Actual source code: matimpl.h
petsc-3.7.7 2017-09-25
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      2: #ifndef __MATIMPL_H

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

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

     19: /*
     20:   This file defines the parts of the matrix data structure that are
     21:   shared by all matrix types.
     22: */

     24: /*
     25:     If you add entries here also add them to the MATOP enum
     26:     in include/petscmat.h and include/petsc/finclude/petscmat.h
     27: */
     28: typedef struct _MatOps *MatOps;
     29: struct _MatOps {
     30:   /* 0*/
     31:   PetscErrorCode (*setvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
     32:   PetscErrorCode (*getrow)(Mat,PetscInt,PetscInt *,PetscInt*[],PetscScalar*[]);
     33:   PetscErrorCode (*restorerow)(Mat,PetscInt,PetscInt *,PetscInt *[],PetscScalar *[]);
     34:   PetscErrorCode (*mult)(Mat,Vec,Vec);
     35:   PetscErrorCode (*multadd)(Mat,Vec,Vec,Vec);
     36:   /* 5*/
     37:   PetscErrorCode (*multtranspose)(Mat,Vec,Vec);
     38:   PetscErrorCode (*multtransposeadd)(Mat,Vec,Vec,Vec);
     39:   PetscErrorCode (*solve)(Mat,Vec,Vec);
     40:   PetscErrorCode (*solveadd)(Mat,Vec,Vec,Vec);
     41:   PetscErrorCode (*solvetranspose)(Mat,Vec,Vec);
     42:   /*10*/
     43:   PetscErrorCode (*solvetransposeadd)(Mat,Vec,Vec,Vec);
     44:   PetscErrorCode (*lufactor)(Mat,IS,IS,const MatFactorInfo*);
     45:   PetscErrorCode (*choleskyfactor)(Mat,IS,const MatFactorInfo*);
     46:   PetscErrorCode (*sor)(Mat,Vec,PetscReal,MatSORType,PetscReal,PetscInt,PetscInt,Vec);
     47:   PetscErrorCode (*transpose)(Mat,MatReuse,Mat *);
     48:   /*15*/
     49:   PetscErrorCode (*getinfo)(Mat,MatInfoType,MatInfo*);
     50:   PetscErrorCode (*equal)(Mat,Mat,PetscBool  *);
     51:   PetscErrorCode (*getdiagonal)(Mat,Vec);
     52:   PetscErrorCode (*diagonalscale)(Mat,Vec,Vec);
     53:   PetscErrorCode (*norm)(Mat,NormType,PetscReal*);
     54:   /*20*/
     55:   PetscErrorCode (*assemblybegin)(Mat,MatAssemblyType);
     56:   PetscErrorCode (*assemblyend)(Mat,MatAssemblyType);
     57:   PetscErrorCode (*setoption)(Mat,MatOption,PetscBool );
     58:   PetscErrorCode (*zeroentries)(Mat);
     59:   /*24*/
     60:   PetscErrorCode (*zerorows)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
     61:   PetscErrorCode (*lufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
     62:   PetscErrorCode (*lufactornumeric)(Mat,Mat,const MatFactorInfo*);
     63:   PetscErrorCode (*choleskyfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
     64:   PetscErrorCode (*choleskyfactornumeric)(Mat,Mat,const MatFactorInfo*);
     65:   /*29*/
     66:   PetscErrorCode (*setup)(Mat);
     67:   PetscErrorCode (*ilufactorsymbolic)(Mat,Mat,IS,IS,const MatFactorInfo*);
     68:   PetscErrorCode (*iccfactorsymbolic)(Mat,Mat,IS,const MatFactorInfo*);
     69:   PetscErrorCode (*placeholder_32)(Mat);
     70:   PetscErrorCode (*placeholder_33)(Mat);
     71:   /*34*/
     72:   PetscErrorCode (*duplicate)(Mat,MatDuplicateOption,Mat*);
     73:   PetscErrorCode (*forwardsolve)(Mat,Vec,Vec);
     74:   PetscErrorCode (*backwardsolve)(Mat,Vec,Vec);
     75:   PetscErrorCode (*ilufactor)(Mat,IS,IS,const MatFactorInfo*);
     76:   PetscErrorCode (*iccfactor)(Mat,IS,const MatFactorInfo*);
     77:   /*39*/
     78:   PetscErrorCode (*axpy)(Mat,PetscScalar,Mat,MatStructure);
     79:   PetscErrorCode (*getsubmatrices)(Mat,PetscInt,const IS[],const IS[],MatReuse,Mat *[]);
     80:   PetscErrorCode (*increaseoverlap)(Mat,PetscInt,IS[],PetscInt);
     81:   PetscErrorCode (*getvalues)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],PetscScalar []);
     82:   PetscErrorCode (*copy)(Mat,Mat,MatStructure);
     83:   /*44*/
     84:   PetscErrorCode (*getrowmax)(Mat,Vec,PetscInt[]);
     85:   PetscErrorCode (*scale)(Mat,PetscScalar);
     86:   PetscErrorCode (*shift)(Mat,PetscScalar);
     87:   PetscErrorCode (*diagonalset)(Mat,Vec,InsertMode);
     88:   PetscErrorCode (*zerorowscolumns)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
     89:   /*49*/
     90:   PetscErrorCode (*setrandom)(Mat,PetscRandom);
     91:   PetscErrorCode (*getrowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     92:   PetscErrorCode (*restorerowij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt *,const PetscInt *[],const PetscInt *[],PetscBool  *);
     93:   PetscErrorCode (*getcolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     94:   PetscErrorCode (*restorecolumnij)(Mat,PetscInt,PetscBool ,PetscBool ,PetscInt*,const PetscInt *[],const PetscInt *[],PetscBool  *);
     95:   /*54*/
     96:   PetscErrorCode (*fdcoloringcreate)(Mat,ISColoring,MatFDColoring);
     97:   PetscErrorCode (*coloringpatch)(Mat,PetscInt,PetscInt,ISColoringValue[],ISColoring*);
     98:   PetscErrorCode (*setunfactored)(Mat);
     99:   PetscErrorCode (*permute)(Mat,IS,IS,Mat*);
    100:   PetscErrorCode (*setvaluesblocked)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    101:   /*59*/
    102:   PetscErrorCode (*getsubmatrix)(Mat,IS,IS,MatReuse,Mat*);
    103:   PetscErrorCode (*destroy)(Mat);
    104:   PetscErrorCode (*view)(Mat,PetscViewer);
    105:   PetscErrorCode (*convertfrom)(Mat, MatType,MatReuse,Mat*);
    106:   PetscErrorCode (*matmatmult)(Mat,Mat,Mat,MatReuse,PetscReal,Mat*);
    107:   /*64*/
    108:   PetscErrorCode (*matmatmultsymbolic)(Mat,Mat,Mat,PetscReal,Mat*);
    109:   PetscErrorCode (*matmatmultnumeric)(Mat,Mat,Mat,Mat);
    110:   PetscErrorCode (*setlocaltoglobalmapping)(Mat,ISLocalToGlobalMapping,ISLocalToGlobalMapping);
    111:   PetscErrorCode (*setvalueslocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    112:   PetscErrorCode (*zerorowslocal)(Mat,PetscInt,const PetscInt[],PetscScalar,Vec,Vec);
    113:   /*69*/
    114:   PetscErrorCode (*getrowmaxabs)(Mat,Vec,PetscInt[]);
    115:   PetscErrorCode (*getrowminabs)(Mat,Vec,PetscInt[]);
    116:   PetscErrorCode (*convert)(Mat, MatType,MatReuse,Mat*);
    117:   PetscErrorCode (*setcoloring)(Mat,ISColoring);
    118:   PetscErrorCode (*placeholder_73)(Mat,void*);
    119:   /*74*/
    120:   PetscErrorCode (*setvaluesadifor)(Mat,PetscInt,void*);
    121:   PetscErrorCode (*fdcoloringapply)(Mat,MatFDColoring,Vec,void*);
    122:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,Mat);
    123:   PetscErrorCode (*multconstrained)(Mat,Vec,Vec);
    124:   PetscErrorCode (*multtransposeconstrained)(Mat,Vec,Vec);
    125:   /*79*/
    126:   PetscErrorCode (*findzerodiagonals)(Mat,IS*);
    127:   PetscErrorCode (*mults)(Mat, Vecs, Vecs);
    128:   PetscErrorCode (*solves)(Mat, Vecs, Vecs);
    129:   PetscErrorCode (*getinertia)(Mat,PetscInt*,PetscInt*,PetscInt*);
    130:   PetscErrorCode (*load)(Mat, PetscViewer);
    131:   /*84*/
    132:   PetscErrorCode (*issymmetric)(Mat,PetscReal,PetscBool *);
    133:   PetscErrorCode (*ishermitian)(Mat,PetscReal,PetscBool *);
    134:   PetscErrorCode (*isstructurallysymmetric)(Mat,PetscBool *);
    135:   PetscErrorCode (*setvaluesblockedlocal)(Mat,PetscInt,const PetscInt[],PetscInt,const PetscInt[],const PetscScalar[],InsertMode);
    136:   PetscErrorCode (*getvecs)(Mat,Vec*,Vec*);
    137:   /*89*/
    138:   PetscErrorCode (*matmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    139:   PetscErrorCode (*matmultsymbolic)(Mat,Mat,PetscReal,Mat*);
    140:   PetscErrorCode (*matmultnumeric)(Mat,Mat,Mat);
    141:   PetscErrorCode (*ptap)(Mat,Mat,MatReuse,PetscReal,Mat*);
    142:   PetscErrorCode (*ptapsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
    143:   /*94*/
    144:   PetscErrorCode (*ptapnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
    145:   PetscErrorCode (*mattransposemult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    146:   PetscErrorCode (*mattransposemultsymbolic)(Mat,Mat,PetscReal,Mat*);
    147:   PetscErrorCode (*mattransposemultnumeric)(Mat,Mat,Mat);
    148:   PetscErrorCode (*placeholder_98)(Mat);
    149:   /*99*/
    150:   PetscErrorCode (*placeholder_99)(Mat);
    151:   PetscErrorCode (*placeholder_100)(Mat);
    152:   PetscErrorCode (*placeholder_101)(Mat);
    153:   PetscErrorCode (*conjugate)(Mat);                              /* complex conjugate */
    154:   PetscErrorCode (*placeholder_103)(void);
    155:   /*104*/
    156:   PetscErrorCode (*setvaluesrow)(Mat,PetscInt,const PetscScalar[]);
    157:   PetscErrorCode (*realpart)(Mat);
    158:   PetscErrorCode (*imaginarypart)(Mat);
    159:   PetscErrorCode (*getrowuppertriangular)(Mat);
    160:   PetscErrorCode (*restorerowuppertriangular)(Mat);
    161:   /*109*/
    162:   PetscErrorCode (*matsolve)(Mat,Mat,Mat);
    163:   PetscErrorCode (*placeholder_110)(Mat);
    164:   PetscErrorCode (*getrowmin)(Mat,Vec,PetscInt[]);
    165:   PetscErrorCode (*getcolumnvector)(Mat,Vec,PetscInt);
    166:   PetscErrorCode (*missingdiagonal)(Mat,PetscBool *,PetscInt*);
    167:   /*114*/
    168:   PetscErrorCode (*getseqnonzerostructure)(Mat,Mat *);
    169:   PetscErrorCode (*create)(Mat);
    170:   PetscErrorCode (*getghosts)(Mat,PetscInt*,const PetscInt *[]);
    171:   PetscErrorCode (*getlocalsubmatrix)(Mat,IS,IS,Mat*);
    172:   PetscErrorCode (*restorelocalsubmatrix)(Mat,IS,IS,Mat*);
    173:   /*119*/
    174:   PetscErrorCode (*multdiagonalblock)(Mat,Vec,Vec);
    175:   PetscErrorCode (*hermitiantranspose)(Mat,MatReuse,Mat*);
    176:   PetscErrorCode (*multhermitiantranspose)(Mat,Vec,Vec);
    177:   PetscErrorCode (*multhermitiantransposeadd)(Mat,Vec,Vec,Vec);
    178:   PetscErrorCode (*getmultiprocblock)(Mat,MPI_Comm,MatReuse,Mat*);
    179:   /*124*/
    180:   PetscErrorCode (*findnonzerorows)(Mat,IS*);
    181:   PetscErrorCode (*getcolumnnorms)(Mat,NormType,PetscReal*);
    182:   PetscErrorCode (*invertblockdiagonal)(Mat,const PetscScalar**);
    183:   PetscErrorCode (*placeholder_127)(Mat,Vec,Vec,Vec);
    184:   PetscErrorCode (*getsubmatricesmpi)(Mat,PetscInt,const IS[], const IS[], MatReuse, Mat**);
    185:   /*129*/
    186:   PetscErrorCode (*setvaluesbatch)(Mat,PetscInt,PetscInt,PetscInt*,const PetscScalar*);
    187:   PetscErrorCode (*transposematmult)(Mat,Mat,MatReuse,PetscReal,Mat*);
    188:   PetscErrorCode (*transposematmultsymbolic)(Mat,Mat,PetscReal,Mat*);
    189:   PetscErrorCode (*transposematmultnumeric)(Mat,Mat,Mat);
    190:   PetscErrorCode (*transposecoloringcreate)(Mat,ISColoring,MatTransposeColoring);
    191:   /*134*/
    192:   PetscErrorCode (*transcoloringapplysptoden)(MatTransposeColoring,Mat,Mat);
    193:   PetscErrorCode (*transcoloringapplydentosp)(MatTransposeColoring,Mat,Mat);
    194:   PetscErrorCode (*rart)(Mat,Mat,MatReuse,PetscReal,Mat*);
    195:   PetscErrorCode (*rartsymbolic)(Mat,Mat,PetscReal,Mat*); /* double dispatch wrapper routine */
    196:   PetscErrorCode (*rartnumeric)(Mat,Mat,Mat);             /* double dispatch wrapper routine */
    197:   /*139*/
    198:   PetscErrorCode (*setblocksizes)(Mat,PetscInt,PetscInt);
    199:   PetscErrorCode (*aypx)(Mat,PetscScalar,Mat,MatStructure);
    200:   PetscErrorCode (*residual)(Mat,Vec,Vec,Vec);
    201:   PetscErrorCode (*fdcoloringsetup)(Mat,ISColoring,MatFDColoring);
    202:   PetscErrorCode (*findoffblockdiagonalentries)(Mat,IS*);
    203:   /*144*/
    204:   PetscErrorCode (*creatempimatconcatenateseqmat)(MPI_Comm,Mat,PetscInt,MatReuse,Mat*);

    206: };
    207: /*
    208:     If you add MatOps entries above also add them to the MATOP enum
    209:     in include/petscmat.h and include/petsc/finclude/petscmat.h
    210: */

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

    216: typedef struct _p_MatBaseName* MatBaseName;
    217: struct _p_MatBaseName {
    218:   char        *bname,*sname,*mname;
    219:   MatBaseName next;
    220: };

    222: PETSC_EXTERN MatBaseName MatBaseNameList;

    224: /*
    225:    Utility private matrix routines
    226: */
    227: PETSC_INTERN PetscErrorCode MatConvert_Basic(Mat, MatType,MatReuse,Mat*);
    228: PETSC_INTERN PetscErrorCode MatCopy_Basic(Mat,Mat,MatStructure);
    229: PETSC_INTERN PetscErrorCode MatHeaderMerge(Mat,Mat*);
    230: PETSC_EXTERN PetscErrorCode MatHeaderReplace(Mat,Mat*);
    231: PETSC_INTERN PetscErrorCode MatDiagonalSet_Default(Mat,Vec,InsertMode);

    233: #if defined(PETSC_USE_DEBUG)
    234: #  define MatCheckPreallocated(A,arg) do {                              \
    235:     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); \
    236:   } while (0)
    237: #else
    238: #  define MatCheckPreallocated(A,arg) do {} while (0)
    239: #endif

    241: /*
    242:   The stash is used to temporarily store inserted matrix values that
    243:   belong to another processor. During the assembly phase the stashed
    244:   values are moved to the correct processor and
    245: */

    247: typedef struct _MatStashSpace *PetscMatStashSpace;

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

    258: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceGet(PetscInt,PetscInt,PetscMatStashSpace *);
    259: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceContiguous(PetscInt,PetscMatStashSpace *,PetscScalar *,PetscInt *,PetscInt *);
    260: PETSC_EXTERN PetscErrorCode PetscMatStashSpaceDestroy(PetscMatStashSpace*);

    262: typedef struct {
    263:   PetscInt    count;
    264: } MatStashHeader;

    266: typedef struct {
    267:   void        *buffer;          /* Of type blocktype, dynamically constructed  */
    268:   PetscInt    count;
    269:   char        pending;
    270: } MatStashFrame;

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

    282:   PetscErrorCode (*ScatterBegin)(Mat,MatStash*,PetscInt*);
    283:   PetscErrorCode (*ScatterGetMesg)(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);
    284:   PetscErrorCode (*ScatterEnd)(MatStash*);
    285:   PetscErrorCode (*ScatterDestroy)(MatStash*);

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

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

    332: PETSC_INTERN PetscErrorCode MatStashCreate_Private(MPI_Comm,PetscInt,MatStash*);
    333: PETSC_INTERN PetscErrorCode MatStashDestroy_Private(MatStash*);
    334: PETSC_INTERN PetscErrorCode MatStashScatterEnd_Private(MatStash*);
    335: PETSC_INTERN PetscErrorCode MatStashSetInitialSize_Private(MatStash*,PetscInt);
    336: PETSC_INTERN PetscErrorCode MatStashGetInfo_Private(MatStash*,PetscInt*,PetscInt*);
    337: PETSC_INTERN PetscErrorCode MatStashValuesRow_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscBool );
    338: PETSC_INTERN PetscErrorCode MatStashValuesCol_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscBool );
    339: PETSC_INTERN PetscErrorCode MatStashValuesRowBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    340: PETSC_INTERN PetscErrorCode MatStashValuesColBlocked_Private(MatStash*,PetscInt,PetscInt,const PetscInt[],const PetscScalar[],PetscInt,PetscInt,PetscInt);
    341: PETSC_INTERN PetscErrorCode MatStashScatterBegin_Private(Mat,MatStash*,PetscInt*);
    342: PETSC_INTERN PetscErrorCode MatStashScatterGetMesg_Private(MatStash*,PetscMPIInt*,PetscInt**,PetscInt**,PetscScalar**,PetscInt*);

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

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

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

    370: struct _p_Mat {
    371:   PETSCHEADER(struct _MatOps);
    372:   PetscLayout            rmap,cmap;
    373:   void                   *data;            /* implementation-specific data */
    374:   MatFactorType          factortype;       /* MAT_FACTOR_LU, ILU, CHOLESKY or ICC */
    375:   PetscBool              assembled;        /* is the matrix assembled? */
    376:   PetscBool              was_assembled;    /* new values inserted into assembled mat */
    377:   PetscInt               num_ass;          /* number of times matrix has been assembled */
    378:   PetscObjectState       nonzerostate;     /* each time new nonzeros locations are introduced into the matrix this is updated */
    379:   MatInfo                info;             /* matrix information */
    380:   InsertMode             insertmode;       /* have values been inserted in matrix or added? */
    381:   MatStash               stash,bstash;     /* used for assembling off-proc mat emements */
    382:   MatNullSpace           nullsp;           /* null space (operator is singular) */
    383:   MatNullSpace           transnullsp;      /* null space of transpose of operator */
    384:   MatNullSpace           nearnullsp;       /* near null space to be used by multigrid methods */
    385:   PetscBool              preallocated;
    386:   MatStencilInfo         stencil;          /* information for structured grid */
    387:   PetscBool              symmetric,hermitian,structurally_symmetric,spd;
    388:   PetscBool              symmetric_set,hermitian_set,structurally_symmetric_set,spd_set; /* if true, then corresponding flag is correct*/
    389:   PetscBool              symmetric_eternal;
    390:   PetscBool              nooffprocentries,nooffproczerorows;
    391:   PetscBool              subsetoffprocentries;
    392: #if defined(PETSC_HAVE_CUSP)
    393:   PetscCUSPFlag          valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
    394: #elif defined(PETSC_HAVE_VIENNACL)
    395:   PetscViennaCLFlag      valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
    396: #elif defined(PETSC_HAVE_VECCUDA)
    397:   PetscCUDAFlag          valid_GPU_matrix; /* flag pointing to the matrix on the gpu*/
    398: #endif
    399:   void                   *spptr;          /* pointer for special library like SuperLU */
    400:   MatSolverPackage       solvertype;
    401:   PetscBool              checksymmetryonassembly,checknullspaceonassembly;
    402:   PetscReal              checksymmetrytol;
    403:   Mat_Redundant          *redundant;        /* used by MatCreateRedundantMatrix() */
    404:   PetscBool              erroriffailure;    /* Generate an error if detected (for example a zero pivot) instead of returning */
    405:   MatFactorError         errortype;         /* type of error */
    406: };

    408: PETSC_INTERN PetscErrorCode MatAXPY_Basic(Mat,PetscScalar,Mat,MatStructure);
    409: PETSC_INTERN PetscErrorCode MatAXPY_BasicWithPreallocation(Mat,Mat,PetscScalar,Mat,MatStructure);
    410: /*
    411:     Object for partitioning graphs
    412: */

    414: typedef struct _MatPartitioningOps *MatPartitioningOps;
    415: struct _MatPartitioningOps {
    416:   PetscErrorCode (*apply)(MatPartitioning,IS*);
    417:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatPartitioning);
    418:   PetscErrorCode (*destroy)(MatPartitioning);
    419:   PetscErrorCode (*view)(MatPartitioning,PetscViewer);
    420: };

    422: struct _p_MatPartitioning {
    423:   PETSCHEADER(struct _MatPartitioningOps);
    424:   Mat         adj;
    425:   PetscInt    *vertex_weights;
    426:   PetscReal   *part_weights;
    427:   PetscInt    n;                                 /* number of partitions */
    428:   void        *data;
    429:   PetscInt    setupcalled;
    430: };

    432: /*
    433:     Object for coarsen graphs
    434: */
    435: typedef struct _MatCoarsenOps *MatCoarsenOps;
    436: struct _MatCoarsenOps {
    437:   PetscErrorCode (*apply)(MatCoarsen);
    438:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatCoarsen);
    439:   PetscErrorCode (*destroy)(MatCoarsen);
    440:   PetscErrorCode (*view)(MatCoarsen,PetscViewer);
    441: };

    443: struct _p_MatCoarsen {
    444:   PETSCHEADER(struct _MatCoarsenOps);
    445:   Mat              graph;
    446:   PetscInt         setupcalled;
    447:   void             *subctx;
    448:   /* */
    449:   PetscBool        strict_aggs;
    450:   IS               perm;
    451:   PetscCoarsenData *agg_lists;
    452: };

    454: PETSC_EXTERN PetscErrorCode PetscCDCreate(PetscInt,PetscCoarsenData**);
    455: PETSC_EXTERN PetscErrorCode PetscCDDestroy(PetscCoarsenData*);
    456: PETSC_EXTERN PetscErrorCode PetscLLNSetID(PetscCDIntNd*,PetscInt);
    457: PETSC_EXTERN PetscErrorCode PetscLLNGetID(const PetscCDIntNd*,PetscInt*);
    458: PETSC_EXTERN PetscErrorCode PetscCDAppendID(PetscCoarsenData*,PetscInt,PetscInt);
    459: PETSC_EXTERN PetscErrorCode PetscCDAppendRemove(PetscCoarsenData*,PetscInt,PetscInt);
    460: PETSC_EXTERN PetscErrorCode PetscCDAppendNode(PetscCoarsenData*,PetscInt,PetscCDIntNd*);
    461: PETSC_EXTERN PetscErrorCode PetscCDRemoveNextNode(PetscCoarsenData*,PetscInt,PetscCDIntNd*);
    462: PETSC_EXTERN PetscErrorCode PetscCDRemoveAllAt(PetscCoarsenData*,PetscInt);
    463: PETSC_EXTERN PetscErrorCode PetscCDSizeAt(const PetscCoarsenData*,PetscInt,PetscInt*);
    464: PETSC_EXTERN PetscErrorCode PetscCDEmptyAt(const PetscCoarsenData*,PetscInt,PetscBool*);
    465: PETSC_EXTERN PetscErrorCode PetscCDSetChuckSize(PetscCoarsenData*,PetscInt);
    466: PETSC_EXTERN PetscErrorCode PetscCDPrint(const PetscCoarsenData*,MPI_Comm);
    467: PETSC_EXTERN PetscErrorCode PetscCDGetMIS(PetscCoarsenData*,IS*);
    468: PETSC_EXTERN PetscErrorCode PetscCDGetMat(const PetscCoarsenData*,Mat*);
    469: PETSC_EXTERN PetscErrorCode PetscCDSetMat(PetscCoarsenData*,Mat);

    471: typedef PetscCDIntNd *PetscCDPos;
    472: PETSC_EXTERN PetscErrorCode PetscCDGetHeadPos(const PetscCoarsenData*,PetscInt,PetscCDPos*);
    473: PETSC_EXTERN PetscErrorCode PetscCDGetNextPos(const PetscCoarsenData*,PetscInt,PetscCDPos*);
    474: PETSC_EXTERN PetscErrorCode PetscCDGetASMBlocks(const PetscCoarsenData*,const PetscInt,PetscInt*,IS**);
    475: /* PetscErrorCode PetscCDSetRemovedIS( PetscCoarsenData *ail, MPI_Comm, const PetscInt, PetscInt[] ); */
    476: /* PetscErrorCode PetscCDGetRemovedIS( PetscCoarsenData *ail, IS * ); */

    478: /*
    479:     MatFDColoring is used to compute Jacobian matrices efficiently
    480:   via coloring. The data structure is explained below in an example.

    482:    Color =   0    1     0    2   |   2      3       0
    483:    ---------------------------------------------------
    484:             00   01              |          05
    485:             10   11              |   14     15               Processor  0
    486:                        22    23  |          25
    487:                        32    33  |
    488:    ===================================================
    489:                                  |   44     45     46
    490:             50                   |          55               Processor 1
    491:                                  |   64            66
    492:    ---------------------------------------------------

    494:     ncolors = 4;

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

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

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

    513: */
    514: typedef struct {
    515:   PetscInt     row;
    516:   PetscInt     col;
    517:   PetscScalar  *valaddr;   /* address of value */
    518: } MatEntry;

    520: typedef struct {
    521:   PetscInt     row;
    522:   PetscScalar  *valaddr;   /* address of value */
    523: } MatEntry2;

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

    551: typedef struct _MatColoringOps *MatColoringOps;
    552: struct _MatColoringOps {
    553:   PetscErrorCode (*destroy)(MatColoring);
    554:   PetscErrorCode (*setfromoptions)(PetscOptionItems*,MatColoring);
    555:   PetscErrorCode (*view)(MatColoring,PetscViewer);
    556:   PetscErrorCode (*apply)(MatColoring,ISColoring*);
    557:   PetscErrorCode (*weights)(MatColoring,PetscReal**,PetscInt**);
    558: };

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

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

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

    590: /*
    591:    Null space context for preconditioner/operators
    592: */
    593: struct _p_MatNullSpace {
    594:   PETSCHEADER(int);
    595:   PetscBool      has_cnst;
    596:   PetscInt       n;
    597:   Vec*           vecs;
    598:   PetscScalar*   alpha;                 /* for projections */
    599:   PetscErrorCode (*remove)(MatNullSpace,Vec,void*);  /* for user provided removal function */
    600:   void*          rmctx;                 /* context for remove() function */
    601: };

    603: /*
    604:    Checking zero pivot for LU, ILU preconditioners.
    605: */
    606: typedef struct {
    607:   PetscInt       nshift,nshift_max;
    608:   PetscReal      shift_amount,shift_lo,shift_hi,shift_top,shift_fraction;
    609:   PetscBool      newshift;
    610:   PetscReal      rs;  /* active row sum of abs(offdiagonals) */
    611:   PetscScalar    pv;  /* pivot of the active row */
    612: } FactorShiftCtx;

    614: PETSC_EXTERN PetscErrorCode MatFactorDumpMatrix(Mat);
    615: PETSC_INTERN PetscErrorCode MatShift_Basic(Mat,PetscScalar);

    619: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_nz(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    620: {
    621:   PetscReal _rs   = sctx->rs;
    622:   PetscReal _zero = info->zeropivot*_rs;

    625:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    626:     /* force |diag| > zeropivot*rs */
    627:     if (!sctx->nshift) sctx->shift_amount = info->shiftamount;
    628:     else sctx->shift_amount *= 2.0;
    629:     sctx->newshift = PETSC_TRUE;
    630:     (sctx->nshift)++;
    631:   } else {
    632:     sctx->newshift = PETSC_FALSE;
    633:   }
    634:   return(0);
    635: }

    639: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_pd(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    640: {
    641:   PetscReal _rs   = sctx->rs;
    642:   PetscReal _zero = info->zeropivot*_rs;

    645:   if (PetscRealPart(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    646:     /* force matfactor to be diagonally dominant */
    647:     if (sctx->nshift == sctx->nshift_max) {
    648:       sctx->shift_fraction = sctx->shift_hi;
    649:     } else {
    650:       sctx->shift_lo = sctx->shift_fraction;
    651:       sctx->shift_fraction = (sctx->shift_hi+sctx->shift_lo)/2.;
    652:     }
    653:     sctx->shift_amount = sctx->shift_fraction * sctx->shift_top;
    654:     sctx->nshift++;
    655:     sctx->newshift = PETSC_TRUE;
    656:   } else {
    657:     sctx->newshift = PETSC_FALSE;
    658:   }
    659:   return(0);
    660: }

    664: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_inblocks(Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    665: {
    666:   PetscReal _zero = info->zeropivot;

    669:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)){
    670:     sctx->pv          += info->shiftamount;
    671:     sctx->shift_amount = 0.0;
    672:     sctx->nshift++;
    673:   }
    674:   sctx->newshift = PETSC_FALSE;
    675:   return(0);
    676: }

    680: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck_none(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    681: {
    682:   PetscReal      _zero = info->zeropivot;

    686:   sctx->newshift = PETSC_FALSE;
    687:   if (PetscAbsScalar(sctx->pv) <= _zero && !PetscIsNanScalar(sctx->pv)) {
    688:     if (!mat->erroriffailure) {
    689:       PetscInfo3(mat,"Detected zero pivot in factorization in row %D value %g tolerance %g",row,(double)PetscAbsScalar(sctx->pv),(double)_zero);
    690:       fact->errortype = MAT_FACTOR_NUMERIC_ZEROPIVOT;
    691:     } else SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_MAT_LU_ZRPVT,"Zero pivot row %D value %g tolerance %g",row,(double)PetscAbsScalar(sctx->pv),(double)_zero);
    692:   }
    693:   return(0);
    694: }

    698: PETSC_STATIC_INLINE PetscErrorCode MatPivotCheck(Mat fact,Mat mat,const MatFactorInfo *info,FactorShiftCtx *sctx,PetscInt row)
    699: {

    703:   if (info->shifttype == (PetscReal) MAT_SHIFT_NONZERO){
    704:     MatPivotCheck_nz(mat,info,sctx,row);
    705:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_POSITIVE_DEFINITE){
    706:     MatPivotCheck_pd(mat,info,sctx,row);
    707:   } else if (info->shifttype == (PetscReal) MAT_SHIFT_INBLOCKS){
    708:     MatPivotCheck_inblocks(mat,info,sctx,row);
    709:   } else {
    710:     MatPivotCheck_none(fact,mat,info,sctx,row);
    711:   }
    712:   return(0);
    713: }

    715: /*
    716:   Create and initialize a linked list
    717:   Input Parameters:
    718:     idx_start - starting index of the list
    719:     lnk_max   - max value of lnk indicating the end of the list
    720:     nlnk      - max length of the list
    721:   Output Parameters:
    722:     lnk       - list initialized
    723:     bt        - PetscBT (bitarray) with all bits set to false
    724:     lnk_empty - flg indicating the list is empty
    725: */
    726: #define PetscLLCreate(idx_start,lnk_max,nlnk,lnk,bt) \
    727:   (PetscMalloc1(nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,0))

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

    732: /*
    733:   Add an index set into a sorted linked list
    734:   Input Parameters:
    735:     nidx      - number of input indices
    736:     indices   - interger array
    737:     idx_start - starting index of the list
    738:     lnk       - linked list(an integer array) that is created
    739:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    740:   output Parameters:
    741:     nlnk      - number of newly added indices
    742:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    743:     bt        - updated PetscBT (bitarray)
    744: */
    745: #define PetscLLAdd(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    746: {\
    747:   PetscInt _k,_entry,_location,_lnkdata;\
    748:   nlnk     = 0;\
    749:   _lnkdata = idx_start;\
    750:   for (_k=0; _k<nidx; _k++){\
    751:     _entry = indices[_k];\
    752:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    753:       /* search for insertion location */\
    754:       /* start from the beginning if _entry < previous _entry */\
    755:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    756:       do {\
    757:         _location = _lnkdata;\
    758:         _lnkdata  = lnk[_location];\
    759:       } while (_entry > _lnkdata);\
    760:       /* insertion location is found, add entry into lnk */\
    761:       lnk[_location] = _entry;\
    762:       lnk[_entry]    = _lnkdata;\
    763:       nlnk++;\
    764:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    765:     }\
    766:   }\
    767: }

    769: /*
    770:   Add a permuted index set into a sorted linked list
    771:   Input Parameters:
    772:     nidx      - number of input indices
    773:     indices   - interger array
    774:     perm      - permutation of indices
    775:     idx_start - starting index of the list
    776:     lnk       - linked list(an integer array) that is created
    777:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    778:   output Parameters:
    779:     nlnk      - number of newly added indices
    780:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    781:     bt        - updated PetscBT (bitarray)
    782: */
    783: #define PetscLLAddPerm(nidx,indices,perm,idx_start,nlnk,lnk,bt) 0;\
    784: {\
    785:   PetscInt _k,_entry,_location,_lnkdata;\
    786:   nlnk     = 0;\
    787:   _lnkdata = idx_start;\
    788:   for (_k=0; _k<nidx; _k++){\
    789:     _entry = perm[indices[_k]];\
    790:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    791:       /* search for insertion location */\
    792:       /* start from the beginning if _entry < previous _entry */\
    793:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    794:       do {\
    795:         _location = _lnkdata;\
    796:         _lnkdata  = lnk[_location];\
    797:       } while (_entry > _lnkdata);\
    798:       /* insertion location is found, add entry into lnk */\
    799:       lnk[_location] = _entry;\
    800:       lnk[_entry]    = _lnkdata;\
    801:       nlnk++;\
    802:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    803:     }\
    804:   }\
    805: }

    807: /*
    808:   Add a SORTED ascending index set into a sorted linked list - same as PetscLLAdd() bus skip 'if (_k && _entry < _lnkdata) _lnkdata  = idx_start;'
    809:   Input Parameters:
    810:     nidx      - number of input indices
    811:     indices   - sorted interger array
    812:     idx_start - starting index of the list
    813:     lnk       - linked list(an integer array) that is created
    814:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    815:   output Parameters:
    816:     nlnk      - number of newly added indices
    817:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    818:     bt        - updated PetscBT (bitarray)
    819: */
    820: #define PetscLLAddSorted(nidx,indices,idx_start,nlnk,lnk,bt) 0;\
    821: {\
    822:   PetscInt _k,_entry,_location,_lnkdata;\
    823:   nlnk      = 0;\
    824:   _lnkdata  = idx_start;\
    825:   for (_k=0; _k<nidx; _k++){\
    826:     _entry = indices[_k];\
    827:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    828:       /* search for insertion location */\
    829:       do {\
    830:         _location = _lnkdata;\
    831:         _lnkdata  = lnk[_location];\
    832:       } while (_entry > _lnkdata);\
    833:       /* insertion location is found, add entry into lnk */\
    834:       lnk[_location] = _entry;\
    835:       lnk[_entry]    = _lnkdata;\
    836:       nlnk++;\
    837:       _lnkdata = _entry; /* next search starts from here */\
    838:     }\
    839:   }\
    840: }

    842: #define PetscLLAddSorted_new(nidx,indices,idx_start,lnk_empty,nlnk,lnk,bt) 0; \
    843: {\
    844:   PetscInt _k,_entry,_location,_lnkdata;\
    845:   if (lnk_empty){\
    846:     _lnkdata  = idx_start;                      \
    847:     for (_k=0; _k<nidx; _k++){                  \
    848:       _entry = indices[_k];                             \
    849:       PetscBTSet(bt,_entry);  /* mark the new entry */          \
    850:           _location = _lnkdata;                                 \
    851:           _lnkdata  = lnk[_location];                           \
    852:         /* insertion location is found, add entry into lnk */   \
    853:         lnk[_location] = _entry;                                \
    854:         lnk[_entry]    = _lnkdata;                              \
    855:         _lnkdata = _entry; /* next search starts from here */   \
    856:     }                                                           \
    857:     /*\
    858:     lnk[indices[nidx-1]] = lnk[idx_start];\
    859:     lnk[idx_start]       = indices[0];\
    860:     PetscBTSet(bt,indices[0]);  \
    861:     for (_k=1; _k<nidx; _k++){                  \
    862:       PetscBTSet(bt,indices[_k]);                                          \
    863:       lnk[indices[_k-1]] = indices[_k];                                  \
    864:     }                                                           \
    865:      */\
    866:     nlnk      = nidx;\
    867:     lnk_empty = PETSC_FALSE;\
    868:   } else {\
    869:     nlnk      = 0;                              \
    870:     _lnkdata  = idx_start;                      \
    871:     for (_k=0; _k<nidx; _k++){                  \
    872:       _entry = indices[_k];                             \
    873:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */       \
    874:         /* search for insertion location */                     \
    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 */   \
    884:       }                                                         \
    885:     }                                                           \
    886:   }                                                             \
    887: }

    889: /*
    890:   Add a SORTED index set into a sorted linked list used for LUFactorSymbolic()
    891:   Same as PetscLLAddSorted() with an additional operation:
    892:        count the number of input indices that are no larger than 'diag'
    893:   Input Parameters:
    894:     indices   - sorted interger array
    895:     idx_start - starting index of the list, index of pivot row
    896:     lnk       - linked list(an integer array) that is created
    897:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    898:     diag      - index of the active row in LUFactorSymbolic
    899:     nzbd      - number of input indices with indices <= idx_start
    900:     im        - im[idx_start] is initialized as num of nonzero entries in row=idx_start
    901:   output Parameters:
    902:     nlnk      - number of newly added indices
    903:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from indices
    904:     bt        - updated PetscBT (bitarray)
    905:     im        - im[idx_start]: unchanged if diag is not an entry
    906:                              : num of entries with indices <= diag if diag is an entry
    907: */
    908: #define PetscLLAddSortedLU(indices,idx_start,nlnk,lnk,bt,diag,nzbd,im) 0;\
    909: {\
    910:   PetscInt _k,_entry,_location,_lnkdata,_nidx;\
    911:   nlnk     = 0;\
    912:   _lnkdata = idx_start;\
    913:   _nidx = im[idx_start] - nzbd; /* num of entries with idx_start < index <= diag */\
    914:   for (_k=0; _k<_nidx; _k++){\
    915:     _entry = indices[_k];\
    916:     nzbd++;\
    917:     if ( _entry== diag) im[idx_start] = nzbd;\
    918:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    919:       /* search for insertion location */\
    920:       do {\
    921:         _location = _lnkdata;\
    922:         _lnkdata  = lnk[_location];\
    923:       } while (_entry > _lnkdata);\
    924:       /* insertion location is found, add entry into lnk */\
    925:       lnk[_location] = _entry;\
    926:       lnk[_entry]    = _lnkdata;\
    927:       nlnk++;\
    928:       _lnkdata = _entry; /* next search starts from here */\
    929:     }\
    930:   }\
    931: }

    933: /*
    934:   Copy data on the list into an array, then initialize the list
    935:   Input Parameters:
    936:     idx_start - starting index of the list
    937:     lnk_max   - max value of lnk indicating the end of the list
    938:     nlnk      - number of data on the list to be copied
    939:     lnk       - linked list
    940:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    941:   output Parameters:
    942:     indices   - array that contains the copied data
    943:     lnk       - linked list that is cleaned and initialize
    944:     bt        - PetscBT (bitarray) with all bits set to false
    945: */
    946: #define PetscLLClean(idx_start,lnk_max,nlnk,lnk,indices,bt) 0;\
    947: {\
    948:   PetscInt _j,_idx=idx_start;\
    949:   for (_j=0; _j<nlnk; _j++){\
    950:     _idx = lnk[_idx];\
    951:     indices[_j] = _idx;\
    952:     PetscBTClear(bt,_idx);\
    953:   }\
    954:   lnk[idx_start] = lnk_max;\
    955: }
    956: /*
    957:   Free memories used by the list
    958: */
    959: #define PetscLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    961: /* Routines below are used for incomplete matrix factorization */
    962: /*
    963:   Create and initialize a linked list and its levels
    964:   Input Parameters:
    965:     idx_start - starting index of the list
    966:     lnk_max   - max value of lnk indicating the end of the list
    967:     nlnk      - max length of the list
    968:   Output Parameters:
    969:     lnk       - list initialized
    970:     lnk_lvl   - array of size nlnk for storing levels of lnk
    971:     bt        - PetscBT (bitarray) with all bits set to false
    972: */
    973: #define PetscIncompleteLLCreate(idx_start,lnk_max,nlnk,lnk,lnk_lvl,bt)\
    974:   (PetscIntMultError(2,nlnk,NULL) || PetscMalloc1(2*nlnk,&lnk) || PetscBTCreate(nlnk,&(bt)) || (lnk[idx_start] = lnk_max,lnk_lvl = lnk + nlnk,0))

    976: /*
    977:   Initialize a sorted linked list used for ILU and ICC
    978:   Input Parameters:
    979:     nidx      - number of input idx
    980:     idx       - interger array used for storing column indices
    981:     idx_start - starting index of the list
    982:     perm      - indices of an IS
    983:     lnk       - linked list(an integer array) that is created
    984:     lnklvl    - levels of lnk
    985:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    986:   output Parameters:
    987:     nlnk     - number of newly added idx
    988:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    989:     lnklvl   - levels of lnk
    990:     bt       - updated PetscBT (bitarray)
    991: */
    992: #define PetscIncompleteLLInit(nidx,idx,idx_start,perm,nlnk,lnk,lnklvl,bt) 0;\
    993: {\
    994:   PetscInt _k,_entry,_location,_lnkdata;\
    995:   nlnk     = 0;\
    996:   _lnkdata = idx_start;\
    997:   for (_k=0; _k<nidx; _k++){\
    998:     _entry = perm[idx[_k]];\
    999:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1000:       /* search for insertion location */\
    1001:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1002:       do {\
    1003:         _location = _lnkdata;\
    1004:         _lnkdata  = lnk[_location];\
    1005:       } while (_entry > _lnkdata);\
    1006:       /* insertion location is found, add entry into lnk */\
    1007:       lnk[_location]  = _entry;\
    1008:       lnk[_entry]     = _lnkdata;\
    1009:       lnklvl[_entry] = 0;\
    1010:       nlnk++;\
    1011:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1012:     }\
    1013:   }\
    1014: }

    1016: /*
    1017:   Add a SORTED index set into a sorted linked list for ILU
    1018:   Input Parameters:
    1019:     nidx      - number of input indices
    1020:     idx       - sorted interger array used for storing column indices
    1021:     level     - level of fill, e.g., ICC(level)
    1022:     idxlvl    - level of idx
    1023:     idx_start - starting index of the list
    1024:     lnk       - linked list(an integer array) that is created
    1025:     lnklvl    - levels of lnk
    1026:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1027:     prow      - the row number of idx
    1028:   output Parameters:
    1029:     nlnk     - number of newly added idx
    1030:     lnk      - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1031:     lnklvl   - levels of lnk
    1032:     bt       - updated PetscBT (bitarray)

    1034:   Note: the level of factor(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(i,prow)+lvl(prow,j)+1)
    1035:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1036: */
    1037: #define PetscILULLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,lnklvl_prow) 0;\
    1038: {\
    1039:   PetscInt _k,_entry,_location,_lnkdata,_incrlev,_lnklvl_prow=lnklvl[prow];\
    1040:   nlnk     = 0;\
    1041:   _lnkdata = idx_start;\
    1042:   for (_k=0; _k<nidx; _k++){\
    1043:     _incrlev = idxlvl[_k] + _lnklvl_prow + 1;\
    1044:     if (_incrlev > level) continue;\
    1045:     _entry = idx[_k];\
    1046:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1047:       /* search for insertion location */\
    1048:       do {\
    1049:         _location = _lnkdata;\
    1050:         _lnkdata  = lnk[_location];\
    1051:       } while (_entry > _lnkdata);\
    1052:       /* insertion location is found, add entry into lnk */\
    1053:       lnk[_location]  = _entry;\
    1054:       lnk[_entry]     = _lnkdata;\
    1055:       lnklvl[_entry] = _incrlev;\
    1056:       nlnk++;\
    1057:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1058:     } else { /* existing entry: update lnklvl */\
    1059:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1060:     }\
    1061:   }\
    1062: }

    1064: /*
    1065:   Add a index set into a sorted linked list
    1066:   Input Parameters:
    1067:     nidx      - number of input idx
    1068:     idx   - interger array used for storing column indices
    1069:     level     - level of fill, e.g., ICC(level)
    1070:     idxlvl - level of idx
    1071:     idx_start - starting index of the list
    1072:     lnk       - linked list(an integer array) that is created
    1073:     lnklvl   - levels of lnk
    1074:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1075:   output Parameters:
    1076:     nlnk      - number of newly added idx
    1077:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1078:     lnklvl   - levels of lnk
    1079:     bt        - updated PetscBT (bitarray)
    1080: */
    1081: #define PetscIncompleteLLAdd(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1082: {\
    1083:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1084:   nlnk     = 0;\
    1085:   _lnkdata = idx_start;\
    1086:   for (_k=0; _k<nidx; _k++){\
    1087:     _incrlev = idxlvl[_k] + 1;\
    1088:     if (_incrlev > level) continue;\
    1089:     _entry = idx[_k];\
    1090:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1091:       /* search for insertion location */\
    1092:       if (_k && _entry < _lnkdata) _lnkdata  = idx_start;\
    1093:       do {\
    1094:         _location = _lnkdata;\
    1095:         _lnkdata  = lnk[_location];\
    1096:       } while (_entry > _lnkdata);\
    1097:       /* insertion location is found, add entry into lnk */\
    1098:       lnk[_location]  = _entry;\
    1099:       lnk[_entry]     = _lnkdata;\
    1100:       lnklvl[_entry] = _incrlev;\
    1101:       nlnk++;\
    1102:       _lnkdata = _entry; /* next search starts from here if next_entry > _entry */\
    1103:     } else { /* existing entry: update lnklvl */\
    1104:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1105:     }\
    1106:   }\
    1107: }

    1109: /*
    1110:   Add a SORTED index set into a sorted linked list
    1111:   Input Parameters:
    1112:     nidx      - number of input indices
    1113:     idx   - sorted interger array used for storing column indices
    1114:     level     - level of fill, e.g., ICC(level)
    1115:     idxlvl - level of idx
    1116:     idx_start - starting index of the list
    1117:     lnk       - linked list(an integer array) that is created
    1118:     lnklvl    - levels of lnk
    1119:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1120:   output Parameters:
    1121:     nlnk      - number of newly added idx
    1122:     lnk       - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1123:     lnklvl    - levels of lnk
    1124:     bt        - updated PetscBT (bitarray)
    1125: */
    1126: #define PetscIncompleteLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt) 0;\
    1127: {\
    1128:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1129:   nlnk = 0;\
    1130:   _lnkdata = idx_start;\
    1131:   for (_k=0; _k<nidx; _k++){\
    1132:     _incrlev = idxlvl[_k] + 1;\
    1133:     if (_incrlev > level) continue;\
    1134:     _entry = idx[_k];\
    1135:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1136:       /* search for insertion location */\
    1137:       do {\
    1138:         _location = _lnkdata;\
    1139:         _lnkdata  = lnk[_location];\
    1140:       } while (_entry > _lnkdata);\
    1141:       /* insertion location is found, add entry into lnk */\
    1142:       lnk[_location] = _entry;\
    1143:       lnk[_entry]    = _lnkdata;\
    1144:       lnklvl[_entry] = _incrlev;\
    1145:       nlnk++;\
    1146:       _lnkdata = _entry; /* next search starts from here */\
    1147:     } else { /* existing entry: update lnklvl */\
    1148:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1149:     }\
    1150:   }\
    1151: }

    1153: /*
    1154:   Add a SORTED index set into a sorted linked list for ICC
    1155:   Input Parameters:
    1156:     nidx      - number of input indices
    1157:     idx       - sorted interger array used for storing column indices
    1158:     level     - level of fill, e.g., ICC(level)
    1159:     idxlvl    - level of idx
    1160:     idx_start - starting index of the list
    1161:     lnk       - linked list(an integer array) that is created
    1162:     lnklvl    - levels of lnk
    1163:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1164:     idxlvl_prow - idxlvl[prow], where prow is the row number of the idx
    1165:   output Parameters:
    1166:     nlnk   - number of newly added indices
    1167:     lnk    - the sorted(increasing order) linked list containing new and non-redundate entries from idx
    1168:     lnklvl - levels of lnk
    1169:     bt     - updated PetscBT (bitarray)
    1170:   Note: the level of U(i,j) is set as lvl(i,j) = min{ lvl(i,j), lvl(prow,i)+lvl(prow,j)+1)
    1171:         where idx = non-zero columns of U(prow,prow+1:n-1), prow<i
    1172: */
    1173: #define PetscICCLLAddSorted(nidx,idx,level,idxlvl,idx_start,nlnk,lnk,lnklvl,bt,idxlvl_prow) 0;\
    1174: {\
    1175:   PetscInt _k,_entry,_location,_lnkdata,_incrlev;\
    1176:   nlnk = 0;\
    1177:   _lnkdata = idx_start;\
    1178:   for (_k=0; _k<nidx; _k++){\
    1179:     _incrlev = idxlvl[_k] + idxlvl_prow + 1;\
    1180:     if (_incrlev > level) continue;\
    1181:     _entry = idx[_k];\
    1182:     if (!PetscBTLookupSet(bt,_entry)){  /* new entry */\
    1183:       /* search for insertion location */\
    1184:       do {\
    1185:         _location = _lnkdata;\
    1186:         _lnkdata  = lnk[_location];\
    1187:       } while (_entry > _lnkdata);\
    1188:       /* insertion location is found, add entry into lnk */\
    1189:       lnk[_location] = _entry;\
    1190:       lnk[_entry]    = _lnkdata;\
    1191:       lnklvl[_entry] = _incrlev;\
    1192:       nlnk++;\
    1193:       _lnkdata = _entry; /* next search starts from here */\
    1194:     } else { /* existing entry: update lnklvl */\
    1195:       if (lnklvl[_entry] > _incrlev) lnklvl[_entry] = _incrlev;\
    1196:     }\
    1197:   }\
    1198: }

    1200: /*
    1201:   Copy data on the list into an array, then initialize the list
    1202:   Input Parameters:
    1203:     idx_start - starting index of the list
    1204:     lnk_max   - max value of lnk indicating the end of the list
    1205:     nlnk      - number of data on the list to be copied
    1206:     lnk       - linked list
    1207:     lnklvl    - level of lnk
    1208:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1209:   output Parameters:
    1210:     indices - array that contains the copied data
    1211:     lnk     - linked list that is cleaned and initialize
    1212:     lnklvl  - level of lnk that is reinitialized
    1213:     bt      - PetscBT (bitarray) with all bits set to false
    1214: */
    1215: #define PetscIncompleteLLClean(idx_start,lnk_max,nlnk,lnk,lnklvl,indices,indiceslvl,bt) 0;\
    1216: {\
    1217:   PetscInt _j,_idx=idx_start;\
    1218:   for (_j=0; _j<nlnk; _j++){\
    1219:     _idx = lnk[_idx];\
    1220:     *(indices+_j) = _idx;\
    1221:     *(indiceslvl+_j) = lnklvl[_idx];\
    1222:     lnklvl[_idx] = -1;\
    1223:     PetscBTClear(bt,_idx);\
    1224:   }\
    1225:   lnk[idx_start] = lnk_max;\
    1226: }
    1227: /*
    1228:   Free memories used by the list
    1229: */
    1230: #define PetscIncompleteLLDestroy(lnk,bt) (PetscFree(lnk) || PetscBTDestroy(&(bt)))

    1232: /* -------------------------------------------------------------------------------------------------------*/
    1233: #include <petscbt.h>
    1236: /*
    1237:   Create and initialize a condensed linked list -
    1238:     same as PetscLLCreate(), but uses a scalable array 'lnk' with size of max number of entries, not O(N).
    1239:     Barry suggested this approach (Dec. 6, 2011):
    1240:       I've thought of an alternative way of representing a linked list that is efficient but doesn't have the O(N) scaling issue
    1241:       (it may be faster than the O(N) even sequentially due to less crazy memory access).

    1243:       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
    1244:       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
    1245:       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
    1246:       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.
    1247:       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
    1248:       to each other so memory access is much better than using the big array.

    1250:   Example:
    1251:      nlnk_max=5, lnk_max=36:
    1252:      Initial list: [0, 0 | 36, 2 | 0, 0 | 0, 0 | 0, 0 | 0, 0 | 0, 0]
    1253:      here, head_node has index 2 with value lnk[2]=lnk_max=36,
    1254:            0-th entry is used to store the number of entries in the list,
    1255:      The initial lnk represents head -> tail(marked by 36) with number of entries = lnk[0]=0.

    1257:      Now adding a sorted set {2,4}, the list becomes
    1258:      [2, 0 | 36, 4 |2, 6 | 4, 2 | 0, 0 | 0, 0 | 0, 0 ]
    1259:      represents head -> 2 -> 4 -> tail with number of entries = lnk[0]=2.

    1261:      Then adding a sorted set {0,3,35}, the list
    1262:      [5, 0 | 36, 8 | 2, 10 | 4, 12 | 0, 4 | 3, 6 | 35, 2 ]
    1263:      represents head -> 0 -> 2 -> 3 -> 4 -> 35 -> tail with number of entries = lnk[0]=5.

    1265:   Input Parameters:
    1266:     nlnk_max  - max length of the list
    1267:     lnk_max   - max value of the entries
    1268:   Output Parameters:
    1269:     lnk       - list created and initialized
    1270:     bt        - PetscBT (bitarray) with all bits set to false. Note: bt has size lnk_max, not nln_max!
    1271: */
    1272: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate(PetscInt nlnk_max,PetscInt lnk_max,PetscInt **lnk,PetscBT *bt)
    1273: {
    1275:   PetscInt       *llnk,lsize = 0;

    1278:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1279:   PetscMalloc1(lsize,lnk);
    1280:   PetscBTCreate(lnk_max,bt);
    1281:   llnk = *lnk;
    1282:   llnk[0] = 0;         /* number of entries on the list */
    1283:   llnk[2] = lnk_max;   /* value in the head node */
    1284:   llnk[3] = 2;         /* next for the head node */
    1285:   return(0);
    1286: }

    1290: /*
    1291:   Add a SORTED ascending index set into a sorted linked list. See PetscLLCondensedCreate() for detailed description.
    1292:   Input Parameters:
    1293:     nidx      - number of input indices
    1294:     indices   - sorted interger array
    1295:     lnk       - condensed linked list(an integer array) that is created
    1296:     bt        - PetscBT (bitarray), bt[idx]=true marks idx is in lnk
    1297:   output Parameters:
    1298:     lnk       - the sorted(increasing order) linked list containing previous and newly added non-redundate indices
    1299:     bt        - updated PetscBT (bitarray)
    1300: */
    1301: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted(PetscInt nidx,const PetscInt indices[],PetscInt lnk[],PetscBT bt)
    1302: {
    1303:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;

    1306:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1307:   _location = 2; /* head */
    1308:     for (_k=0; _k<nidx; _k++){
    1309:       _entry = indices[_k];
    1310:       if (!PetscBTLookupSet(bt,_entry)){  /* new entry */
    1311:         /* search for insertion location */
    1312:         do {
    1313:           _next     = _location + 1; /* link from previous node to next node */
    1314:           _location = lnk[_next];    /* idx of next node */
    1315:           _lnkdata  = lnk[_location];/* value of next node */
    1316:         } while (_entry > _lnkdata);
    1317:         /* insertion location is found, add entry into lnk */
    1318:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1319:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1320:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1321:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1322:         _location       = _newnode;      /* next search starts from the new node */
    1323:         _nlnk++;
    1324:       }   \
    1325:     }\
    1326:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1327:   return(0);
    1328: }

    1332: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean(PetscInt lnk_max,PetscInt nidx,PetscInt *indices,PetscInt lnk[],PetscBT bt)
    1333: {
    1335:   PetscInt       _k,_next,_nlnk;

    1338:   _next = lnk[3];       /* head node */
    1339:   _nlnk = lnk[0];       /* num of entries on the list */
    1340:   for (_k=0; _k<_nlnk; _k++){
    1341:     indices[_k] = lnk[_next];
    1342:     _next       = lnk[_next + 1];
    1343:     PetscBTClear(bt,indices[_k]);
    1344:   }
    1345:   lnk[0] = 0;          /* num of entries on the list */
    1346:   lnk[2] = lnk_max;    /* initialize head node */
    1347:   lnk[3] = 2;          /* head node */
    1348:   return(0);
    1349: }

    1353: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView(PetscInt *lnk)
    1354: {
    1356:   PetscInt       k;

    1359:   PetscPrintf(PETSC_COMM_SELF,"LLCondensed of size %D, (val,  next)\n",lnk[0]);
    1360:   for (k=2; k< lnk[0]+2; k++){
    1361:     PetscPrintf(PETSC_COMM_SELF," %D: (%D, %D)\n",2*k,lnk[2*k],lnk[2*k+1]);
    1362:   }
    1363:   return(0);
    1364: }

    1368: /*
    1369:   Free memories used by the list
    1370: */
    1371: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy(PetscInt *lnk,PetscBT bt)
    1372: {

    1376:   PetscFree(lnk);
    1377:   PetscBTDestroy(&bt);
    1378:   return(0);
    1379: }

    1381: /* -------------------------------------------------------------------------------------------------------*/
    1384: /*
    1385:  Same as PetscLLCondensedCreate(), but does not use non-scalable O(lnk_max) bitarray
    1386:   Input Parameters:
    1387:     nlnk_max  - max length of the list
    1388:   Output Parameters:
    1389:     lnk       - list created and initialized
    1390: */
    1391: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_Scalable(PetscInt nlnk_max,PetscInt **lnk)
    1392: {
    1394:   PetscInt       *llnk,lsize = 0;

    1397:   PetscIntMultError(2,nlnk_max+2,&lsize);
    1398:   PetscMalloc1(lsize,lnk);
    1399:   llnk = *lnk;
    1400:   llnk[0] = 0;               /* number of entries on the list */
    1401:   llnk[2] = PETSC_MAX_INT;   /* value in the head node */
    1402:   llnk[3] = 2;               /* next for the head node */
    1403:   return(0);
    1404: }

    1408: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_Scalable(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1409: {
    1410:   PetscInt _k,_entry,_location,_next,_lnkdata,_nlnk,_newnode;
    1411:   _nlnk     = lnk[0]; /* num of entries on the input lnk */
    1412:   _location = 2; /* head */ \
    1413:     for (_k=0; _k<nidx; _k++){
    1414:       _entry = indices[_k];
    1415:       /* search for insertion location */
    1416:       do {
    1417:         _next     = _location + 1; /* link from previous node to next node */
    1418:         _location = lnk[_next];    /* idx of next node */
    1419:         _lnkdata  = lnk[_location];/* value of next node */
    1420:       } while (_entry > _lnkdata);
    1421:       if (_entry < _lnkdata) {
    1422:         /* insertion location is found, add entry into lnk */
    1423:         _newnode        = 2*(_nlnk+2);   /* index for this new node */
    1424:         lnk[_next]      = _newnode;      /* connect previous node to the new node */
    1425:         lnk[_newnode]   = _entry;        /* set value of the new node */
    1426:         lnk[_newnode+1] = _location;     /* connect new node to next node */
    1427:         _location       = _newnode;      /* next search starts from the new node */
    1428:         _nlnk++;
    1429:       }
    1430:     }
    1431:   lnk[0]   = _nlnk;   /* number of entries in the list */
    1432:   return 0;
    1433: }

    1437: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_Scalable(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1438: {
    1439:   PetscInt _k,_next,_nlnk;
    1440:   _next = lnk[3];       /* head node */
    1441:   _nlnk = lnk[0];
    1442:   for (_k=0; _k<_nlnk; _k++){
    1443:     indices[_k] = lnk[_next];
    1444:     _next       = lnk[_next + 1];
    1445:   }
    1446:   lnk[0] = 0;          /* num of entries on the list */
    1447:   lnk[3] = 2;          /* head node */
    1448:   return 0;
    1449: }

    1453: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_Scalable(PetscInt *lnk)
    1454: {
    1455:   return PetscFree(lnk);
    1456: }

    1458: /* -------------------------------------------------------------------------------------------------------*/
    1459: /*
    1460:       lnk[0]   number of links
    1461:       lnk[1]   number of entries
    1462:       lnk[3n]  value
    1463:       lnk[3n+1] len
    1464:       lnk[3n+2] link to next value

    1466:       The next three are always the first link

    1468:       lnk[3]    PETSC_MIN_INT+1
    1469:       lnk[4]    1
    1470:       lnk[5]    link to first real entry

    1472:       The next three are always the last link

    1474:       lnk[6]    PETSC_MAX_INT - 1
    1475:       lnk[7]    1
    1476:       lnk[8]    next valid link (this is the same as lnk[0] but without the decreases)
    1477: */

    1481: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedCreate_fast(PetscInt nlnk_max,PetscInt **lnk)
    1482: {
    1484:   PetscInt       *llnk,lsize = 0;

    1487:   PetscIntMultError(3,nlnk_max+3,&lsize);
    1488:   PetscMalloc1(lsize,lnk);
    1489:   llnk = *lnk;
    1490:   llnk[0] = 0;   /* nlnk: number of entries on the list */
    1491:   llnk[1] = 0;          /* number of integer entries represented in list */
    1492:   llnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1493:   llnk[4] = 1;           /* count for the first node */
    1494:   llnk[5] = 6;         /* next for the first node */
    1495:   llnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1496:   llnk[7] = 1;           /* count for the last node */
    1497:   llnk[8] = 0;         /* next valid node to be used */
    1498:   return(0);
    1499: }

    1501: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedAddSorted_fast(PetscInt nidx,const PetscInt indices[],PetscInt lnk[])
    1502: {
    1503:   PetscInt k,entry,prev,next;
    1504:   prev      = 3;      /* first value */
    1505:   next      = lnk[prev+2];
    1506:   for (k=0; k<nidx; k++){
    1507:     entry = indices[k];
    1508:     /* search for insertion location */
    1509:     while (entry >= lnk[next]) {
    1510:       prev = next;
    1511:       next = lnk[next+2];
    1512:     }
    1513:     /* entry is in range of previous list */
    1514:     if (entry < lnk[prev]+lnk[prev+1]) continue;
    1515:     lnk[1]++;
    1516:     /* entry is right after previous list */
    1517:     if (entry == lnk[prev]+lnk[prev+1]) {
    1518:       lnk[prev+1]++;
    1519:       if (lnk[next] == entry+1) { /* combine two contiquous strings */
    1520:         lnk[prev+1] += lnk[next+1];
    1521:         lnk[prev+2]  = lnk[next+2];
    1522:         next         = lnk[next+2];
    1523:         lnk[0]--;
    1524:       }
    1525:       continue;
    1526:     }
    1527:     /* entry is right before next list */
    1528:     if (entry == lnk[next]-1) {
    1529:       lnk[next]--;
    1530:       lnk[next+1]++;
    1531:       prev = next;
    1532:       next = lnk[prev+2];
    1533:       continue;
    1534:     }
    1535:     /*  add entry into lnk */
    1536:     lnk[prev+2]    = 3*((lnk[8]++)+3);      /* connect previous node to the new node */
    1537:     prev           = lnk[prev+2];
    1538:     lnk[prev]      = entry;        /* set value of the new node */
    1539:     lnk[prev+1]    = 1;             /* number of values in contiquous string is one to start */
    1540:     lnk[prev+2]    = next;          /* connect new node to next node */
    1541:     lnk[0]++;
    1542:   }
    1543:   return 0;
    1544: }

    1546: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedClean_fast(PetscInt nidx,PetscInt *indices,PetscInt *lnk)
    1547: {
    1548:   PetscInt _k,_next,_nlnk,cnt,j;
    1549:   _next = lnk[5];       /* first node */
    1550:   _nlnk = lnk[0];
    1551:   cnt   = 0;
    1552:   for (_k=0; _k<_nlnk; _k++){
    1553:     for (j=0; j<lnk[_next+1]; j++) {
    1554:       indices[cnt++] = lnk[_next] + j;
    1555:     }
    1556:     _next       = lnk[_next + 2];
    1557:   }
    1558:   lnk[0] = 0;   /* nlnk: number of links */
    1559:   lnk[1] = 0;          /* number of integer entries represented in list */
    1560:   lnk[3] = PETSC_MIN_INT+1;   /* value in the first node */
    1561:   lnk[4] = 1;           /* count for the first node */
    1562:   lnk[5] = 6;         /* next for the first node */
    1563:   lnk[6] = PETSC_MAX_INT-1;   /* value in the last node */
    1564:   lnk[7] = 1;           /* count for the last node */
    1565:   lnk[8] = 0;         /* next valid location to make link */
    1566:   return 0;
    1567: }

    1569: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedView_fast(PetscInt *lnk)
    1570: {
    1571:   PetscInt k,next,nlnk;
    1572:   next = lnk[5];       /* first node */
    1573:   nlnk = lnk[0];
    1574:   for (k=0; k<nlnk; k++){
    1575: #if 0                           /* Debugging code */
    1576:     printf("%d value %d len %d next %d\n",next,lnk[next],lnk[next+1],lnk[next+2]);
    1577: #endif
    1578:     next = lnk[next + 2];
    1579:   }
    1580:   return 0;
    1581: }

    1583: PETSC_STATIC_INLINE PetscErrorCode PetscLLCondensedDestroy_fast(PetscInt *lnk)
    1584: {
    1585:   return PetscFree(lnk);
    1586: }

    1588: /* alias PetscSortIntWithScalarArray while MatScalar == PetscScalar */
    1589: PETSC_STATIC_INLINE PetscErrorCode PetscSortIntWithMatScalarArray(PetscInt n,PetscInt *idx,PetscScalar *val)
    1590: {
    1591: #if !defined(PETSC_USE_REAL_MAT_SINGLE)
    1592:   return PetscSortIntWithScalarArray(n,idx,val);
    1593: #else
    1594:   {
    1595:     MatScalar mtmp;
    1596:     return PetscSortIntWithDataArray(n,idx,val,sizeof(MatScalar),&mtmp);
    1597:   }
    1598: #endif
    1599: }

    1601: PETSC_EXTERN PetscLogEvent MAT_Mult, MAT_MultMatrixFree, MAT_Mults, MAT_MultConstrained, MAT_MultAdd, MAT_MultTranspose;
    1602: PETSC_EXTERN PetscLogEvent MAT_MultTransposeConstrained, MAT_MultTransposeAdd, MAT_Solve, MAT_Solves, MAT_SolveAdd, MAT_SolveTranspose;
    1603: PETSC_EXTERN PetscLogEvent MAT_SolveTransposeAdd, MAT_SOR, MAT_ForwardSolve, MAT_BackwardSolve, MAT_LUFactor, MAT_LUFactorSymbolic;
    1604: PETSC_EXTERN PetscLogEvent MAT_LUFactorNumeric, MAT_CholeskyFactor, MAT_CholeskyFactorSymbolic, MAT_CholeskyFactorNumeric, MAT_ILUFactor;
    1605: PETSC_EXTERN PetscLogEvent MAT_ILUFactorSymbolic, MAT_ICCFactorSymbolic, MAT_Copy, MAT_Convert, MAT_Scale, MAT_AssemblyBegin;
    1606: PETSC_EXTERN PetscLogEvent MAT_AssemblyEnd, MAT_SetValues, MAT_GetValues, MAT_GetRow, MAT_GetRowIJ, MAT_GetSubMatrices, MAT_GetColoring, MAT_GetOrdering, MAT_RedundantMat;
    1607: PETSC_EXTERN PetscLogEvent MAT_IncreaseOverlap, MAT_Partitioning, MAT_Coarsen, MAT_ZeroEntries, MAT_Load, MAT_View, MAT_AXPY, MAT_FDColoringCreate, MAT_TransposeColoringCreate;
    1608: PETSC_EXTERN PetscLogEvent MAT_FDColoringSetUp, MAT_FDColoringApply, MAT_Transpose, MAT_FDColoringFunction,MAT_GetSubMatrix;
    1609: PETSC_EXTERN PetscLogEvent MAT_MatMult, MAT_MatSolve,MAT_MatMultSymbolic, MAT_MatMultNumeric,MAT_Getlocalmatcondensed,MAT_GetBrowsOfAcols,MAT_GetBrowsOfAocols;
    1610: PETSC_EXTERN PetscLogEvent MAT_PtAP, MAT_PtAPSymbolic, MAT_PtAPNumeric,MAT_Seqstompinum,MAT_Seqstompisym,MAT_Seqstompi,MAT_Getlocalmat;
    1611: PETSC_EXTERN PetscLogEvent MAT_RARt, MAT_RARtSymbolic, MAT_RARtNumeric;
    1612: PETSC_EXTERN PetscLogEvent MAT_MatTransposeMult, MAT_MatTransposeMultSymbolic, MAT_MatTransposeMultNumeric;
    1613: PETSC_EXTERN PetscLogEvent MAT_TransposeMatMult, MAT_TransposeMatMultSymbolic, MAT_TransposeMatMultNumeric;
    1614: PETSC_EXTERN PetscLogEvent MAT_MatMatMult, MAT_MatMatMultSymbolic, MAT_MatMatMultNumeric;
    1615: PETSC_EXTERN PetscLogEvent MAT_Applypapt, MAT_Applypapt_symbolic, MAT_Applypapt_numeric;
    1616: PETSC_EXTERN PetscLogEvent MAT_Getsymtranspose, MAT_Transpose_SeqAIJ, MAT_Getsymtransreduced,MAT_GetSequentialNonzeroStructure;

    1618: PETSC_EXTERN PetscLogEvent MATMFFD_Mult;
    1619: PETSC_EXTERN PetscLogEvent MAT_GetMultiProcBlock;
    1620: PETSC_EXTERN PetscLogEvent MAT_CUSPCopyToGPU, MAT_CUSPARSECopyToGPU, MAT_SetValuesBatch, MAT_SetValuesBatchI, MAT_SetValuesBatchII, MAT_SetValuesBatchIII, MAT_SetValuesBatchIV;
    1621: PETSC_EXTERN PetscLogEvent MAT_ViennaCLCopyToGPU;
    1622: PETSC_EXTERN PetscLogEvent MAT_Merge,MAT_Residual;
    1623: PETSC_EXTERN PetscLogEvent Mat_Coloring_Apply,Mat_Coloring_Comm,Mat_Coloring_Local,Mat_Coloring_ISCreate,Mat_Coloring_SetUp,Mat_Coloring_Weights;

    1625: #endif