat,PetscReal,Mat);
    150:   PetscErrorCode (*mattransposemultnumeric)(Mat,Mat,Mat);
    151:   PetscErrorCode (*bindtocpu)(Mat,PetscBool);
    152:   /*99*/
    153:   PetscErrorCode (*productsetfromoptions)(Mat);
    154:   PetscErrorCode (*productsymbolic)(Mat);
    155:   PetscErrorCode (*productnumeric)(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 (*placeholder_130)(void);
    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 (*placeholder_136)(void);
    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:   PetscErrorCode (*creatempimatconcatenateseqmat)(MPI_Comm,Mat,PetscInt,MatReuse,Mat*);
    207:   /*145*/
    208:   PetscErrorCode (*destroysubmatrices)(PetscInt,Mat*[]);
    209:   PetscErrorCode (*mattransposesolve)(Mat,Mat,Mat);
    210:   PetscErrorCode (*getvalueslocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],PetscScalar[]);
    211: };
    212: /*
    213:     If you add MatOps entries above also add them to the MATOP enum
    214:     in include/petscmat.h and src/mat/f90-mod/petscmat.h
    215: */

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

    221: typedef struct _p_MatRootName* MatRootName;
    222: struct _p_MatRootName {
    223:   char        *rname,*sname,*mname;
    224:   MatRootName next;
    225: };

    227: PETSC_EXTERN MatRootName MatRootNameList;

    229: /*
    230:    Utility private matrix routines
    231: */
    232: PETSC_INTERN PetscErrorCode MatFindNonzeroRowsOrCols_Basic(Mat,PetscBool,PetscReal,IS*);
    233: PETSC_INTERN PetscErrorCode MatConvert_Basic(Mat,MatType,MatReuse,Mat*);
    234: PETSC_INTERN PetscErrorCode MatConvert_Shell(Mat,MatType,MatReuse,Mat*);
    235: PETSC_INTERN PetscErrorCode MatConvertFrom_Shell(Mat,MatType,MatReuse,Mat*);
    236: PETSC_INTERN PetscErrorCode MatCopy_Basic(Mat,Mat,MatStructure);
    237: PETSC_INTERN PetscErrorCode MatDiagonalSet_Default(Mat,Vec,InsertMode);
    238: #if defined(PETSC_HAVE_SCALAPACK)
    239: PETSC_INTERN PetscErrorCode MatConvert_Dense_ScaLAPACK(Mat,MatType,MatReuse,Mat*);
    240: #endif
    241: PETSC_INTERN PetscErrorCode MatSetPreallocationCOO_Basic(Mat,PetscInt,const PetscInt[],const PetscInt[]);
    242: PETSC_INTERN PetscErrorCode MatSetValuesCOO_Basic(Mat,const PetscScalar[],InsertMode);

    244: /* these callbacks rely on the old matrix function pointers for
    245:    matmat operations. They are unsafe, and should be removed.
    246:    However, the amount of work needed to clean up all the
    247:    implementations is not negligible */
    248: PETSC_INTERN PetscErrorCode MatProductSymbolic_AB(Mat);
    249: PETSC_INTERN PetscErrorCode MatProductNumeric_AB(Mat);
    250: PETSC_INTERN PetscErrorCode MatProductSymbolic_AtB(Mat);
    251: PETSC_INTERN PetscErrorCode MatProductNumeric_AtB(Mat);
    252: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABt(Mat);
    253: PETSC_INTERN PetscErrorCode MatProductNumeric_ABt(Mat);
    254: PETSC_INTERN PetscErrorCode MatProductNumeric_PtAP(Mat);
    255: PETSC_INTERN PetscErrorCode MatProductNumeric_RARt(Mat);
    256: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABC(Mat);
    257: PETSC_INTERN PetscErrorCode MatProductNumeric_ABC(Mat);

    259: PETSC_INTERN PetscErrorCode MatProductCreate_Private(Mat,Mat,Mat,Mat);
    260: /* this callback handles all the different triple products and
    261:    does not rely on the function pointers; used by cuSPARSE and KOKKOS-KERNELS */
    262: PETSC_INTERN PetscErrorCode MatProductSymbolic_ABC_Basic(Mat);

    265: #if defined(PETSC_USE_DEBUG)
    266: #  define MatCheckPreallocated(A,arg) do {                              \
    267:     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); \
    268:   } while (0)
    269: #else
    270: #  define MatCheckPreallocated(A,arg) do {} while (0)
    271: #endif

    273: #if defined(PETSC_USE_DEBUG)
    274: #  define MatCheckProduct(A,arg) do {                              \
    275:     if (PetscUnlikely(!(A)->product)) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"Argument %D \"%s\" is not a matrix obtained from MatProductCreate()",(arg),#A); \
    276:   } while (0)
    277: #else
    278: #  define MatCheckProduct(A,arg) do {} while (0)
    279: #endif

    281: /*
    282:   The stash is used to temporarily store inserted matrix values that
    283:   belong to another processor. During the assembly phase the stashed
    284:   values are moved to the correct processor and
    285: */

    287: typedef struct _MatStashSpace *PetscMatStashSpace;

    289: struct _MatStashSpace {
    290:   PetscMatStashSpace next;
    291:   PetscScalar        *space_head,*val;
    292:   PetscInt           *idx,*idy;
    293:   PetscInt           total_space_size;
    294:   PetscInt           local_used;
    295:   PetscInt           local_remaining;
    296: };

    298: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceGet(PetscInt,PetscInt,PetscMatStashSpace *);
    299: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceContiguous(PetscInt,PetscMatStashSpace *,PetscScalar *,PetscInt *,PetscInt *);
    300: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceDestroy(PetscMatStashSpace*);

    302: typedef struct {
    303:   PetscInt    count;
    304: } MatStashHeader;

    306: typedef struct {
    307:   void        *buffer;          /* Of type blocktype, dynamically constructed  */
    308:   PetscInt    count;
    309:   char        pending;
    310: } MatStashFrame;

    312: typedef struct _MatStash MatStash;
    313: struct _MatStash {
    314:   PetscInt      nmax;                   /* maximum stash size */
    315:   PetscInt      umax;                   /* user specified max-size */
    316:   PetscInt      oldnmax;                /* the nmax value used previously */
    317:   PetscInt      n;                      /* stash size */
    318:   PetscInt      bs;                     /* block size of the stash */
    319:   PetscInt      reallocs;               /* preserve the no of mallocs invoked */
    320:   PetscMatStashSpace space_head,space;  /* linked list to hold stashed global row/column numbers and matrix values */

    322:   PetscErrorCode (*ScatterBegin)(Mat,MatStash*,PetscInt*);
    323:   PetscErrorCode (*ScatterGetMesg)(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    324:   PetscErrorCode (*ScatterEnd)(MatStash*);
    325:   PetscErrorCode (*ScatterDestroy)(MatStash*);

    327:   /* The following variables are used for communication */
    328:   MPI_Comm      comm;
    329:   PetscMPIInt   size,rank;
    330:   PetscMPIInt   tag1,tag2;
    331:   MPI_Request   *send_waits;            /* array of send requests */
    332:   MPI_Request   *recv_waits;            /* array of receive requests */
    333:   MPI_Status    *send_status;           /* array of send status */
    334:   PetscInt      nsends,nrecvs;          /* numbers of sends and receives */
    335:   PetscScalar   *svalues;               /* sending data */
    336:   PetscInt      *sindices;
    337:   PetscScalar   **rvalues;              /* receiving data (values) */
    338:   PetscInt      **rindices;             /* receiving data (indices) */
    339:   PetscInt      nprocessed;             /* number of messages already processed */
    340:   PetscMPIInt   *flg_v;                 /* indicates what messages have arrived so far and from whom */
    341:   PetscBool     reproduce;
    342:   PetscInt      reproduce_count;

    344:   /* The following variables are used for BTS communication */
    345:   PetscBool      first_assembly_done;   /* Is the first time matrix assembly done? */
    346:   PetscBool      use_status;            /* Use MPI_Status to determine number of items in each message */
    347:   PetscMPIInt    nsendranks;
    348:   PetscMPIInt    nrecvranks;
    349:   PetscMPIInt    *sendranks;
    350:   PetscMPIInt    *recvranks;
    351:   MatStashHeader *sendhdr,*recvhdr;
    352:   MatStashFrame  *sendframes;   /* pointers to the main messages */
    353:   MatStashFrame  *recvframes;
    354:   MatStashFrame  *recvframe_active;
    355:   PetscInt       recvframe_i;     /* index of block within active frame */
    356:   PetscMPIInt    recvframe_count; /* Count actually sent for current frame */
    357:   PetscInt       recvcount;       /* Number of receives processed so far */
    358:   PetscMPIInt    *some_indices;   /* From last call to MPI_Waitsome */
    359:   MPI_Status     *some_statuses;  /* Statuses from last call to MPI_Waitsome */
    360:   PetscMPIInt    some_count;      /* Number of requests completed in last call to MPI_Waitsome */
    361:   PetscMPIInt    some_i;          /* Index of request currently being processed */
    362:   MPI_Request    *sendreqs;
    363:   MPI_Request    *recvreqs;
    364:   PetscSegBuffer segsendblocks;
    365:   PetscSegBuffer segrecvframe;
    366:   PetscSegBuffer segrecvblocks;
    367:   MPI_Datatype   blocktype;
    368:   size_t         blocktype_size;
    369:   InsertMode     *insertmode;   /* Pointer to check mat->insertmode and set upon message arrival in case no local values have been set. */
    370: };

    372: #if !defined(PETSC_HAVE_MPIUNI)
    373: PETSC_INTERN PetscErrorCode MatStashScatterDestroy_BTS(MatStash*);
    374: #endif
    375: PETSC_INTERN PetscErrorCode MatStashCreate_Private(MPI_Comm,PetscInt,MatStash*);
    376: PETSC_INTERN PetscErrorCode MatStashDestroy_Private(MatStash*);
    377: PETSC_INTERN PetscErrorCode MatStashScatterEnd_Private(MatStash*);
    378: PETSC_INTERN PetscErrorCode MatStashSetInitialSize_Private(MatStash*,PetscInt);
    379: PETSC_INTERN PetscErrorCode MatStashGetInfo_Private(MatStash*,PetscInt*,PetscInt*);
    380: PETSC_INTERN PetscErrorCode MatStashValuesRow_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscBool);
    381: PETSC_INTERN PetscErrorCode MatStashValuesCol_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscBool);
    382: PETSC_INTERN PetscErrorCode MatStashValuesRowBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    383: PETSC_INTERN PetscErrorCode MatStashValuesColBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    384: PETSC_INTERN PetscErrorCode MatStashScatterBegin_Private(Mat,MatStash*,PetscInt*);
    385: PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Private(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    386: PETSC_INTERN PetscErrorCode MatGetInfo_External(Mat,MatInfoType,MatInfo*);

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

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

    404: typedef struct { /* used by MatCreateRedundantMatrix() for reusing matredundant */
    405:   PetscInt     nzlocal,nsends,nrecvs;
    406:   PetscMPIInt  *send_rank,*recv_rank;
    407:   PetscInt     *sbuf_nz,*rbuf_nz,*sbuf_j,**rbuf_j;
    408:   PetscScalar  *sbuf_a,**rbuf_a;
    409:   MPI_Comm     subcomm;   /* when user does not provide a subcomm */
    410:   IS           isrow,iscol;
    411:   Mat          *matseq;
    412: } Mat_Redundant;

    414: typedef struct { /* used by MatProduct() */
    415:   MatProductType type;
    416:   char           *alg;
    417:   Mat            A,B,C,Dwork;
    418:   PetscReal      fill;
    419:   PetscBool      api_user; /* used to distinguish command line options and to indicate the matrix values are ready to be consumed at symbolic phase if needed */

    421:   /* Some products may display the information on the algorithm used */
    422:   PetscErrorCode (*view)(Mat,PetscViewer);

    424:   /* many products have intermediate data structures, each specific to Mat types and product type */
    425:   PetscBool      clear;             /* whether or not to clear the data structures after MatProductNumeric has been called */
    426:   void           *data;             /* where to stash those structures */
    427:   PetscErrorCode (*destroy)(void*); /* destroy routine */
    428: } Mat_Product;

    430: #define CSRDataStructure(datatype)  \
    431:   int         *i; \
    432:   int         *j; \
    433:   datatype    *a;\
    434:   PetscInt    n;\
    435:   PetscInt    ignorezeroentries;

    437: typedef struct {
    438:   CSRDataStructure(PetscScalar)
    439: } PetscCSRDataStructure;

    441: struct _p_SplitCSRMat {
    442:   PetscInt              cstart,cend,rstart,rend;
    443:   PetscCSRDataStructure diag,offdiag;
    444:   PetscInt              *colmap;
    445:   PetscMPIInt           rank;
    446: };

    448: struct _p_Mat {
    449:   PETSCHEADER(struct _MatOps);
    450:   PetscLayout            rmap,cmap;
    451:   void                   *data;            /* implementation-specific data */
    452:   MatFactorType          factortype;       /* MAT_FACTOR_LU, ILU, CHOLESKY or ICC */
    453:   PetscBool              useordering;      /* factorization using ordering provide to routine (most PETSc implementations) */
    454:   PetscBool              assembled;        /* is the matrix assembled? */
    455:   PetscBool              was_assembled;    /* new values inserted into assembled mat */
    456:   PetscInt               num_ass;          /* number of times matrix has been assembled */
    457:   PetscObjectState       nonzerostate;     /* each time new nonzeros locations are introduced into the matrix this is updated */
    458:   PetscObjectState       ass_nonzerostate; /* nonzero state at last assembly */
    459:   MatInfo                info;             /* matrix information */
    460:   InsertMode             insertmode;       /* have values been inserted in matrix or added? */
    461:   MatStash               stash,bstash;     /* used for assembling off-proc mat emements */
    462:   MatNullSpace           nullsp;           /* null space (operator is singular) */
    463:   MatNullSpace           transnullsp;      /* null space of transpose of operator */
    464:   MatNullSpace           nearnullsp;       /* near null space to be used by multigrid methods */
    465:   PetscInt               congruentlayouts; /* are the rows and columns layouts congruent? */
    466:   PetscBool              preallocated;
    467:   MatStencilInfo         stencil;          /* information for structured grid */
    468:   PetscBool              symmetric,hermitian,structurally_symmetric,spd;
    469:   PetscBool              symmetric_set,hermitian_set,structurally_symmetric_set,spd_set; /* if true, then corresponding flag is correct*/
    470:   PetscBool              symmetric_eternal;
    471:   PetscBool              nooffprocentries,nooffproczerorows;
    472:   PetscBool              assembly_subset;  /* set by MAT_SUBSET_OFF_PROC_ENTRIES */
    473:   PetscBool              submat_singleis;  /* for efficient PCSetUp_ASM() */
    474:   PetscBool              structure_only;
    475:   PetscBool              sortedfull;       /* full, sorted rows are inserted */
    476:   PetscBool              force_diagonals;  /* set by MAT_FORCE_DIAGONAL_ENTRIES */
    477: #if defined(PETSC_HAVE_DEVICE)
    478:   PetscOffloadMask       offloadmask;      /* a mask which indicates where the valid matrix data is (GPU, CPU or both) */
    479:   PetscBool              boundtocpu;
    480: #endif
    481:   void                   *spptr;          /* pointer for special library like SuperLU */
    482:   char                   *solvertype;
    483:   PetscBool              checksymmetryonassembly,checknullspaceonassembly;
    484:   PetscReal              checksymmetrytol;
    485:   Mat                    schur;             /* Schur complement matrix */
    486:   MatFactorSchurStatus   schur_status;      /* status of the Schur complement matrix */
    487:   Mat_Redundant          *redundant;        /* used by MatCreateRedundantMatrix() */
    488:   PetscBool              erroriffailure;    /* Generate an error if detected (for example a zero pivot) instead of returning */
    489:   MatFactorError         factorerrortype;               /* type of error in factorization */
    490:   PetscReal              factorerror_zeropivot_value;   /* If numerical zero pivot was detected this is the computed value */
    491:   PetscInt               factorerror_zeropivot_row;     /* Row where zero pivot was detected */
    492:   PetscInt               nblocks,*bsizes;   /* support for MatSetVariableBlockSizes() */
    493:   char                   *defaultvectype;
    494:   Mat_Product            *product;
    495:   PetscBool              form_explicit_transpose; /* hint to generate an explicit mat tranpsose for operations like MatMultTranspose() */
    496:   PetscBool              transupdated;            /* whether or not the explicitly generated transpose is up-to-date */
    497: };

    499: PETSC_INTERN PetscErrorCode MatAXPY_Basic(Mat,PetscScalar,Mat,MatStructure);
    500: PETSC_INTERN PetscErrorCode MatAXPY_BasicWithPreallocation(Mat,Mat,PetscScalar,Mat,MatStructure);
    501: PETSC_INTERN PetscErrorCode MatAXPY_Basic_Preallocate(Mat,Mat,Mat*);
    502: PETSC_INTERN PetscErrorCode MatAXPY_Dense_Nest(Mat,PetscScalar,Mat);

    504: /*
    505:     Utility for MatFactor (Schur complement)
    506: */
    507: PETSC_INTERN PetscErrorCode MatFactorFactorizeSchurComplement_Private(Mat);
    508: PETSC_INTERN PetscErrorCode MatFactorInvertSchurComplement_Private(Mat);
    509: PETSC_INTERN PetscErrorCode MatFactorUpdateSchurStatus_Private(Mat);
    510: PETSC_INTERN PetscErrorCode MatFactorSetUpInPlaceSchur_Private(Mat);

    512: /*
    513:     Utility for MatZeroRows
    514: */
    515: PETSC_INTERN PetscErrorCode MatZeroRowsMapLocal_Private(Mat,PetscInt,const PetscInt*,PetscInt*,PetscInt**);

    517: /*
    518:     Utility for MatView/MatLoad
    519: */
    520: PETSC_INTERN PetscErrorCode MatView_Binary_BlockSizes(Mat,PetscViewer);
    521: PETSC_INTERN PetscErrorCode MatLoad_Binary_BlockSizes(Mat,PetscViewer);

    524: /*
    525:     Object for partitioning graphs
    526: */

    528: typedef struct _MatPartitioningOps *MatPartitioningOps;
    529: struct _MatPartitioningOps {
    530:   PetscErrorCode (*apply)(MatPartitioning,IS*);
    531:   PetscErrorCode (*applynd)(MatPartitioning,IS*);
    532:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatPartitioning);
    533:   PetscErrorCode (*destroy)(MatPartitioning);
    534:   PetscErrorCode (*view)(MatPartitioning,PetscViewer);
    535:   PetscErrorCode (*improve)(MatPartitioning,IS*);
    536: };

    538: struct _p_MatPartitioning {
    539:   PETSCHEADER(struct _MatPartitioningOps);
    540:   Mat         adj;
    541:   PetscInt    *vertex_weights;
    542:   PetscReal   *part_weights;
    543:   PetscInt    n;                                 /* number of partitions */
    544:   void        *data;
    545:   PetscInt    setupcalled;
    546:   PetscBool   use_edge_weights;  /* A flag indicates whether or not to use edge weights */
    547: };

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

    552: /*
    553:     Object for coarsen graphs
    554: */
    555: typedef struct _MatCoarsenOps *MatCoarsenOps;
    556: struct _MatCoarsenOps {
    557:   PetscErrorCode (*apply)(MatCoarsen);
    558:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatCoarsen);
    559:   PetscErrorCode (*destroy)(MatCoarsen);
    560:   PetscErrorCode (*view)(MatCoarsen,PetscViewer);
    561: };

    563: struct _p_MatCoarsen {
    564:   PETSCHEADER(struct _MatCoarsenOps);
    565:   Mat              graph;
    566:   void             *subctx;
    567:   /* */
    568:   PetscBool        strict_aggs;
    569:   IS               perm;
    570:   PetscCoarsenData *agg_lists;
    571: };

    573: /*
    574:     MatFDColoring is used to compute Jacobian matrices efficiently
    575:   via coloring. The data structure is explained below in an example.

    577:    Color =   0    1     0    2   |   2      3       0
    578:    ---------------------------------------------------
    579:             00   01              |          05
    580:             10   11              |   14     15               Processor  0
    581:                        22    23  |          25
    582:                        32    33  |
    583:    ===================================================
    584:                                  |   44     45     46
    585:             50                   |          55               Processor 1
    586:                                  |   64            66
    587:    ---------------------------------------------------

    589:     ncolors = 4;

    591:     ncolumns      = {2,1,1,0}
    592:     columns       = {{0,2},{1},{3},{}}
    593:     nrows         = {4,2,3,3}
    594:     rows          = {{0,1,2,3},{0,1},{1,2,3},{0,1,2}}
    595:     vwscale       = {dx(0),dx(1),dx(2),dx(3)}               MPI Vec
    596:     vscale        = {dx(0),dx(1),dx(2),dx(3),dx(4),dx(5)}   Seq Vec

    598:     ncolumns      = {1,0,1,1}
    599:     columns       = {{6},{},{4},{5}}
    600:     nrows         = {3,0,2,2}
    601:     rows          = {{0,1,2},{},{1,2},{1,2}}
    602:     vwscale       = {dx(4),dx(5),dx(6)}              MPI Vec
    603:     vscale        = {dx(0),dx(4),dx(5),dx(6)}        Seq Vec

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

    608: */
    609: typedef struct {
    610:   PetscInt     row;
    611:   PetscInt     col;
    612:   PetscScalar  *valaddr;   /* address of value */
    613: } MatEntry;

    615: typedef struct {
    616:   PetscInt     row;
    617:   PetscScalar  *valaddr;   /* address of value */
    618: } MatEntry2;

    620: struct  _p_MatFDColoring{
    621:   PETSCHEADER(int);
    622:   PetscInt       M,N,m;            /* total rows, columns; local rows */
    623:   PetscInt       rstart;           /* first row owned by local processor */
    624:   PetscInt       ncolors;          /* number of colors */
    625:   PetscInt       *ncolumns;        /* number of local columns for a color */
    626:   PetscInt       **columns;        /* lists the local columns of each color (using global column numbering) */
    627:   IS             *isa;             /* these are the IS that contain the column values given in columns */
    628:   PetscInt       *nrows;           /* number of local rows for each color */
    629:   MatEntry       *matentry;        /* holds (row, column, address of value) for Jacobian matrix entry */
    630:   MatEntry2      *matentry2;       /* holds (row, address of value) for Jacobian matrix entry */
    631:   PetscScalar    *dy;              /* store a block of F(x+dx)-F(x) when J is in BAIJ format */
    632:   PetscReal      error_rel;        /* square root of relative error in computing function */
    633:   PetscReal      umin;             /* minimum allowable u'dx value */
    634:   Vec            w1,w2,w3;         /* work vectors used in computing Jacobian */
    635:   PetscBool      fset;             /* indicates that the initial function value F(X) is set */
    636:   PetscErrorCode (*f)(void);       /* function that defines Jacobian */
    637:   void           *fctx;            /* optional user-defined context for use by the function f */
    638:   Vec            vscale;           /* holds FD scaling, i.e. 1/dx for each perturbed column */
    639:   PetscInt       currentcolor;     /* color for which function evaluation is being done now */
    640:   const char     *htype;           /* "wp" or "ds" */
    641:   ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_LOCAL */
    642:   PetscInt       brows,bcols;      /* number of block rows or columns for speedup inserting the dense matrix into sparse Jacobian */
    643:   PetscBool      setupcalled;      /* true if setup has been called */
    644:   PetscBool      viewed;           /* true if the -mat_fd_coloring_view has been triggered already */
    645:   void           (*ftn_func_pointer)(void),*ftn_func_cntx; /* serve the same purpose as *fortran_func_pointers in PETSc objects */
    646:   PetscObjectId  matid;            /* matrix this object was created with, must always be the same */
    647: };

    649: typedef struct _MatColoringOps *MatColoringOps;
    650: struct _MatColoringOps {
    651:   PetscErrorCode (*destroy)(MatColoring);
    652:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatColoring);
    653:   PetscErrorCode (*view)(MatColoring,PetscViewer);
    654:   PetscErrorCode (*apply)(MatColoring,ISColoring*);
    655:   PetscErrorCode (*weights)(MatColoring,PetscReal**,PetscInt**);
    656: };

    658: struct _p_MatColoring {
    659:   PETSCHEADER(struct _MatColoringOps);
    660:   Mat                   mat;
    661:   PetscInt              dist;             /* distance of the coloring */
    662:   PetscInt              maxcolors;        /* the maximum number of colors returned, maxcolors=1 for MIS */
    663:   void                  *data;            /* inner context */
    664:   PetscBool             valid;            /* check to see if what is produced is a valid coloring */
    665:   MatColoringWeightType weight_type;      /* type of weight computation to be performed */
    666:   PetscReal             *user_weights;    /* custom weights and permutation */
    667:   PetscInt              *user_lperm;
    668:   PetscBool             valid_iscoloring; /* check to see if matcoloring is produced a valid iscoloring */
    669: };

    671: struct  _p_MatTransposeColoring{
    672:   PETSCHEADER(int);
    673:   PetscInt       M,N,m;            /* total rows, columns; local rows */
    674:   PetscInt       rstart;           /* first row owned by local processor */
    675:   PetscInt       ncolors;          /* number of colors */
    676:   PetscInt       *ncolumns;        /* number of local columns for a color */
    677:   PetscInt       *nrows;           /* number of local rows for each color */
    678:   PetscInt       currentcolor;     /* color for which function evaluation is being done now */
    679:   ISColoringType ctype;            /* IS_COLORING_GLOBAL or IS_COLORING_LOCAL */

    681:   PetscInt       *colorforrow,*colorforcol;  /* pointer to rows and columns */
    682:   PetscInt       *rows;                      /* lists the local rows for each color (using the local row numbering) */
    683:   PetscInt       *den2sp;                    /* maps (row,color) in the dense matrix to index of sparse matrix array a->a */
    684:   PetscInt       *columns;                   /* lists the local columns of each color (using global column numbering) */
    685:   PetscInt       brows;                      /* number of rows for efficient implementation of MatTransColoringApplyDenToSp() */
    686:   PetscInt       *lstart;                    /* array used for loop over row blocks of Csparse */
    687: };

    689: /*
    690:    Null space context for preconditioner/operators
    691: */
    692: struct _p_MatNullSpace {
    693:   PETSCHEADER(int);
    694:   PetscBool      has_cnst;
    695:   PetscInt       n;
    696:   Vec*           vecs;
    697:   PetscScalar*   alpha;                 /* for projections */
    698:   PetscErrorCode (*remove)(MatNullSpace,Vec,void*);  /* for user provided removal function */
    699:   void*          rmctx;                 /* context for remove() function */
    700: };

    702: /*
    703:    Checking zero pivot for LU, ILU preconditioners.
    704: */
    705: typedef struct {
    706:   PetscInt       nshift,nshift_max;
    707:   PetscReal      shift_amount,shift_lo,shift_hi,shift_top,shift_fraction;
    708:   PetscBool      newshift;
    709:   PetscReal      rs;  /* active row sum of abs(offdiagonals) */
    710:   PetscScalar    pv;  /* pivot of the active row */
    711: } FactorShiftCtx;

    713: /*
    714:  Used by MatCreateSubMatrices_MPIXAIJ_Local()
    715: */
    716: #include <petscctable.h>
    717: typedef struct { /* used by MatCreateSubMatrices_MPIAIJ_SingleIS_Local() and MatCreateSubMatrices_MPIAIJ_Local */
    718:   PetscInt   id;   /* index of submats, only submats[0] is responsible for deleting some arrays below */
    719:   PetscInt   nrqs,nrqr;
    720:   PetscInt   **rbuf1,**rbuf2,**rbuf3,**sbuf1,**sbuf2;
    721:   PetscInt   **ptr;
    722:   PetscInt   *tmp;
    723:   PetscInt   *ctr;
    724:   PetscInt   *pa; /* proc array */
    725:   PetscInt   *req_size,*req_source1,*req_source2;
    726:   PetscBool  allcolumns,allrows;
    727:   PetscBool  singleis;
    728:   PetscInt   *row2proc; /* row to proc map */
    729:   PetscInt   nstages;
    730: #if defined(PETSC_USE_CTABLE)
    731:   PetscTable cmap,rmap;
    732:   PetscInt   *cmap_loc,*rmap_loc;
    733: #else
    734:   PetscInt   *cmap,*rmap;
    735: #endif

    737:   PetscErrorCode (*destroy)(Mat);
    738: } Mat_SubSppt;

    740: PETSC_EXTERN PetscErrorCode MatFactorDumpMatrix(Mat);
    741: PETSC_INTERN PetscErrorCode MatShift_Basic(Mat,PetscScalar);
    742: PETSC_INTERN PetscErrorCode MatSetBlockSizes_Default(Mat,PetscInt,PetscInt);

    744: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_nz(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    745: {
    746:   PetscReal _rs   = sctx->rs;
    747:   PetscReal _zero = info->zeropivot*_rs;

    750:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    751:     /* force |diag| > zeropivot*rs */
    752:     if (!sctx->nshift) sctx->shift_amount = info->shiftamount;
    753:     else sctx->shift_amount *= 2.0;
    754:     sctx->newshift = PETSC_TRUE;
    755:     (sctx->nshift)++;
    756:   } else {
    757:     sctx->newshift = PETSC_FALSE;
    758:   }
    759:   return(0);
    760: }

    762: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_pd(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    763: {
    764:   PetscReal _rs   = sctx->rs;
    765:   PetscReal _zero = info->zeropivot*_rs;

    768:   if (PetscRealPart(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    769:     /* force matfactor to be diagonally dominant */
    770:     if (sctx->nshift == sctx->nshift_max) {
    771:       sctx->shift_fraction = sctx->shift_hi;
    772:     } else {
    773:       sctx->shift_lo = sctx->shift_fraction;
    774:       sctx->shift_fraction = (sctx->shift_hi+sctx->shift_lo)/2.;
    775:     }
    776:     sctx->shift_amount = sctx->shift_fraction * sctx->shift_top;
    777:     sctx->nshift++;
    778:     sctx->newshift = PETSC_TRUE;
    779:   } else {
    780:     sctx->newshift = PETSC_FALSE;
    781:   }
    782:   return(0);
    783: }

    785: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_inblocks(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    786: {
    787:   PetscReal _zero = info->zeropivot;

    790:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    791:     sctx->pv          += info->shiftamount;
    792:     sctx->shift_amount = 0.0;
    793:     sctx->nshift++;
    794:   }
    795:   sctx->newshift = PETSC_FALSE;
    796:   return(0);
    797: }

    799: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_none(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    800: {
    801:   PetscReal      _zero = info->zeropivot;

    805:   sctx->newshift = PETSC_FALSE;
    806:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)) {
    807:     if (!mat->erroriffailure) {
    808:       PetscInfo3(mat,"Detected zero pivot in factorization in row %D value %g tolerance %g\n",row,(double)PetscAbsScalar(sctx->pv),(double)_zero);
    809:       fact->factorerrortype             = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    810:       fact->factorerror_zeropivot_value = PetscAbsScalar(sctx->pv);
    811:       fact->factorerror_zeropivot_row   = row;
    812:     } 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);
    813:   }
    814:   return(0);
    815: }

    817: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    818: {

    822:   if (info->shifttype == (PetscReal) MAT_SHIFT_NONZERO){
    823:     MatPivotCheck_nz(mat,info,sctx,row);
    824:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE){
    825:     MatPivotCheck_pd(mat,info,sctx,row);
    826:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_INBLOCKS){
    827:     MatPivotCheck_inblocks(mat,info,sctx,row);
    828:   } else {
    829:     MatPivotCheck_none(fact,mat,info,sctx,row);
    830:   }
    831:   return(0);
    832: }

    834: /*
    835:   Create and initialize a linked list
    836:   Input Parameters:
    837:     idx_start - starting index of the list
    838:     lnk_max   - max value of lnk indicating the end of the list
    839:     nlnk      - max length of the list
    840:   Output Parameters:
    841:     lnk       - list initialized
    842:     bt        - PetscBT (bitarray) with all bits set to false
    843:     lnk_empty - flg indicating the list is empty
    844: */
    845: #define PetscLLCreate(idx_start,lnk_max,nlnk,lnk,bt) \
    846:   (PetscMalloc1(nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,0))

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

    851: /*
    852:   Add an index set into a sorted linked list
    853:   Input Parameters:
    854:     nidx      - number of input indices
    855:     indices   - integer array
    856:     idx_start - starting index of the list
    857:     lnk       - linked list(an integer array) that is created
    858:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    859:   output Parameters:
    860:     nlnk      - number of newly added indices
    861:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    862:     bt        - updated PetscBT (bitarray)
    863: */
    864: #define PetscLLAdd(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    865: {\
    866:   PetscInt _k,_entry,_location,_lnkdata;\
    867:   nlnk     = 0;\
    868:   _lnkdata = idx_start;\
    869:   for (_k=0; _k<nidx; _k++){\
    870:     _entry = indices[_k];\
    871:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    872:       /* search for insertion location */\
    873:       /* start from the beginning if _entry < previous _entry */\
    874:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    875:       do {\
    876:         _location = _lnkdata;\
    877:         _lnkdata  = lnk[_location];\
    878:       } while (_entry > _lnkdata);\
    879:       /* insertion location is found, add entry into lnk */\
    880:       lnk[_location] = _entry;\
    881:       lnk[_entry]    = _lnkdata;\
    882:       nlnk++;\
    883:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    884:     }\
    885:   }\
    886: }

    888: /*
    889:   Add a permuted index set into a sorted linked list
    890:   Input Parameters:
    891:     nidx      - number of input indices
    892:     indices   - integer array
    893:     perm      - permutation of indices
    894:     idx_start - starting index of the list
    895:     lnk       - linked list(an integer array) that is created
    896:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    897:   output Parameters:
    898:     nlnk      - number of newly added indices
    899:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    900:     bt        - updated PetscBT (bitarray)
    901: */
    902: #define PetscLLAddPerm(nidx,indices,perm,idx_start,nlnk,lnk,bt) 0;\
    903: {\
    904:   PetscInt _k,_entry,_location,_lnkdata;\
    905:   nlnk     = 0;\
    906:   _lnkdata = idx_start;\
    907:   for (_k=0; _k<nidx; _k++){\
    908:     _entry = perm[indices[_k]];\
    909:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    910:       /* search for insertion location */\
    911:       /* start from the beginning if _entry < previous _entry */\
    912:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    913:       do {\
    914:         _location = _lnkdata;\
    915:         _lnkdata  = lnk[_location];\
    916:       } while (_entry > _lnkdata);\
    917:       /* insertion location is found, add entry into lnk */\
    918:       lnk[_location] = _entry;\
    919:       lnk[_entry]    = _lnkdata;\
    920:       nlnk++;\
    921:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    922:     }\
    923:   }\
    924: }

    926: /*
    927:   Add a SORTED ascending index set into a sorted linked list - same as PetscLLAdd() bus skip 'if (_k && _entry < _lnkdata) _lnkdata  = idx_start;'
    928:   Input Parameters:
    929:     nidx      - number of input indices
    930:     indices   - sorted integer array
    931:     idx_start - starting index of the list
    932:     lnk       - linked list(an integer array) that is created
    933:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    934:   output Parameters:
    935:     nlnk      - number of newly added indices
    936:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    937:     bt        - updated PetscBT (bitarray)
    938: */
    939: #define PetscLLAddSorted(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    940: {\
    941:   PetscInt _k,_entry,_location,_lnkdata;\
    942:   nlnk      = 0;\
    943:   _lnkdata  = idx_start;\
    944:   for (_k=0; _k<nidx; _k++){\
    945:     _entry = indices[_k];\
    946:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    947:       /* search for insertion location */\
    948:       do {\
    949:         _location = _lnkdata;\
    950:         _lnkdata  = lnk[_location];\
    951:       } while (_entry > _lnkdata);\
    952:       /* insertion location is found, add entry into lnk */\
    953:       lnk[_location] = _entry;\
    954:       lnk[_entry]    = _lnkdata;\
    955:       nlnk++;\
    956:       _lnkdata = _entry; /* next search starts from here */\
    957:     }\
    958:   }\
    959: }

    961: #define PetscLLAddSorted_new(nidx,indices,idx_start,lnk_empty,nlnk,lnk,bt) 0; \
    962: {\
    963:   PetscInt _k,_entry,_location,_lnkdata;\
    964:   if (lnk_empty){\
    965:     _lnkdata  = idx_start;                      \
    966:     for (_k=0; _k<nidx; _k++){                  \
    967:       _entry = indices[_k];                             \
    968:       PetscBTSet(bt,_entry);  /* mark the new entry */          \
    969:           _location = _lnkdata;                                 \
    970:           _lnkdata  = lnk[_location];                           \
    971:         /* insertion location is found, add entry into lnk */   \
    972:         lnk[_location] = _entry;                                \
    973:         lnk[_entry]    = _lnkdata;                              \
    974:         _lnkdata = _entry; /* next search starts from here */   \
    975:     }                                                           \
    976:     /*\
    977:     lnk[indices[nidx-1]] = lnk[idx_start];\
    978:     lnk[idx_start]       = indices[0];\
    979:     PetscBTSet(bt,indices[0]);  \
    980:     for (_k=1; _k<nidx; _k++){                  \
    981:       PetscBTSet(bt,indices[_k]);                                          \
    982:       lnk[indices[_k-1]] = indices[_k];                                  \
    983:     }                                                           \
    984:      */\
    985:     nlnk      = nidx;\
    986:     lnk_empty = PETSC_FALSE;\
    987:   } else {\
    988:     nlnk      = 0;                              \
    989:     _lnkdata  = idx_start;                      \
    990:     for (_k=0; _k<nidx; _k++){                  \
    991:       _entry = indices[_k];                             \
    992:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */       \
    993:         /* search for insertion location */                     \
    994:         do {                                                    \
    995:           _location = _lnkdata;                                 \
    996:           _lnkdata  = lnk[_location];                           \
    997:         } while (_entry > _lnkdata);                            \
    998:         /* insertion location is found, add entry into lnk */   \
    999:         lnk[_location] = _entry;                                \
    1000:         lnk[_entry]    = _lnkdata;                              \
    1001:         nlnk++;                                                 \
    1002:         _lnkdata = _entry; /* next search starts from here */   \
    1003:       }                                                         \
    1004:     }                                                           \
    1005:   }                                                             \
    1006: }

    1008: /*
    1009:   Add a SORTED index set into a sorted linked list used for LUFactorSymbolic()
    1010:   Same as PetscLLAddSorted() with an additional operation:
    1011:        count the number of input indices that are no larger than 'diag'
    1012:   Input Parameters:
    1013:     indices   - sorted integer array
    1014:     idx_start - starting index of the list, index of pivot row
    1015:     lnk       - linked list(an integer array) that is created
    1016:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1017:     diag      - index of the active row in LUFactorSymbolic
    1018:     nzbd      - number of input indices with indices <= idx_start
    1019:     im        - im[idx_start] is initialized as num of nonzero entries in row=idx_start
    1020:   output Parameters:
    1021:     nlnk      - number of newly added indices
    1022:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    1023:     bt        - updated PetscBT (bitarray)
    1024:     im        - im[idx_start]: unchanged if diag is not an entry
    1025:                              : num of entries with indices <= diag if diag is an entry
    1026: */
    1027: #define PetscLLAddSortedLU(indices,idx_start,nlnk,lnk,bt,diag,nzbd,im) 0;\
    1028: {\
    1029:   PetscInt _k,_entry,_location,_lnkdata,_nidx;\
    1030:   nlnk     = 0;\
    1031:   _lnkdata = idx_start;\
    1032:   _nidx = im[idx_start] - nzbd; /* num of entries with idx_start < index <= diag */\
    1033:   for (_k=0; _k<_nidx; _k++){\
    1034:     _entry = indices[_k];\
    1035:     nzbd++;\
    1036:     if (_entry== diag) im[idx_start] = nzbd;\
    1037:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1038:       /* search for insertion location */\
    1039:       do {\
    1040:         _location = _lnkdata;\
    1041:         _lnkdata  = lnk[_location];\
    1042:       } while (_entry > _lnkdata);\
    1043:       /* insertion location is found, add entry into lnk */\
    1044:       lnk[_location] = _entry;\
    1045:       lnk[_entry]    = _lnkdata;\
    1046:       nlnk++;\
    1047:       _lnkdata = _entry; /* next search starts from here */\
    1048:     }\
    1049:   }\
    1050: }

    1052: /*
    1053:   Copy data on the list into an array, then initialize the list
    1054:   Input Parameters:
    1055:     idx_start - starting index of the list
    1056:     lnk_max   - max value of lnk indicating the end of the list
    1057:     nlnk      - number of data on the list to be copied
    1058:     lnk       - linked list
    1059:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1060:   output Parameters:
    1061:     indices   - array that contains the copied data
    1062:     lnk       - linked list that is cleaned and initialize
    1063:     bt        - PetscBT (bitarray) with all bits set to false
    1064: */
    1065: #define PetscLLClean(idx_start,lnk_max,nlnk,lnk,indices,bt) 0;\
    1066: {\
    1067:   PetscInt _j,_idx=idx_start;\
    1068:   for (_j=0; _j<nlnk; _j++){\
    1069:     _idx = lnk[_idx];\
    1070:     indices[_j] = _idx;\
    1071:     PetscBTClear(bt,_idx);\
    1072:   }\
    1073:   lnk[idx_start] = lnk_max;\
    1074: }
    1075: /*
    1076:   Free memories used by the list
    1077: */
    1078: #define PetscLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    1080: /* Routines below are used for incomplete matrix factorization */
    1081: /*
    1082:   Create and initialize a linked list and its levels
    1083:   Input Parameters:
    1084:     idx_start - starting index of the list
    1085:     lnk_max   - max value of lnk indicating the end of the list
    1086:     nlnk      - max length of the list
    1087:   Output Parameters:
    1088:     lnk       - list initialized
    1089:     lnk_lvl   - array of size nlnk for storing levels of lnk
    1090:     bt        - PetscBT (bitarray) with all bits set to false
    1091: */
    1092: #define PetscIncompleteLLCreate(idx_start,lnk_max,nlnk,lnk,lnk_lvl,bt)\
    1093:   (PetscIntMultError(2,nlnk,NULL) || PetscMalloc1(2*nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,lnk_lvl = lnk + nlnk,0))

    1095: /*
    1096:   Initialize a sorted linked list used for ILU and ICC
    1097:   Input Parameters:
    1098:     nidx      - number of input idx
    1099:     idx       - integer array used for storing column indices
    1100:     idx_start - starting index of the list
    1101:     perm      - indices of an IS
    1102:     lnk       - linked list(an integer array) that is created
    1103:     lnklvl    - levels of lnk
    1104:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1105:   output Parameters:
    1106:     nlnk     - number of newly added idx
    1107:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1108:     lnklvl   - levels of lnk
    1109:     bt       - updated PetscBT (bitarray)
    1110: */
    1111: #define PetscIncompleteLLInit(nidx,idx,idx_start,perm,nlnk,lnk,lnklvl,bt) 0;\
    1112: {\
    1113:   PetscInt _k,_entry,_location,_lnkdata;\
    1114:   nlnk     = 0;\
    1115:   _lnkdata = idx_start;\
    1116:   for (_k=0; _k<nidx; _k++){\
    1117:     _entry = perm[idx[_k]];\
    1118:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1119:       /* search for insertion location */\
    1120:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1121:       do {\
    1122:         _location = _lnkdata;\
    1123:         _lnkdata  = lnk[_location];\
    1124:       } while (_entry > _lnkdata);\
    1125:       /* insertion location is found, add entry into lnk */\
    1126:       lnk[_location]  = _entry;\
    1127:       lnk[_entry]     = _lnkdata;\
    1128:       lnklvl[_entry] = 0;\
    1129:       nlnk++;\
    1130:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1131:     }\
    1132:   }\
    1133: }

    1135: /*
    1136:   Add a SORTED index set into a sorted linked list for ILU
    1137:   Input Parameters:
    1138:     nidx      - number of input indices
    1139:     idx       - sorted integer array used for storing column indices
    1140:     level     - level of fill, e.g., ICC(level)
    1141:     idxlvl    - level of idx
    1142:     idx_start - starting index of the list
    1143:     lnk       - linked list(an integer array) that is created
    1144:     lnklvl    - levels of lnk
    1145:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1146:     prow      - the row number of idx
    1147:   output Parameters:
    1148:     nlnk     - number of newly added idx
    1149:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1150:     lnklvl   - levels of lnk
    1151:     bt       - updated PetscBT (bitarray)

    1153:   Note: the level of factor(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(i,prow)+lvl(prow,j)+1)
    1154:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1155: */
    1156: #define PetscILULLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,lnklvl_prow) 0;\
    1157: {\
    1158:   PetscInt _k,_entry,_location,_lnkdata,_incrlev,_lnklvl_prow=lnklvl[prow];\
    1159:   nlnk     = 0;\
    1160:   _lnkdata = idx_start;\
    1161:   for (_k=0; _k<nidx; _k++){\
    1162:     _incrlev = idxlvl[_k] + _lnklvl_prow + 1;\
    1163:     if (_incrlev > level) continue;\
    1164:     _entry = idx[_k];\
    1165:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1166:       /* search for insertion location */\
    1167:       do {\
    1168:         _location = _lnkdata;\
    1169:         _lnkdata  = lnk[_location];\
    1170:       } while (_entry > _lnkdata);\
    1171:       /* insertion location is found, add entry into lnk */\
    1172:       lnk[_location]  = _entry;\
    1173:       lnk[_entry]     = _lnkdata;\
    1174:       lnklvl[_entry] = _incrlev;\
    1175:       nlnk++;\
    1176:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1177:     } else { /* existing entry: update lnklvl */\
    1178:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1179:     }\
    1180:   }\
    1181: }

    1183: /*
    1184:   Add a index set into a sorted linked list
    1185:   Input Parameters:
    1186:     nidx      - number of input idx
    1187:     idx   - integer array used for storing column indices
    1188:     level     - level of fill, e.g., ICC(level)
    1189:     idxlvl - level of idx
    1190:     idx_start - starting index of the list
    1191:     lnk       - linked list(an integer array) that is created
    1192:     lnklvl   - levels of lnk
    1193:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1194:   output Parameters:
    1195:     nlnk      - number of newly added idx
    1196:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1197:     lnklvl   - levels of lnk
    1198:     bt        - updated PetscBT (bitarray)
    1199: */
    1200: #define PetscIncompleteLLAdd(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1201: {\
    1202:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1203:   nlnk     = 0;\
    1204:   _lnkdata = idx_start;\
    1205:   for (_k=0; _k<nidx; _k++){\
    1206:     _incrlev = idxlvl[_k] + 1;\
    1207:     if (_incrlev > level) continue;\
    1208:     _entry = idx[_k];\
    1209:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1210:       /* search for insertion location */\
    1211:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1212:       do {\
    1213:         _location = _lnkdata;\
    1214:         _lnkdata  = lnk[_location];\
    1215:       } while (_entry > _lnkdata);\
    1216:       /* insertion location is found, add entry into lnk */\
    1217:       lnk[_location]  = _entry;\
    1218:       lnk[_entry]     = _lnkdata;\
    1219:       lnklvl[_entry] = _incrlev;\
    1220:       nlnk++;\
    1221:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1222:     } else { /* existing entry: update lnklvl */\
    1223:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1224:     }\
    1225:   }\
    1226: }

    1228: /*
    1229:   Add a SORTED index set into a sorted linked list
    1230:   Input Parameters:
    1231:     nidx      - number of input indices
    1232:     idx   - sorted integer array used for storing column indices
    1233:     level     - level of fill, e.g., ICC(level)
    1234:     idxlvl - level of idx
    1235:     idx_start - starting index of the list
    1236:     lnk       - linked list(an integer array) that is created
    1237:     lnklvl    - levels of lnk
    1238:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1239:   output Parameters:
    1240:     nlnk      - number of newly added idx
    1241:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1242:     lnklvl    - levels of lnk
    1243:     bt        - updated PetscBT (bitarray)
    1244: */
    1245: #define PetscIncompleteLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1246: {\
    1247:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1248:   nlnk = 0;\
    1249:   _lnkdata = idx_start;\
    1250:   for (_k=0; _k<nidx; _k++){\
    1251:     _incrlev = idxlvl[_k] + 1;\
    1252:     if (_incrlev > level) continue;\
    1253:     _entry = idx[_k];\
    1254:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1255:       /* search for insertion location */\
    1256:       do {\
    1257:         _location = _lnkdata;\
    1258:         _lnkdata  = lnk[_location];\
    1259:       } while (_entry > _lnkdata);\
    1260:       /* insertion location is found, add entry into lnk */\
    1261:       lnk[_location] = _entry;\
    1262:       lnk[_entry]    = _lnkdata;\
    1263:       lnklvl[_entry] = _incrlev;\
    1264:       nlnk++;\
    1265:       _lnkdata = _entry; /* next search starts from here */\
    1266:     } else { /* existing entry: update lnklvl */\
    1267:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1268:     }\
    1269:   }\
    1270: }

    1272: /*
    1273:   Add a SORTED index set into a sorted linked list for ICC
    1274:   Input Parameters:
    1275:     nidx      - number of input indices
    1276:     idx       - sorted integer array used for storing column indices
    1277:     level     - level of fill, e.g., ICC(level)
    1278:     idxlvl    - level of idx
    1279:     idx_start - starting index of the list
    1280:     lnk       - linked list(an integer array) that is created
    1281:     lnklvl    - levels of lnk
    1282:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1283:     idxlvl_prow - idxlvl[prow], where prow is the row number of the idx
    1284:   output Parameters:
    1285:     nlnk   - number of newly added indices
    1286:     lnk    - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1287:     lnklvl - levels of lnk
    1288:     bt     - updated PetscBT (bitarray)
    1289:   Note: the level of U(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(prow,i)+lvl(prow,j)+1)
    1290:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1291: */
    1292: #define PetscICCLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,idxlvl_prow) 0;\
    1293: {\
    1294:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1295:   nlnk = 0;\
    1296:   _lnkdata = idx_start;\
    1297:   for (_k=0; _k<nidx; _k++){\
    1298:     _incrlev = idxlvl[_k] + idxlvl_prow + 1;\
    1299:     if (_incrlev > level) continue;\
    1300:     _entry = idx[_k];\
    1301:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1302:       /* search for insertion location */\
    1303:       do {\
    1304:         _location = _lnkdata;\
    1305:         _lnkdata  = lnk[_location];\
    1306:       } while (_entry > _lnkdata);\
    1307:       /* insertion location is found, add entry into lnk */\
    1308:       lnk[_location] = _entry;\
    1309:       lnk[_entry]    = _lnkdata;\
    1310:       lnklvl[_entry] = _incrlev;\
    1311:       nlnk++;\
    1312:       _lnkdata = _entry; /* next search starts from here */\
    1313:     } else { /* existing entry: update lnklvl */\
    1314:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1315:     }\
    1316:   }\
    1317: }

    1319: /*
    1320:   Copy data on the list into an array, then initialize the list
    1321:   Input Parameters:
    1322:     idx_start - starting index of the list
    1323:     lnk_max   - max value of lnk indicating the end of the list
    1324:     nlnk      - number of data on the list to be copied
    1325:     lnk       - linked list
    1326:     lnklvl    - level of lnk
    1327:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1328:   output Parameters:
    1329:     indices - array that contains the copied data
    1330:     lnk     - linked list that is cleaned and initialize
    1331:     lnklvl  - level of lnk that is reinitialized
    1332:     bt      - PetscBT (bitarray) with all bits set to false
    1333: */
    1334: #define PetscIncompleteLLClean(idx_start,lnk_max,nlnk,lnk,lnklvl,indices,indiceslvl,bt) 0;\
    1335: do {\
    1336:   PetscInt _j,_idx=idx_start;\
    1337:   for (_j=0; _j<nlnk; _j++){\
    1338:     _idx = lnk[_idx];\
    1339:     *(indices+_j) = _idx;\
    1340:     *(indiceslvl+_j) = lnklvl[_idx];\
    1341:     lnklvl[_idx] = -1;\
    1342:     PetscBTClear(bt,_idx);\
    1343:   }\
    1344:   lnk[idx_start] = lnk_max;\
    1345: } while (0)
    1346: /*
    1347:   Free memories used by the list
    1348: */
    1349: #define PetscIncompleteLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    1351: #define MatCheckSameLocalSize(A,ar1,B,ar2) do { \
    1353:   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);} while (0)

    1355: #define MatCheckSameSize(A,ar1,B,ar2) do { \
    1356:   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);\
    1357:   MatCheckSameLocalSize(A,ar1,B,ar2);} while (0)

    1359: #define VecCheckMatCompatible(M,x,ar1,b,ar2) do { \
    1360:   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); \
    1361:   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);} while (0)

    1363: /* -------------------------------------------------------------------------------------------------------*/
    1364: #include <petscbt.h>
    1365: /*
    1366:   Create and initialize a condensed linked list -
    1367:     same as PetscLLCreate(), but uses a scalable array 'lnk' with size of max number of entries, not O(N).
    1368:     Barry suggested this approach (Dec. 6, 2011):
    1369:       I've thought of an alternative way of representing a linked list that is efficient but doesn't have the O(N) scaling issue
    1370:       (it may be faster than the O(N) even sequentially due to less crazy memory access).

    1372:       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
    1373:       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
    1374:       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
    1375:       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.
    1376:       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
    1377:       to each other so memory access is much better than using the big array.

    1379:   Example:
    1380:      nlnk_max=5, lnk_max=36:
    1381:      Initial list: [0, 0 | 36, 2 | 0, 0 | 0, 0 | 0, 0 | 0, 0 | 0, 0]
    1382:      here, head_node has index 2 with value lnk[2]=lnk_max=36,
    1383:            0-th entry is used to store the number of entries in the list,
    1384:      The initial lnk represents head -> tail(marked by 36) with number of entries = lnk[0]=0.

    1386:      Now adding a sorted set {2,4}, the list becomes
    1387:      [2, 0 | 36, 4 |2, 6 | 4, 2 | 0, 0 | 0, 0 | 0, 0 ]
    1388:      represents head -> 2 -> 4 -> tail with number of entries = lnk[0]=2.

    1390:      Then adding a sorted set {0,3,35}, the list
    1391:      [5, 0 | 36, 8 | 2, 10 | 4, 12 | 0, 4 | 3, 6 | 35, 2 ]
    1392:      represents head -> 0 -> 2 -> 3 -> 4 -> 35 -> tail with number of entries = lnk[0]=5.

    1394:   Input Parameters:
    1395:     nlnk_max  - max length of the list
    1396:     lnk_max   - max value of the entries
    1397:   Output Parameters:
    1398:     lnk       - list created and initialized
    1399:     bt        - PetscBT (bitarray) with all bits set to false. Note: bt has size lnk_max, not nln_max!
    1400: */
    1401: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate(PetscInt nlnk_max,PetscInt lnk_max,PetscInt **lnk,PetscBT *bt)
    1402: {
    1404:   PetscInt       *llnk,lsize = 0;

    1407:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1408:   PetscMalloc1(lsize,lnk);
    1409:   PetscBTCreate(lnk_max,bt);
    1410:   llnk = *lnk;
    1411:   llnk[0] = 0;         /* number of entries on the list */
    1412:   llnk[2] = lnk_max;   /* value in the head node */
    1413:   llnk[3] = 2;         /* next for the head node */
    1414:   return(0);
    1415: }

    1417: /*
    1418:   Add a SORTED ascending index set into a sorted linked list. See PetscLLCondensedCreate() for detailed description.
    1419:   Input Parameters:
    1420:     nidx      - number of input indices
    1421:     indices   - sorted integer array
    1422:     lnk       - condensed linked list(an integer array) that is created
    1423:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1424:   output Parameters:
    1425:     lnk       - the sorted(increasing order) linked list containing previous and newly added non-redundate indices
    1426:     bt        - updated PetscBT (bitarray)
    1427: */
    1428: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted(PetscInt nidx,const PetscInt indices[],PetscInt lnk[],PetscBT bt)
    1429: {
    1430:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;

    1433:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1434:   _location = 2; /* head */
    1435:     for (_k=0; _k<nidx; _k++){
    1436:       _entry = indices[_k];
    1437:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */
    1438:         /* search for insertion location */
    1439:         do {
    1440:           _next     = _location + 1; /* link from previous node to next node */
    1441:           _location = lnk[_next];    /* idx of next node */
    1442:           _lnkdata  = lnk[_location];/* value of next node */
    1443:         } while (_entry > _lnkdata);
    1444:         /* insertion location is found, add entry into lnk */
    1445:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1446:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1447:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1448:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1449:         _location       = _newnode;      /* next search starts from the new node */
    1450:         _nlnk++;
    1451:       }   \
    1452:     }\
    1453:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1454:   return(0);
    1455: }

    1457: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean(PetscInt lnk_max,PetscInt nidx,PetscInt *indices,PetscInt lnk[],PetscBT bt)
    1458: {
    1460:   PetscInt       _k,_next,_nlnk;

    1463:   _next = lnk[3];       /* head node */
    1464:   _nlnk = lnk[0];       /* num of entries on the list */
    1465:   for (_k=0; _k<_nlnk; _k++){
    1466:     indices[_k] = lnk[_next];
    1467:     _next       = lnk[_next + 1];
    1468:     PetscBTClear(bt,indices[_k]);
    1469:   }
    1470:   lnk[0] = 0;          /* num of entries on the list */
    1471:   lnk[2] = lnk_max;    /* initialize head node */
    1472:   lnk[3] = 2;          /* head node */
    1473:   return(0);
    1474: }

    1476: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView(PetscInt *lnk)
    1477: {
    1479:   PetscInt       k;

    1482:   PetscPrintf(PETSC_COMM_SELF,"LLCondensed of size %D, (val,  next)\n",lnk[0]);
    1483:   for (k=2; k< lnk[0]+2; k++){
    1484:     PetscPrintf(PETSC_COMM_SELF," %D: (%D, %D)\n",2*k,lnk[2*k],lnk[2*k+1]);
    1485:   }
    1486:   return(0);
    1487: }

    1489: /*
    1490:   Free memories used by the list
    1491: */
    1492: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy(PetscInt *lnk,PetscBT bt)
    1493: {

    1497:   PetscFree(lnk);
    1498:   PetscBTDestroy(&bt);
    1499:   return(0);
    1500: }

    1502: /* -------------------------------------------------------------------------------------------------------*/
    1503: /*
    1504:  Same as PetscLLCondensedCreate(), but does not use non-scalable O(lnk_max) bitarray
    1505:   Input Parameters:
    1506:     nlnk_max  - max length of the list
    1507:   Output Parameters:
    1508:     lnk       - list created and initialized
    1509: */
    1510: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_Scalable(PetscInt nlnk_max,PetscInt **lnk)
    1511: {
    1513:   PetscInt       *llnk,lsize = 0;

    1516:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1517:   PetscMalloc1(lsize,lnk);
    1518:   llnk = *lnk;
    1519:   llnk[0] = 0;               /* number of entries on the list */
    1520:   llnk[2] = PETSC_MAX_INT;   /* value in the head node */
    1521:   llnk[3] = 2;               /* next for the head node */
    1522:   return(0);
    1523: }

    1525: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedExpand_Scalable(PetscInt nlnk_max,PetscInt **lnk)
    1526: {
    1528:   PetscInt       lsize = 0;

    1531:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1532:   PetscRealloc(lsize*sizeof(PetscInt),lnk);
    1533:   return(0);
    1534: }

    1536: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_Scalable(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1537: {
    1538:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;
    1539:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1540:   _location = 2; /* head */ \
    1541:     for (_k=0; _k<nidx; _k++){
    1542:       _entry = indices[_k];
    1543:       /* search for insertion location */
    1544:       do {
    1545:         _next     = _location + 1; /* link from previous node to next node */
    1546:         _location = lnk[_next];    /* idx of next node */
    1547:         _lnkdata  = lnk[_location];/* value of next node */
    1548:       } while (_entry > _lnkdata);
    1549:       if (_entry < _lnkdata) {
    1550:         /* insertion location is found, add entry into lnk */
    1551:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1552:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1553:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1554:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1555:         _location       = _newnode;      /* next search starts from the new node */
    1556:         _nlnk++;
    1557:       }
    1558:     }
    1559:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1560:   return 0;
    1561: }

    1563: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_Scalable(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1564: {
    1565:   PetscInt _k,_next,_nlnk;
    1566:   _next = lnk[3];       /* head node */
    1567:   _nlnk = lnk[0];
    1568:   for (_k=0; _k<_nlnk; _k++){
    1569:     indices[_k] = lnk[_next];
    1570:     _next       = lnk[_next + 1];
    1571:   }
    1572:   lnk[0] = 0;          /* num of entries on the list */
    1573:   lnk[3] = 2;          /* head node */
    1574:   return 0;
    1575: }

    1577: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_Scalable(PetscInt *lnk)
    1578: {
    1579:   return PetscFree(lnk);
    1580: }

    1582: /* -------------------------------------------------------------------------------------------------------*/
    1583: /*
    1584:       lnk[0]   number of links
    1585:       lnk[1]   number of entries
    1586:       lnk[3n]  value
    1587:       lnk[3n+1] len
    1588:       lnk[3n+2] link to next value

    1590:       The next three are always the first link

    1592:       lnk[3]    PETSC_MIN_INT+1
    1593:       lnk[4]    1
    1594:       lnk[5]    link to first real entry

    1596:       The next three are always the last link

    1598:       lnk[6]    PETSC_MAX_INT - 1
    1599:       lnk[7]    1
    1600:       lnk[8]    next valid link (this is the same as lnk[0] but without the decreases)
    1601: */

    1603: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_fast(PetscInt nlnk_max,PetscInt **lnk)
    1604: {
    1606:   PetscInt       *llnk,lsize = 0;

    1609:   PetscIntMultError(3,nlnk_max+3,&lsize);
    1610:   PetscMalloc1(lsize,lnk);
    1611:   llnk = *lnk;
    1612:   llnk[0] = 0;   /* nlnk: number of entries on the list */
    1613:   llnk[1] = 0;          /* number of integer entries represented in list */
    1614:   llnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1615:   llnk[4] = 1;           /* count for the first node */
    1616:   llnk[5] = 6;         /* next for the first node */
    1617:   llnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1618:   llnk[7] = 1;           /* count for the last node */
    1619:   llnk[8] = 0;         /* next valid node to be used */
    1620:   return(0);
    1621: }

    1623: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_fast(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1624: {
    1625:   PetscInt k,entry,prev,next;
    1626:   prev      = 3;      /* first value */
    1627:   next      = lnk[prev+2];
    1628:   for (k=0; k<nidx; k++){
    1629:     entry = indices[k];
    1630:     /* search for insertion location */
    1631:     while (entry >= lnk[next]) {
    1632:       prev = next;
    1633:       next = lnk[next+2];
    1634:     }
    1635:     /* entry is in range of previous list */
    1636:     if (entry < lnk[prev]+lnk[prev+1]) continue;
    1637:     lnk[1]++;
    1638:     /* entry is right after previous list */
    1639:     if (entry == lnk[prev]+lnk[prev+1]) {
    1640:       lnk[prev+1]++;
    1641:       if (lnk[next] == entry+1) { /* combine two contiguous strings */
    1642:         lnk[prev+1] += lnk[next+1];
    1643:         lnk[prev+2]  = lnk[next+2];
    1644:         next         = lnk[next+2];
    1645:         lnk[0]--;
    1646:       }
    1647:       continue;
    1648:     }
    1649:     /* entry is right before next list */
    1650:     if (entry == lnk[next]-1) {
    1651:       lnk[next]--;
    1652:       lnk[next+1]++;
    1653:       prev = next;
    1654:       next = lnk[prev+2];
    1655:       continue;
    1656:     }
    1657:     /*  add entry into lnk */
    1658:     lnk[prev+2]    = 3*((lnk[8]++)+3);      /* connect previous node to the new node */
    1659:     prev           = lnk[prev+2];
    1660:     lnk[prev]      = entry;        /* set value of the new node */
    1661:     lnk[prev+1]    = 1;             /* number of values in contiguous string is one to start */
    1662:     lnk[prev+2]    = next;          /* connect new node to next node */
    1663:     lnk[0]++;
    1664:   }
    1665:   return 0;
    1666: }

    1668: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_fast(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1669: {
    1670:   PetscInt _k,_next,_nlnk,cnt,j;
    1671:   _next = lnk[5];       /* first node */
    1672:   _nlnk = lnk[0];
    1673:   cnt   = 0;
    1674:   for (_k=0; _k<_nlnk; _k++){
    1675:     for (j=0; j<lnk[_next+1]; j++) {
    1676:       indices[cnt++] = lnk[_next] + j;
    1677:     }
    1678:     _next       = lnk[_next + 2];
    1679:   }
    1680:   lnk[0] = 0;   /* nlnk: number of links */
    1681:   lnk[1] = 0;          /* number of integer entries represented in list */
    1682:   lnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1683:   lnk[4] = 1;           /* count for the first node */
    1684:   lnk[5] = 6;         /* next for the first node */
    1685:   lnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1686:   lnk[7] = 1;           /* count for the last node */
    1687:   lnk[8] = 0;         /* next valid location to make link */
    1688:   return 0;
    1689: }

    1691: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView_fast(PetscInt *lnk)
    1692: {
    1693:   PetscInt k,next,nlnk;
    1694:   next = lnk[5];       /* first node */
    1695:   nlnk = lnk[0];
    1696:   for (k=0; k<nlnk; k++){
    1697: #if 0                           /* Debugging code */
    1698:     printf("%d value %d len %d next %d\n",next,lnk[next],lnk[next+1],lnk[next+2]);
    1699: #endif
    1700:     next = lnk[next + 2];
    1701:   }
    1702:   return 0;
    1703: }

    1705: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_fast(PetscInt *lnk)
    1706: {
    1707:   return PetscFree(lnk);
    1708: }

    1710: /* this is extern because it is used in MatFDColoringUseDM() which is in the DM library */
    1711: PETSC_EXTERN PetscErrorCode MatFDColoringApply_AIJ(Mat,MatFDColoring,Vec,void*);

    1713: PETSC_EXTERN PetscLogEvent MAT_Mult;
    1714: PETSC_EXTERN PetscLogEvent MAT_MultMatrixFree;
    1715: PETSC_EXTERN PetscLogEvent MAT_Mults;
    1716: PETSC_EXTERN PetscLogEvent MAT_MultConstrained;
    1717: PETSC_EXTERN PetscLogEvent MAT_MultAdd;
    1718: PETSC_EXTERN PetscLogEvent MAT_MultTranspose;
    1719: PETSC_EXTERN PetscLogEvent MAT_MultTransposeConstrained;
    1720: PETSC_EXTERN PetscLogEvent MAT_MultTransposeAdd;
    1721: PETSC_EXTERN PetscLogEvent MAT_Solve;
    1722: PETSC_EXTERN PetscLogEvent MAT_Solves;
    1723: PETSC_EXTERN PetscLogEvent MAT_SolveAdd;
    1724: PETSC_EXTERN PetscLogEvent MAT_SolveTranspose;
    1725: PETSC_EXTERN PetscLogEvent MAT_SolveTransposeAdd;
    1726: PETSC_EXTERN PetscLogEvent MAT_SOR;
    1727: PETSC_EXTERN PetscLogEvent MAT_ForwardSolve;
    1728: PETSC_EXTERN PetscLogEvent MAT_BackwardSolve;
    1729: PETSC_EXTERN PetscLogEvent MAT_LUFactor;
    1730: PETSC_EXTERN PetscLogEvent MAT_LUFactorSymbolic;
    1731: PETSC_EXTERN PetscLogEvent MAT_LUFactorNumeric;
    1732: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactor;
    1733: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactorSymbolic;
    1734: PETSC_EXTERN PetscLogEvent MAT_CholeskyFactorNumeric;
    1735: PETSC_EXTERN PetscLogEvent MAT_ILUFactor;
    1736: PETSC_EXTERN PetscLogEvent MAT_ILUFactorSymbolic;
    1737: PETSC_EXTERN PetscLogEvent MAT_ICCFactorSymbolic;
    1738: PETSC_EXTERN PetscLogEvent MAT_Copy;
    1739: PETSC_EXTERN PetscLogEvent MAT_Convert;
    1740: PETSC_EXTERN PetscLogEvent MAT_Scale;
    1741: PETSC_EXTERN PetscLogEvent MAT_AssemblyBegin;
    1742: PETSC_EXTERN PetscLogEvent MAT_AssemblyEnd;
    1743: PETSC_EXTERN PetscLogEvent MAT_SetValues;
    1744: PETSC_EXTERN PetscLogEvent MAT_GetValues;
    1745: PETSC_EXTERN PetscLogEvent MAT_GetRow;
    1746: PETSC_EXTERN PetscLogEvent MAT_GetRowIJ;
    1747: PETSC_EXTERN PetscLogEvent MAT_CreateSubMats;
    1748: PETSC_EXTERN PetscLogEvent MAT_GetColoring;
    1749: PETSC_EXTERN PetscLogEvent MAT_GetOrdering;
    1750: PETSC_EXTERN PetscLogEvent MAT_RedundantMat;
    1751: PETSC_EXTERN PetscLogEvent MAT_IncreaseOverlap;
    1752: PETSC_EXTERN PetscLogEvent MAT_Partitioning;
    1753: PETSC_EXTERN PetscLogEvent MAT_PartitioningND;
    1754: PETSC_EXTERN PetscLogEvent MAT_Coarsen;
    1755: PETSC_EXTERN PetscLogEvent MAT_ZeroEntries;
    1756: PETSC_EXTERN PetscLogEvent MAT_Load;
    1757: PETSC_EXTERN PetscLogEvent MAT_View;
    1758: PETSC_EXTERN PetscLogEvent MAT_AXPY;
    1759: PETSC_EXTERN PetscLogEvent MAT_FDColoringCreate;
    1760: PETSC_EXTERN PetscLogEvent MAT_TransposeColoringCreate;
    1761: PETSC_EXTERN PetscLogEvent MAT_FDColoringSetUp;
    1762: PETSC_EXTERN PetscLogEvent MAT_FDColoringApply;
    1763: PETSC_EXTERN PetscLogEvent MAT_Transpose;
    1764: PETSC_EXTERN PetscLogEvent MAT_FDColoringFunction;
    1765: PETSC_EXTERN PetscLogEvent MAT_CreateSubMat;
    1766: PETSC_EXTERN PetscLogEvent MAT_MatSolve;
    1767: PETSC_EXTERN PetscLogEvent MAT_MatTrSolve;
    1768: PETSC_EXTERN PetscLogEvent MAT_MatMultSymbolic;
    1769: PETSC_EXTERN PetscLogEvent MAT_MatMultNumeric;
    1770: PETSC_EXTERN PetscLogEvent MAT_Getlocalmatcondensed;
    1771: PETSC_EXTERN PetscLogEvent MAT_GetBrowsOfAcols;
    1772: PETSC_EXTERN PetscLogEvent MAT_GetBrowsOfAocols;
    1773: PETSC_EXTERN PetscLogEvent MAT_PtAPSymbolic;
    1774: PETSC_EXTERN PetscLogEvent MAT_PtAPNumeric;
    1775: PETSC_EXTERN PetscLogEvent MAT_Seqstompinum;
    1776: PETSC_EXTERN PetscLogEvent MAT_Seqstompisym;
    1777: PETSC_EXTERN PetscLogEvent MAT_Seqstompi;
    1778: PETSC_EXTERN PetscLogEvent MAT_Getlocalmat;
    1779: PETSC_EXTERN PetscLogEvent MAT_RARtSymbolic;
    1780: PETSC_EXTERN PetscLogEvent MAT_RARtNumeric;
    1781: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMultSymbolic;
    1782: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMultNumeric;
    1783: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMultSymbolic;
    1784: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMultNumeric;
    1785: PETSC_EXTERN PetscLogEvent MAT_MatMatMultSymbolic;
    1786: PETSC_EXTERN PetscLogEvent MAT_MatMatMultNumeric;
    1787: PETSC_EXTERN PetscLogEvent MAT_Applypapt;
    1788: PETSC_EXTERN PetscLogEvent MAT_Applypapt_symbolic;
    1789: PETSC_EXTERN PetscLogEvent MAT_Applypapt_numeric;
    1790: PETSC_EXTERN PetscLogEvent MAT_Getsymtranspose;
    1791: PETSC_EXTERN PetscLogEvent MAT_Getsymtransreduced;
    1792: PETSC_EXTERN PetscLogEvent MAT_GetSequentialNonzeroStructure;
    1793: PETSC_EXTERN PetscLogEvent MATMFFD_Mult;
    1794: PETSC_EXTERN PetscLogEvent MAT_GetMultiProcBlock;
    1795: PETSC_EXTERN PetscLogEvent MAT_CUSPARSECopyToGPU;
    1796: PETSC_EXTERN PetscLogEvent MAT_CUSPARSECopyFromGPU;
    1797: PETSC_EXTERN PetscLogEvent MAT_CUSPARSEGenerateTranspose;
    1798: PETSC_EXTERN PetscLogEvent MAT_CUSPARSESolveAnalysis;
    1799: PETSC_EXTERN PetscLogEvent MAT_SetValuesBatch;
    1800: PETSC_EXTERN PetscLogEvent MAT_ViennaCLCopyToGPU;
    1801: PETSC_EXTERN PetscLogEvent MAT_DenseCopyToGPU;
    1802: PETSC_EXTERN PetscLogEvent MAT_DenseCopyFromGPU;
    1803: PETSC_EXTERN PetscLogEvent MAT_Merge;
    1804: PETSC_EXTERN PetscLogEvent MAT_Residual;
    1805: PETSC_EXTERN PetscLogEvent MAT_SetRandom;
    1806: PETSC_EXTERN PetscLogEvent MAT_FactorFactS;
    1807: PETSC_EXTERN PetscLogEvent MAT_FactorInvS;
    1808: PETSC_EXTERN PetscLogEvent MAT_PreallCOO;
    1809: PETSC_EXTERN PetscLogEvent MAT_SetVCOO;
    1810: PETSC_EXTERN PetscLogEvent MATCOLORING_Apply;
    1811: PETSC_EXTERN PetscLogEvent MATCOLORING_Comm;
    1812: PETSC_EXTERN PetscLogEvent MATCOLORING_Local;
    1813: PETSC_EXTERN PetscLogEvent MATCOLORING_ISCreate;
    1814: PETSC_EXTERN PetscLogEvent MATCOLORING_SetUp;
    1815: PETSC_EXTERN PetscLogEvent MATCOLORING_Weights;

    1817: #endif