Actual source code: aij.h

      1: #pragma once

      3: #include <petsc/private/matimpl.h>
      4: #include <petsc/private/hashmapi.h>
      5: #include <petsc/private/hashmapijv.h>

      7: /*
      8:  Used by MatCreateSubMatrices_MPIXAIJ_Local()
      9: */
     10: typedef struct {   /* used by MatCreateSubMatrices_MPIAIJ_SingleIS_Local() and MatCreateSubMatrices_MPIAIJ_Local */
     11:   PetscInt     id; /* index of submats, only submats[0] is responsible for deleting some arrays below */
     12:   PetscMPIInt  nrqs, nrqr;
     13:   PetscInt   **rbuf1, **rbuf2, **rbuf3, **sbuf1, **sbuf2;
     14:   PetscInt   **ptr;
     15:   PetscInt    *tmp;
     16:   PetscInt    *ctr;
     17:   PetscMPIInt *pa; /* process array */
     18:   PetscInt    *req_size;
     19:   PetscMPIInt *req_source1, *req_source2;
     20:   PetscBool    allcolumns, allrows;
     21:   PetscBool    singleis;
     22:   PetscMPIInt *row2proc; /* row to process (MPI rank) map */
     23:   PetscInt     nstages;
     24: #if defined(PETSC_USE_CTABLE)
     25:   PetscHMapI cmap, rmap;
     26:   PetscInt  *cmap_loc, *rmap_loc;
     27: #else
     28:   PetscInt *cmap, *rmap;
     29: #endif
     30:   PetscErrorCode (*destroy)(Mat);
     31: } Mat_SubSppt;

     33: /* Operations provided by MATSEQAIJ and its subclasses */
     34: typedef struct {
     35:   PetscErrorCode (*getarray)(Mat, PetscScalar **);
     36:   PetscErrorCode (*restorearray)(Mat, PetscScalar **);
     37:   PetscErrorCode (*getarrayread)(Mat, const PetscScalar **);
     38:   PetscErrorCode (*restorearrayread)(Mat, const PetscScalar **);
     39:   PetscErrorCode (*getarraywrite)(Mat, PetscScalar **);
     40:   PetscErrorCode (*restorearraywrite)(Mat, PetscScalar **);
     41:   PetscErrorCode (*getcsrandmemtype)(Mat, const PetscInt **, const PetscInt **, PetscScalar **, PetscMemType *);
     42: } Mat_SeqAIJOps;

     44: /*
     45:     Struct header shared by SeqAIJ, SeqBAIJ and SeqSBAIJ matrix formats
     46: */
     47: #define SEQAIJHEADER(datatype) \
     48:   PetscBool         roworiented; /* if true, row-oriented input, default */ \
     49:   PetscInt          nonew;       /* 1 don't add new nonzeros, -1 generate error on new */ \
     50:   PetscInt          nounused;    /* -1 generate error on unused space */ \
     51:   PetscInt          maxnz;       /* allocated nonzeros */ \
     52:   PetscInt         *imax;        /* maximum space allocated for each row */ \
     53:   PetscInt         *ilen;        /* actual length of each row */ \
     54:   PetscInt         *ipre;        /* space preallocated for each row by user */ \
     55:   PetscBool         free_imax_ilen; \
     56:   PetscInt          reallocs;           /* number of mallocs done during MatSetValues() \
     57:                                         as more values are set than were prealloced */ \
     58:   PetscInt          rmax;               /* max nonzeros in any row */ \
     59:   PetscBool         keepnonzeropattern; /* keeps matrix nonzero structure same in calls to MatZeroRows()*/ \
     60:   PetscBool         ignorezeroentries; \
     61:   PetscBool         free_ij;       /* free the column indices j and row offsets i when the matrix is destroyed */ \
     62:   PetscBool         free_a;        /* free the numerical values when matrix is destroy */ \
     63:   Mat_CompressedRow compressedrow; /* use compressed row format */ \
     64:   PetscInt          nz;            /* nonzeros */ \
     65:   PetscInt         *i;             /* pointer to beginning of each row */ \
     66:   PetscInt         *j;             /* column values: j + i[k] - 1 is start of row k */ \
     67:   PetscInt         *diag;          /* pointers to diagonal elements */ \
     68:   PetscInt          nonzerorowcnt; /* how many rows have nonzero entries */ \
     69:   PetscBool         free_diag; \
     70:   datatype         *a;              /* nonzero elements */ \
     71:   PetscScalar      *solve_work;     /* work space used in MatSolve */ \
     72:   IS                row, col, icol; /* index sets, used for reorderings */ \
     73:   PetscBool         pivotinblocks;  /* pivot inside factorization of each diagonal block */ \
     74:   Mat               parent;         /* set if this matrix was formed with MatDuplicate(...,MAT_SHARE_NONZERO_PATTERN,....); \
     75:                                          means that this shares some data structures with the parent including diag, ilen, imax, i, j */ \
     76:   Mat_SubSppt      *submatis1;      /* used by MatCreateSubMatrices_MPIXAIJ_Local */ \
     77:   Mat_SeqAIJOps     ops[1]          /* operations for SeqAIJ and its subclasses */

     79: typedef struct {
     80:   MatTransposeColoring matcoloring;
     81:   Mat                  Bt_den;  /* dense matrix of B^T */
     82:   Mat                  ABt_den; /* dense matrix of A*B^T */
     83:   PetscBool            usecoloring;
     84: } Mat_MatMatTransMult;

     86: typedef struct { /* used by MatTransposeMatMult() */
     87:   Mat At;        /* transpose of the first matrix */
     88:   Mat mA;        /* maij matrix of A */
     89:   Vec bt, ct;    /* vectors to hold locally transposed arrays of B and C */
     90:   /* used by PtAP */
     91:   void *data;
     92:   PetscErrorCode (*destroy)(void *);
     93: } Mat_MatTransMatMult;

     95: typedef struct {
     96:   PetscInt    *api, *apj; /* symbolic structure of A*P */
     97:   PetscScalar *apa;       /* temporary array for storing one row of A*P */
     98: } Mat_AP;

    100: typedef struct {
    101:   MatTransposeColoring matcoloring;
    102:   Mat                  Rt;   /* sparse or dense matrix of R^T */
    103:   Mat                  RARt; /* dense matrix of R*A*R^T */
    104:   Mat                  ARt;  /* A*R^T used for the case -matrart_color_art */
    105:   MatScalar           *work; /* work array to store columns of A*R^T used in MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqDense() */
    106:   /* free intermediate products needed for PtAP */
    107:   void *data;
    108:   PetscErrorCode (*destroy)(void *);
    109: } Mat_RARt;

    111: typedef struct {
    112:   Mat BC; /* temp matrix for storing B*C */
    113: } Mat_MatMatMatMult;

    115: /*
    116:   MATSEQAIJ format - Compressed row storage (also called Yale sparse matrix
    117:   format) or compressed sparse row (CSR).  The i[] and j[] arrays start at 0. For example,
    118:   j[i[k]+p] is the pth column in row k.  Note that the diagonal
    119:   matrix elements are stored with the rest of the nonzeros (not separately).
    120: */

    122: /* Info about i-nodes (identical nodes) helper class for SeqAIJ */
    123: typedef struct {
    124:   MatScalar *bdiag, *ibdiag, *ssor_work; /* diagonal blocks of matrix used for MatSOR_SeqAIJ_Inode() */
    125:   PetscInt   bdiagsize;                  /* length of bdiag and ibdiag */
    126:   PetscBool  ibdiagvalid;                /* do ibdiag[] and bdiag[] contain the most recent values */

    128:   PetscBool        use;
    129:   PetscInt         node_count;       /* number of inodes */
    130:   PetscInt        *size;             /* size of each inode */
    131:   PetscInt         limit;            /* inode limit */
    132:   PetscInt         max_limit;        /* maximum supported inode limit */
    133:   PetscBool        checked;          /* if inodes have been checked for */
    134:   PetscObjectState mat_nonzerostate; /* non-zero state when inodes were checked for */
    135: } Mat_SeqAIJ_Inode;

    137: PETSC_INTERN PetscErrorCode MatView_SeqAIJ_Inode(Mat, PetscViewer);
    138: PETSC_INTERN PetscErrorCode MatAssemblyEnd_SeqAIJ_Inode(Mat, MatAssemblyType);
    139: PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ_Inode(Mat);
    140: PETSC_INTERN PetscErrorCode MatCreate_SeqAIJ_Inode(Mat);
    141: PETSC_INTERN PetscErrorCode MatSetOption_SeqAIJ_Inode(Mat, MatOption, PetscBool);
    142: PETSC_INTERN PetscErrorCode MatDuplicate_SeqAIJ_Inode(Mat, MatDuplicateOption, Mat *);
    143: PETSC_INTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat, Mat, MatDuplicateOption, PetscBool);
    144: PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode(Mat, Mat, const MatFactorInfo *);
    145: PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat, PetscScalar **);
    146: PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat, PetscScalar **);

    148: typedef struct {
    149:   SEQAIJHEADER(MatScalar);
    150:   Mat_SeqAIJ_Inode inode;
    151:   MatScalar       *saved_values; /* location for stashing nonzero values of matrix */

    153:   PetscScalar *idiag, *mdiag, *ssor_work; /* inverse of diagonal entries, diagonal values and workspace for Eisenstat trick */
    154:   PetscBool    idiagvalid;                /* current idiag[] and mdiag[] are valid */
    155:   PetscScalar *ibdiag;                    /* inverses of block diagonals */
    156:   PetscBool    ibdiagvalid;               /* inverses of block diagonals are valid. */
    157:   PetscBool    diagonaldense;             /* all entries along the diagonal have been set; i.e. no missing diagonal terms */
    158:   PetscScalar  fshift, omega;             /* last used omega and fshift */

    160:   /* MatSetValues() via hash related fields */
    161:   PetscHMapIJV   ht;
    162:   PetscInt      *dnz;
    163:   struct _MatOps cops;
    164: } Mat_SeqAIJ;

    166: typedef struct {
    167:   PetscInt    nz;   /* nz of the matrix after assembly */
    168:   PetscCount  n;    /* Number of entries in MatSetPreallocationCOO() */
    169:   PetscCount  Atot; /* Total number of valid (i.e., w/ non-negative indices) entries in the COO array */
    170:   PetscCount *jmap; /* perm[jmap[i]..jmap[i+1]) give indices of entries in v[] associated with i-th nonzero of the matrix */
    171:   PetscCount *perm; /* The permutation array in sorting (i,j) by row and then by col */
    172: } MatCOOStruct_SeqAIJ;

    174: #define MatSeqXAIJGetOptions_Private(A) \
    175:   { \
    176:     const PetscBool oldvalues = (PetscBool)(A != PETSC_NULLPTR); \
    177:     PetscInt        nonew = 0, nounused = 0; \
    178:     PetscBool       roworiented = PETSC_FALSE; \
    179:     if (oldvalues) { \
    180:       nonew       = ((Mat_SeqAIJ *)A->data)->nonew; \
    181:       nounused    = ((Mat_SeqAIJ *)A->data)->nounused; \
    182:       roworiented = ((Mat_SeqAIJ *)A->data)->roworiented; \
    183:     } \
    184:     (void)0

    186: #define MatSeqXAIJRestoreOptions_Private(A) \
    187:   if (oldvalues) { \
    188:     ((Mat_SeqAIJ *)A->data)->nonew       = nonew; \
    189:     ((Mat_SeqAIJ *)A->data)->nounused    = nounused; \
    190:     ((Mat_SeqAIJ *)A->data)->roworiented = roworiented; \
    191:   } \
    192:   } \
    193:   (void)0

    195: static inline PetscErrorCode MatXAIJAllocatea(Mat A, PetscInt nz, PetscScalar **array)
    196: {
    197:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

    199:   PetscFunctionBegin;
    200:   PetscCall(PetscShmgetAllocateArray(nz, sizeof(PetscScalar), (void **)array));
    201:   a->free_a = PETSC_TRUE;
    202:   PetscFunctionReturn(PETSC_SUCCESS);
    203: }

    205: static inline PetscErrorCode MatXAIJDeallocatea(Mat A, PetscScalar **array)
    206: {
    207:   Mat_SeqAIJ *a = (Mat_SeqAIJ *)A->data;

    209:   PetscFunctionBegin;
    210:   if (a->free_a) PetscCall(PetscShmgetDeallocateArray((void **)array));
    211:   a->free_a = PETSC_FALSE;
    212:   PetscFunctionReturn(PETSC_SUCCESS);
    213: }

    215: /*
    216:   Frees the a, i, and j arrays from the XAIJ (AIJ, BAIJ, and SBAIJ) matrix types
    217: */
    218: static inline PetscErrorCode MatSeqXAIJFreeAIJ(Mat AA, MatScalar **a, PetscInt **j, PetscInt **i)
    219: {
    220:   Mat_SeqAIJ *A = (Mat_SeqAIJ *)AA->data;

    222:   PetscFunctionBegin;
    223:   if (A->free_a) PetscCall(PetscShmgetDeallocateArray((void **)a));
    224:   if (A->free_ij) PetscCall(PetscShmgetDeallocateArray((void **)j));
    225:   if (A->free_ij) PetscCall(PetscShmgetDeallocateArray((void **)i));
    226:   PetscFunctionReturn(PETSC_SUCCESS);
    227: }
    228: /*
    229:     Allocates larger a, i, and j arrays for the XAIJ (AIJ, BAIJ, and SBAIJ) matrix types
    230:     This is a macro because it takes the datatype as an argument which can be either a Mat or a MatScalar
    231: */
    232: #define MatSeqXAIJReallocateAIJ(Amat, AM, BS2, NROW, ROW, COL, RMAX, AA, AI, AJ, RP, AP, AIMAX, NONEW, datatype) \
    233:   do { \
    234:     if (NROW >= RMAX) { \
    235:       Mat_SeqAIJ *Ain       = (Mat_SeqAIJ *)Amat->data; \
    236:       PetscInt    CHUNKSIZE = 15, new_nz = AI[AM] + CHUNKSIZE, len, *new_i = NULL, *new_j = NULL; \
    237:       datatype   *new_a; \
    238: \
    239:       PetscCheck(NONEW != -2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "New nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") caused a malloc. Use MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE) to turn off this check", ROW, COL); \
    240:       /* malloc new storage space */ \
    241:       PetscCall(PetscShmgetAllocateArray(BS2 *new_nz, sizeof(PetscScalar), (void **)&new_a)); \
    242:       PetscCall(PetscShmgetAllocateArray(new_nz, sizeof(PetscInt), (void **)&new_j)); \
    243:       PetscCall(PetscShmgetAllocateArray(AM + 1, sizeof(PetscInt), (void **)&new_i)); \
    244:       Ain->free_a  = PETSC_TRUE; \
    245:       Ain->free_ij = PETSC_TRUE; \
    246:       /* copy over old data into new slots */ \
    247:       for (ii = 0; ii < ROW + 1; ii++) new_i[ii] = AI[ii]; \
    248:       for (ii = ROW + 1; ii < AM + 1; ii++) new_i[ii] = AI[ii] + CHUNKSIZE; \
    249:       PetscCall(PetscArraycpy(new_j, AJ, AI[ROW] + NROW)); \
    250:       len = (new_nz - CHUNKSIZE - AI[ROW] - NROW); \
    251:       PetscCall(PetscArraycpy(new_j + AI[ROW] + NROW + CHUNKSIZE, PetscSafePointerPlusOffset(AJ, AI[ROW] + NROW), len)); \
    252:       PetscCall(PetscArraycpy(new_a, AA, BS2 *(AI[ROW] + NROW))); \
    253:       PetscCall(PetscArrayzero(new_a + BS2 * (AI[ROW] + NROW), BS2 * CHUNKSIZE)); \
    254:       PetscCall(PetscArraycpy(new_a + BS2 * (AI[ROW] + NROW + CHUNKSIZE), PetscSafePointerPlusOffset(AA, BS2 * (AI[ROW] + NROW)), BS2 * len)); \
    255:       /* free up old matrix storage */ \
    256:       PetscCall(MatSeqXAIJFreeAIJ(A, &Ain->a, &Ain->j, &Ain->i)); \
    257:       AA     = new_a; \
    258:       Ain->a = (MatScalar *)new_a; \
    259:       AI = Ain->i = new_i; \
    260:       AJ = Ain->j = new_j; \
    261: \
    262:       RP   = AJ + AI[ROW]; \
    263:       AP   = AA + BS2 * AI[ROW]; \
    264:       RMAX = AIMAX[ROW] = AIMAX[ROW] + CHUNKSIZE; \
    265:       Ain->maxnz += BS2 * CHUNKSIZE; \
    266:       Ain->reallocs++; \
    267:       Amat->nonzerostate++; \
    268:     } \
    269:   } while (0)

    271: #define MatSeqXAIJReallocateAIJ_structure_only(Amat, AM, BS2, NROW, ROW, COL, RMAX, AI, AJ, RP, AIMAX, NONEW, datatype) \
    272:   do { \
    273:     if (NROW >= RMAX) { \
    274:       Mat_SeqAIJ *Ain = (Mat_SeqAIJ *)Amat->data; \
    275:       /* there is no extra room in row, therefore enlarge */ \
    276:       PetscInt CHUNKSIZE = 15, new_nz = AI[AM] + CHUNKSIZE, len, *new_i = NULL, *new_j = NULL; \
    277: \
    278:       PetscCheck(NONEW != -2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "New nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") caused a malloc. Use MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE) to turn off this check", ROW, COL); \
    279:       /* malloc new storage space */ \
    280:       PetscCall(PetscShmgetAllocateArray(new_nz, sizeof(PetscInt), (void **)&new_j)); \
    281:       PetscCall(PetscShmgetAllocateArray(AM + 1, sizeof(PetscInt), (void **)&new_i)); \
    282:       Ain->free_a  = PETSC_FALSE; \
    283:       Ain->free_ij = PETSC_TRUE; \
    284: \
    285:       /* copy over old data into new slots */ \
    286:       for (ii = 0; ii < ROW + 1; ii++) new_i[ii] = AI[ii]; \
    287:       for (ii = ROW + 1; ii < AM + 1; ii++) new_i[ii] = AI[ii] + CHUNKSIZE; \
    288:       PetscCall(PetscArraycpy(new_j, AJ, AI[ROW] + NROW)); \
    289:       len = (new_nz - CHUNKSIZE - AI[ROW] - NROW); \
    290:       PetscCall(PetscArraycpy(new_j + AI[ROW] + NROW + CHUNKSIZE, AJ + AI[ROW] + NROW, len)); \
    291: \
    292:       /* free up old matrix storage */ \
    293:       PetscCall(MatSeqXAIJFreeAIJ(A, &Ain->a, &Ain->j, &Ain->i)); \
    294:       Ain->a = NULL; \
    295:       AI = Ain->i = new_i; \
    296:       AJ = Ain->j = new_j; \
    297: \
    298:       RP   = AJ + AI[ROW]; \
    299:       RMAX = AIMAX[ROW] = AIMAX[ROW] + CHUNKSIZE; \
    300:       Ain->maxnz += BS2 * CHUNKSIZE; \
    301:       Ain->reallocs++; \
    302:       Amat->nonzerostate++; \
    303:     } \
    304:   } while (0)

    306: PETSC_INTERN PetscErrorCode MatSeqAIJSetPreallocation_SeqAIJ(Mat, PetscInt, const PetscInt *);
    307: PETSC_INTERN PetscErrorCode MatSetPreallocationCOO_SeqAIJ(Mat, PetscCount, PetscInt[], PetscInt[]);

    309: PETSC_INTERN PetscErrorCode MatILUFactorSymbolic_SeqAIJ(Mat, Mat, IS, IS, const MatFactorInfo *);
    310: PETSC_INTERN PetscErrorCode MatILUFactorSymbolic_SeqAIJ_ilu0(Mat, Mat, IS, IS, const MatFactorInfo *);

    312: PETSC_INTERN PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat, Mat, IS, const MatFactorInfo *);
    313: PETSC_INTERN PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat, Mat, IS, const MatFactorInfo *);
    314: PETSC_INTERN PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat, Mat, const MatFactorInfo *);
    315: PETSC_INTERN PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat, Mat, const MatFactorInfo *);
    316: PETSC_INTERN PetscErrorCode MatDuplicate_SeqAIJ(Mat, MatDuplicateOption, Mat *);
    317: PETSC_INTERN PetscErrorCode MatCopy_SeqAIJ(Mat, Mat, MatStructure);
    318: PETSC_INTERN PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat, PetscBool *, PetscInt *);
    319: PETSC_INTERN PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat);
    320: PETSC_INTERN PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat, PetscInt *, PetscInt **);

    322: PETSC_INTERN PetscErrorCode MatMult_SeqAIJ(Mat, Vec, Vec);
    323: PETSC_INTERN PetscErrorCode MatMult_SeqAIJ_Inode(Mat, Vec, Vec);
    324: PETSC_INTERN PetscErrorCode MatMultAdd_SeqAIJ(Mat, Vec, Vec, Vec);
    325: PETSC_INTERN PetscErrorCode MatMultAdd_SeqAIJ_Inode(Mat, Vec, Vec, Vec);
    326: PETSC_INTERN PetscErrorCode MatMultTranspose_SeqAIJ(Mat, Vec, Vec);
    327: PETSC_INTERN PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat, Vec, Vec, Vec);
    328: PETSC_INTERN PetscErrorCode MatSOR_SeqAIJ(Mat, Vec, PetscReal, MatSORType, PetscReal, PetscInt, PetscInt, Vec);
    329: PETSC_INTERN PetscErrorCode MatSOR_SeqAIJ_Inode(Mat, Vec, PetscReal, MatSORType, PetscReal, PetscInt, PetscInt, Vec);

    331: PETSC_INTERN PetscErrorCode MatSetOption_SeqAIJ(Mat, MatOption, PetscBool);

    333: PETSC_INTERN PetscErrorCode MatGetSymbolicTranspose_SeqAIJ(Mat, PetscInt *[], PetscInt *[]);
    334: PETSC_INTERN PetscErrorCode MatRestoreSymbolicTranspose_SeqAIJ(Mat, PetscInt *[], PetscInt *[]);
    335: PETSC_INTERN PetscErrorCode MatGetSymbolicTransposeReduced_SeqAIJ(Mat, PetscInt, PetscInt, PetscInt *[], PetscInt *[]);
    336: PETSC_INTERN PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat, Mat *);
    337: PETSC_INTERN PetscErrorCode MatTranspose_SeqAIJ(Mat, MatReuse, Mat *);

    339: PETSC_INTERN PetscErrorCode MatToSymmetricIJ_SeqAIJ(PetscInt, PetscInt *, PetscInt *, PetscBool, PetscInt, PetscInt, PetscInt **, PetscInt **);
    340: PETSC_INTERN PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat, Mat, IS, IS, const MatFactorInfo *);
    341: PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat, Mat, const MatFactorInfo *);
    342: PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat, Mat, const MatFactorInfo *);
    343: PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat, Mat, const MatFactorInfo *);
    344: PETSC_INTERN PetscErrorCode MatLUFactor_SeqAIJ(Mat, IS, IS, const MatFactorInfo *);
    345: PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_inplace(Mat, Vec, Vec);
    346: PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ(Mat, Vec, Vec);
    347: PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_Inode(Mat, Vec, Vec);
    348: PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat, Vec, Vec);
    349: PETSC_INTERN PetscErrorCode MatSolveAdd_SeqAIJ(Mat, Vec, Vec, Vec);
    350: PETSC_INTERN PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat, Vec, Vec);
    351: PETSC_INTERN PetscErrorCode MatSolveTranspose_SeqAIJ(Mat, Vec, Vec);
    352: PETSC_INTERN PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat, Vec, Vec, Vec);
    353: PETSC_INTERN PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat, Vec, Vec, Vec);
    354: PETSC_INTERN PetscErrorCode MatMatSolve_SeqAIJ(Mat, Mat, Mat);
    355: PETSC_INTERN PetscErrorCode MatMatSolveTranspose_SeqAIJ(Mat, Mat, Mat);
    356: PETSC_INTERN PetscErrorCode MatEqual_SeqAIJ(Mat, Mat, PetscBool *);
    357: PETSC_INTERN PetscErrorCode MatFDColoringCreate_SeqXAIJ(Mat, ISColoring, MatFDColoring);
    358: PETSC_INTERN PetscErrorCode MatFDColoringSetUp_SeqXAIJ(Mat, ISColoring, MatFDColoring);
    359: PETSC_INTERN PetscErrorCode MatFDColoringSetUpBlocked_AIJ_Private(Mat, MatFDColoring, PetscInt);
    360: PETSC_INTERN PetscErrorCode MatLoad_AIJ_HDF5(Mat, PetscViewer);
    361: PETSC_INTERN PetscErrorCode MatLoad_SeqAIJ_Binary(Mat, PetscViewer);
    362: PETSC_INTERN PetscErrorCode MatLoad_SeqAIJ(Mat, PetscViewer);
    363: PETSC_INTERN PetscErrorCode RegisterApplyPtAPRoutines_Private(Mat);

    365: #if defined(PETSC_HAVE_HYPRE)
    366: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_Transpose_AIJ_AIJ(Mat);
    367: #endif
    368: PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat);

    370: PETSC_INTERN PetscErrorCode MatProductSymbolic_SeqAIJ_SeqAIJ(Mat);
    371: PETSC_INTERN PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ(Mat);
    372: PETSC_INTERN PetscErrorCode MatProductSymbolic_RARt_SeqAIJ_SeqAIJ(Mat);

    374: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
    375: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat, Mat, PetscReal, Mat);
    376: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat, Mat, PetscReal, Mat);
    377: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat, Mat, PetscReal, Mat);
    378: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat, Mat, PetscReal, Mat);
    379: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat, Mat, PetscReal, Mat);
    380: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat, Mat, PetscReal, Mat);
    381: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat, Mat, PetscReal, Mat);
    382: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat, Mat, PetscReal, Mat);
    383: #if defined(PETSC_HAVE_HYPRE)
    384: PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat, Mat, PetscReal, Mat);
    385: #endif

    387: PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
    388: PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat, Mat, Mat);

    390: PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat, Mat, Mat);
    391: PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat, Mat, Mat);

    393: PETSC_INTERN PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat, Mat, PetscReal, Mat);
    394: PETSC_INTERN PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
    395: PETSC_INTERN PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat, Mat, Mat);

    397: PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
    398: PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat, Mat, PetscReal, Mat);
    399: PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat, Mat, PetscReal, Mat);
    400: PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
    401: PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat, Mat, Mat);
    402: PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat, Mat, Mat);

    404: PETSC_INTERN PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
    405: PETSC_INTERN PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
    406: PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *);

    408: PETSC_INTERN PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
    409: PETSC_INTERN PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
    410: PETSC_INTERN PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat, ISColoring, MatTransposeColoring);
    411: PETSC_INTERN PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring, Mat, Mat);
    412: PETSC_INTERN PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring, Mat, Mat);

    414: PETSC_INTERN PetscErrorCode MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Mat, Mat, Mat, PetscReal, Mat);
    415: PETSC_INTERN PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(Mat, Mat, Mat, Mat);

    417: PETSC_INTERN PetscErrorCode MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat, PetscInt, PetscInt, PetscRandom);
    418: PETSC_INTERN PetscErrorCode MatSetValues_SeqAIJ(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
    419: PETSC_INTERN PetscErrorCode MatGetRow_SeqAIJ(Mat, PetscInt, PetscInt *, PetscInt **, PetscScalar **);
    420: PETSC_INTERN PetscErrorCode MatRestoreRow_SeqAIJ(Mat, PetscInt, PetscInt *, PetscInt **, PetscScalar **);
    421: PETSC_INTERN PetscErrorCode MatScale_SeqAIJ(Mat, PetscScalar);
    422: PETSC_INTERN PetscErrorCode MatDiagonalScale_SeqAIJ(Mat, Vec, Vec);
    423: PETSC_INTERN PetscErrorCode MatDiagonalSet_SeqAIJ(Mat, Vec, InsertMode);
    424: PETSC_INTERN PetscErrorCode MatAXPY_SeqAIJ(Mat, PetscScalar, Mat, MatStructure);
    425: PETSC_INTERN PetscErrorCode MatGetRowIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
    426: PETSC_INTERN PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
    427: PETSC_INTERN PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
    428: PETSC_INTERN PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
    429: PETSC_INTERN PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscInt *[], PetscBool *);
    430: PETSC_INTERN PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscInt *[], PetscBool *);
    431: PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ(Mat);
    432: PETSC_INTERN PetscErrorCode MatView_SeqAIJ(Mat, PetscViewer);

    434: PETSC_INTERN PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat);
    435: PETSC_INTERN PetscErrorCode MatSeqAIJInvalidateDiagonal_Inode(Mat);
    436: PETSC_INTERN PetscErrorCode MatSeqAIJCheckInode(Mat);
    437: PETSC_INTERN PetscErrorCode MatSeqAIJCheckInode_FactorLU(Mat);

    439: PETSC_INTERN PetscErrorCode MatAXPYGetPreallocation_SeqAIJ(Mat, Mat, PetscInt *);

    441: #if defined(PETSC_HAVE_MATLAB)
    442: PETSC_EXTERN PetscErrorCode MatlabEnginePut_SeqAIJ(PetscObject, void *);
    443: PETSC_EXTERN PetscErrorCode MatlabEngineGet_SeqAIJ(PetscObject, void *);
    444: #endif
    445: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqSBAIJ(Mat, MatType, MatReuse, Mat *);
    446: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqBAIJ(Mat, MatType, MatReuse, Mat *);
    447: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat, MatType, MatReuse, Mat *);
    448: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat, MatType, MatReuse, Mat *);
    449: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
    450: #if defined(PETSC_HAVE_SCALAPACK)
    451: PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
    452: #endif
    453: PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
    454: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJPERM(Mat, MatType, MatReuse, Mat *);
    455: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJSELL(Mat, MatType, MatReuse, Mat *);
    456: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJMKL(Mat, MatType, MatReuse, Mat *);
    457: PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJViennaCL(Mat, MatType, MatReuse, Mat *);
    458: PETSC_INTERN PetscErrorCode MatReorderForNonzeroDiagonal_SeqAIJ(Mat, PetscReal, IS, IS);
    459: PETSC_INTERN PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat, Mat, MatReuse, PetscReal, Mat *);
    460: PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat);
    461: PETSC_INTERN PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat, MatAssemblyType);
    462: PETSC_EXTERN PetscErrorCode MatZeroEntries_SeqAIJ(Mat);

    464: PETSC_INTERN PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt, const PetscInt *, const PetscInt *, const PetscInt *, const PetscInt *, PetscInt *);
    465: PETSC_INTERN PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm, Mat, PetscInt, MatReuse, Mat *);
    466: PETSC_INTERN PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm, Mat, PetscInt, MatReuse, Mat *);

    468: PETSC_INTERN PetscErrorCode MatSetSeqMat_SeqAIJ(Mat, IS, IS, MatStructure, Mat);
    469: PETSC_INTERN PetscErrorCode MatEliminateZeros_SeqAIJ(Mat, PetscBool);
    470: PETSC_INTERN PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *);
    471: PETSC_INTERN PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat);
    472: PETSC_INTERN PetscErrorCode MatDestroySubMatrix_Dummy(Mat);
    473: PETSC_INTERN PetscErrorCode MatDestroySubMatrices_Dummy(PetscInt, Mat *[]);
    474: PETSC_INTERN PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat, IS, IS, PetscInt, MatReuse, Mat *);

    476: PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], MatType, Mat);

    478: PETSC_INTERN PetscErrorCode MatResetPreallocation_SeqAIJ_Private(Mat A, PetscBool *memoryreset);

    480: PETSC_SINGLE_LIBRARY_INTERN PetscErrorCode MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat, ISLocalToGlobalMapping *);

    482: /*
    483:     PetscSparseDenseMinusDot - The inner kernel of triangular solves and Gauss-Siedel smoothing. \sum_i xv[i] * r[xi[i]] for CSR storage

    485:   Input Parameters:
    486: +  nnz - the number of entries
    487: .  r - the array of vector values
    488: .  xv - the matrix values for the row
    489: -  xi - the column indices of the nonzeros in the row

    491:   Output Parameter:
    492: .  sum - negative the sum of results

    494:   PETSc compile flags:
    495: +   PETSC_KERNEL_USE_UNROLL_4
    496: -   PETSC_KERNEL_USE_UNROLL_2

    498:   Developer Note:
    499:     The macro changes sum but not other parameters

    501: .seealso: `PetscSparseDensePlusDot()`
    502: */
    503: #if defined(PETSC_KERNEL_USE_UNROLL_4)
    504:   #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    505:     do { \
    506:       if (nnz > 0) { \
    507:         PetscInt nnz2 = nnz, rem = nnz & 0x3; \
    508:         switch (rem) { \
    509:         case 3: \
    510:           sum -= *xv++ * r[*xi++]; \
    511:         case 2: \
    512:           sum -= *xv++ * r[*xi++]; \
    513:         case 1: \
    514:           sum -= *xv++ * r[*xi++]; \
    515:           nnz2 -= rem; \
    516:         } \
    517:         while (nnz2 > 0) { \
    518:           sum -= xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
    519:           xv += 4; \
    520:           xi += 4; \
    521:           nnz2 -= 4; \
    522:         } \
    523:         xv -= nnz; \
    524:         xi -= nnz; \
    525:       } \
    526:     } while (0)

    528: #elif defined(PETSC_KERNEL_USE_UNROLL_2)
    529:   #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    530:     do { \
    531:       PetscInt __i, __i1, __i2; \
    532:       for (__i = 0; __i < nnz - 1; __i += 2) { \
    533:         __i1 = xi[__i]; \
    534:         __i2 = xi[__i + 1]; \
    535:         sum -= (xv[__i] * r[__i1] + xv[__i + 1] * r[__i2]); \
    536:       } \
    537:       if (nnz & 0x1) sum -= xv[__i] * r[xi[__i]]; \
    538:     } while (0)

    540: #else
    541:   #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    542:     do { \
    543:       PetscInt __i; \
    544:       for (__i = 0; __i < nnz; __i++) sum -= xv[__i] * r[xi[__i]]; \
    545:     } while (0)
    546: #endif

    548: /*
    549:     PetscSparseDensePlusDot - The inner kernel of matrix-vector product \sum_i xv[i] * r[xi[i]] for CSR storage

    551:   Input Parameters:
    552: +  nnz - the number of entries
    553: .  r - the array of vector values
    554: .  xv - the matrix values for the row
    555: -  xi - the column indices of the nonzeros in the row

    557:   Output Parameter:
    558: .  sum - the sum of results

    560:   PETSc compile flags:
    561: +   PETSC_KERNEL_USE_UNROLL_4
    562: -   PETSC_KERNEL_USE_UNROLL_2

    564:   Developer Note:
    565:     The macro changes sum but not other parameters

    567: .seealso: `PetscSparseDenseMinusDot()`
    568: */
    569: #if defined(PETSC_KERNEL_USE_UNROLL_4)
    570:   #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    571:     do { \
    572:       if (nnz > 0) { \
    573:         PetscInt nnz2 = nnz, rem = nnz & 0x3; \
    574:         switch (rem) { \
    575:         case 3: \
    576:           sum += *xv++ * r[*xi++]; \
    577:         case 2: \
    578:           sum += *xv++ * r[*xi++]; \
    579:         case 1: \
    580:           sum += *xv++ * r[*xi++]; \
    581:           nnz2 -= rem; \
    582:         } \
    583:         while (nnz2 > 0) { \
    584:           sum += xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
    585:           xv += 4; \
    586:           xi += 4; \
    587:           nnz2 -= 4; \
    588:         } \
    589:         xv -= nnz; \
    590:         xi -= nnz; \
    591:       } \
    592:     } while (0)

    594: #elif defined(PETSC_KERNEL_USE_UNROLL_2)
    595:   #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    596:     do { \
    597:       PetscInt __i, __i1, __i2; \
    598:       for (__i = 0; __i < nnz - 1; __i += 2) { \
    599:         __i1 = xi[__i]; \
    600:         __i2 = xi[__i + 1]; \
    601:         sum += (xv[__i] * r[__i1] + xv[__i + 1] * r[__i2]); \
    602:       } \
    603:       if (nnz & 0x1) sum += xv[__i] * r[xi[__i]]; \
    604:     } while (0)

    606: #elif !(defined(__GNUC__) && defined(_OPENMP)) && defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES) && !defined(PETSC_SKIP_IMMINTRIN_H_CUDAWORKAROUND)
    607:   #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) PetscSparseDensePlusDot_AVX512_Private(&(sum), (r), (xv), (xi), (nnz))

    609: #else
    610:   #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    611:     do { \
    612:       PetscInt __i; \
    613:       for (__i = 0; __i < nnz; __i++) sum += xv[__i] * r[xi[__i]]; \
    614:     } while (0)
    615: #endif

    617: #if defined(PETSC_USE_AVX512_KERNELS) && defined(PETSC_HAVE_IMMINTRIN_H) && defined(__AVX512F__) && defined(PETSC_USE_REAL_DOUBLE) && !defined(PETSC_USE_COMPLEX) && !defined(PETSC_USE_64BIT_INDICES) && !defined(PETSC_SKIP_IMMINTRIN_H_CUDAWORKAROUND)
    618:   #include <immintrin.h>
    619:   #if !defined(_MM_SCALE_8)
    620:     #define _MM_SCALE_8 8
    621:   #endif

    623: static inline void PetscSparseDensePlusDot_AVX512_Private(PetscScalar *sum, const PetscScalar *x, const MatScalar *aa, const PetscInt *aj, PetscInt n)
    624: {
    625:   __m512d  vec_x, vec_y, vec_vals;
    626:   __m256i  vec_idx;
    627:   PetscInt j;

    629:   vec_y = _mm512_setzero_pd();
    630:   for (j = 0; j < (n >> 3); j++) {
    631:     vec_idx  = _mm256_loadu_si256((__m256i const *)aj);
    632:     vec_vals = _mm512_loadu_pd(aa);
    633:     vec_x    = _mm512_i32gather_pd(vec_idx, x, _MM_SCALE_8);
    634:     vec_y    = _mm512_fmadd_pd(vec_x, vec_vals, vec_y);
    635:     aj += 8;
    636:     aa += 8;
    637:   }
    638:   #if defined(__AVX512VL__)
    639:   /* masked load requires avx512vl, which is not supported by KNL */
    640:   if (n & 0x07) {
    641:     __mmask8 mask;
    642:     mask     = (__mmask8)(0xff >> (8 - (n & 0x07)));
    643:     vec_idx  = _mm256_mask_loadu_epi32(vec_idx, mask, aj);
    644:     vec_vals = _mm512_mask_loadu_pd(vec_vals, mask, aa);
    645:     vec_x    = _mm512_mask_i32gather_pd(vec_x, mask, vec_idx, x, _MM_SCALE_8);
    646:     vec_y    = _mm512_mask3_fmadd_pd(vec_x, vec_vals, vec_y, mask);
    647:   }
    648:   *sum += _mm512_reduce_add_pd(vec_y);
    649:   #else
    650:   *sum += _mm512_reduce_add_pd(vec_y);
    651:   for (j = 0; j < (n & 0x07); j++) *sum += aa[j] * x[aj[j]];
    652:   #endif
    653: }
    654: #endif

    656: /*
    657:     PetscSparseDenseMaxDot - The inner kernel of a modified matrix-vector product \max_i xv[i] * r[xi[i]] for CSR storage

    659:   Input Parameters:
    660: +  nnz - the number of entries
    661: .  r - the array of vector values
    662: .  xv - the matrix values for the row
    663: -  xi - the column indices of the nonzeros in the row

    665:   Output Parameter:
    666: .  max - the max of results

    668: .seealso: `PetscSparseDensePlusDot()`, `PetscSparseDenseMinusDot()`
    669: */
    670: #define PetscSparseDenseMaxDot(max, r, xv, xi, nnz) \
    671:   do { \
    672:     for (PetscInt __i = 0; __i < (nnz); __i++) { max = PetscMax(PetscRealPart(max), PetscRealPart((xv)[__i] * (r)[(xi)[__i]])); } \
    673:   } while (0)

    675: /*
    676:  Add column indices into table for counting the max nonzeros of merged rows
    677:  */
    678: #define MatRowMergeMax_SeqAIJ(mat, nrows, ta) \
    679:   do { \
    680:     if (mat) { \
    681:       for (PetscInt _row = 0; _row < (nrows); _row++) { \
    682:         const PetscInt _nz = (mat)->i[_row + 1] - (mat)->i[_row]; \
    683:         for (PetscInt _j = 0; _j < _nz; _j++) { \
    684:           PetscInt *_col = _j + (mat)->j + (mat)->i[_row]; \
    685:           PetscCall(PetscHMapISet((ta), *_col + 1, 1)); \
    686:         } \
    687:       } \
    688:     } \
    689:   } while (0)

    691: /*
    692:  Add column indices into table for counting the nonzeros of merged rows
    693:  */
    694: #define MatMergeRows_SeqAIJ(mat, nrows, rows, ta) \
    695:   do { \
    696:     for (PetscInt _i = 0; _i < (nrows); _i++) { \
    697:       const PetscInt _row = (rows)[_i]; \
    698:       const PetscInt _nz  = (mat)->i[_row + 1] - (mat)->i[_row]; \
    699:       for (PetscInt _j = 0; _j < _nz; _j++) { \
    700:         PetscInt *_col = _j + (mat)->j + (mat)->i[_row]; \
    701:         PetscCall(PetscHMapISetWithMode((ta), *_col + 1, 1, INSERT_VALUES)); \
    702:       } \
    703:     } \
    704:   } while (0)