xref: /petsc/src/mat/impls/aij/seq/aij.h (revision 26cec32642a02ddeaa9481e1a5bd50b8500ffeea)

#ifndef PETSC_MATAIJ_IMPL_H
#define PETSC_MATAIJ_IMPL_H

#include <petsc/private/matimpl.h>
#include <petsc/private/hashmapi.h>
#include <petsc/private/hashmapijv.h>

/*
 Used by MatCreateSubMatrices_MPIXAIJ_Local()
*/
typedef struct { /* used by MatCreateSubMatrices_MPIAIJ_SingleIS_Local() and MatCreateSubMatrices_MPIAIJ_Local */
  PetscInt   id; /* index of submats, only submats[0] is responsible for deleting some arrays below */
  PetscInt   nrqs, nrqr;
  PetscInt **rbuf1, **rbuf2, **rbuf3, **sbuf1, **sbuf2;
  PetscInt **ptr;
  PetscInt  *tmp;
  PetscInt  *ctr;
  PetscInt  *pa; /* proc array */
  PetscInt  *req_size, *req_source1, *req_source2;
  PetscBool  allcolumns, allrows;
  PetscBool  singleis;
  PetscInt  *row2proc; /* row to proc map */
  PetscInt   nstages;
#if defined(PETSC_USE_CTABLE)
  PetscHMapI cmap, rmap;
  PetscInt  *cmap_loc, *rmap_loc;
#else
  PetscInt *cmap, *rmap;
#endif
  PetscErrorCode (*destroy)(Mat);
} Mat_SubSppt;

/* Operations provided by MATSEQAIJ and its subclasses */
typedef struct {
  PetscErrorCode (*getarray)(Mat, PetscScalar **);
  PetscErrorCode (*restorearray)(Mat, PetscScalar **);
  PetscErrorCode (*getarrayread)(Mat, const PetscScalar **);
  PetscErrorCode (*restorearrayread)(Mat, const PetscScalar **);
  PetscErrorCode (*getarraywrite)(Mat, PetscScalar **);
  PetscErrorCode (*restorearraywrite)(Mat, PetscScalar **);
  PetscErrorCode (*getcsrandmemtype)(Mat, const PetscInt **, const PetscInt **, PetscScalar **, PetscMemType *);
} Mat_SeqAIJOps;

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

typedef struct {
  MatTransposeColoring matcoloring;
  Mat                  Bt_den;  /* dense matrix of B^T */
  Mat                  ABt_den; /* dense matrix of A*B^T */
  PetscBool            usecoloring;
} Mat_MatMatTransMult;

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

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

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

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

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

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

  PetscBool        use;
  PetscInt         node_count;       /* number of inodes */
  PetscInt        *size;             /* size of each inode */
  PetscInt         limit;            /* inode limit */
  PetscInt         max_limit;        /* maximum supported inode limit */
  PetscBool        checked;          /* if inodes have been checked for */
  PetscObjectState mat_nonzerostate; /* non-zero state when inodes were checked for */
} Mat_SeqAIJ_Inode;

PETSC_INTERN PetscErrorCode MatView_SeqAIJ_Inode(Mat, PetscViewer);
PETSC_INTERN PetscErrorCode MatAssemblyEnd_SeqAIJ_Inode(Mat, MatAssemblyType);
PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ_Inode(Mat);
PETSC_INTERN PetscErrorCode MatCreate_SeqAIJ_Inode(Mat);
PETSC_INTERN PetscErrorCode MatSetOption_SeqAIJ_Inode(Mat, MatOption, PetscBool);
PETSC_INTERN PetscErrorCode MatDuplicate_SeqAIJ_Inode(Mat, MatDuplicateOption, Mat *);
PETSC_INTERN PetscErrorCode MatDuplicateNoCreate_SeqAIJ(Mat, Mat, MatDuplicateOption, PetscBool);
PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_Inode(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatSeqAIJGetArray_SeqAIJ(Mat, PetscScalar **);
PETSC_INTERN PetscErrorCode MatSeqAIJRestoreArray_SeqAIJ(Mat, PetscScalar **);

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

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

  /* MatSetValuesCOO() related fields on host */
  PetscCount  coo_n; /* Number of entries in MatSetPreallocationCOO() */
  PetscCount  Atot;  /* Total number of valid (i.e., w/ non-negative indices) entries in the COO array */
  PetscCount *jmap;  /* perm[jmap[i]..jmap[i+1]) give indices of entries in v[] associated with i-th nonzero of the matrix */
  PetscCount *perm;  /* The permutation array in sorting (i,j) by row and then by col */

  /* MatSetValues() via hash related fields */
  PetscHMapIJV   ht;
  PetscInt      *dnz;
  struct _MatOps cops;
} Mat_SeqAIJ;

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

  PetscFunctionBegin;
  if (A->singlemalloc) {
    PetscCall(PetscFree3(*a, *j, *i));
  } else {
    if (A->free_a) PetscCall(PetscFree(*a));
    if (A->free_ij) PetscCall(PetscFree(*j));
    if (A->free_ij) PetscCall(PetscFree(*i));
  }
  PetscFunctionReturn(PETSC_SUCCESS);
}
/*
    Allocates larger a, i, and j arrays for the XAIJ (AIJ, BAIJ, and SBAIJ) matrix types
    This is a macro because it takes the datatype as an argument which can be either a Mat or a MatScalar
*/
#define MatSeqXAIJReallocateAIJ(Amat, AM, BS2, NROW, ROW, COL, RMAX, AA, AI, AJ, RP, AP, AIMAX, NONEW, datatype) \
  if (NROW >= RMAX) { \
    Mat_SeqAIJ *Ain = (Mat_SeqAIJ *)Amat->data; \
    /* there is no extra room in row, therefore enlarge */ \
    PetscInt  CHUNKSIZE = 15, new_nz = AI[AM] + CHUNKSIZE, len, *new_i = NULL, *new_j = NULL; \
    datatype *new_a; \
\
    PetscCheck(NONEW != -2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "New nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") caused a malloc\nUse MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE) to turn off this check", ROW, COL); \
    /* malloc new storage space */ \
    PetscCall(PetscMalloc3(BS2 *new_nz, &new_a, new_nz, &new_j, AM + 1, &new_i)); \
\
    /* copy over old data into new slots */ \
    for (ii = 0; ii < ROW + 1; ii++) new_i[ii] = AI[ii]; \
    for (ii = ROW + 1; ii < AM + 1; ii++) new_i[ii] = AI[ii] + CHUNKSIZE; \
    PetscCall(PetscArraycpy(new_j, AJ, AI[ROW] + NROW)); \
    len = (new_nz - CHUNKSIZE - AI[ROW] - NROW); \
    PetscCall(PetscArraycpy(new_j + AI[ROW] + NROW + CHUNKSIZE, AJ + AI[ROW] + NROW, len)); \
    PetscCall(PetscArraycpy(new_a, AA, BS2 *(AI[ROW] + NROW))); \
    PetscCall(PetscArrayzero(new_a + BS2 * (AI[ROW] + NROW), BS2 * CHUNKSIZE)); \
    PetscCall(PetscArraycpy(new_a + BS2 * (AI[ROW] + NROW + CHUNKSIZE), AA + BS2 * (AI[ROW] + NROW), BS2 * len)); \
    /* free up old matrix storage */ \
    PetscCall(MatSeqXAIJFreeAIJ(A, &Ain->a, &Ain->j, &Ain->i)); \
    AA     = new_a; \
    Ain->a = (MatScalar *)new_a; \
    AI = Ain->i = new_i; \
    AJ = Ain->j       = new_j; \
    Ain->singlemalloc = PETSC_TRUE; \
\
    RP   = AJ + AI[ROW]; \
    AP   = AA + BS2 * AI[ROW]; \
    RMAX = AIMAX[ROW] = AIMAX[ROW] + CHUNKSIZE; \
    Ain->maxnz += BS2 * CHUNKSIZE; \
    Ain->reallocs++; \
  }

#define MatSeqXAIJReallocateAIJ_structure_only(Amat, AM, BS2, NROW, ROW, COL, RMAX, AI, AJ, RP, AIMAX, NONEW, datatype) \
  if (NROW >= RMAX) { \
    Mat_SeqAIJ *Ain = (Mat_SeqAIJ *)Amat->data; \
    /* there is no extra room in row, therefore enlarge */ \
    PetscInt CHUNKSIZE = 15, new_nz = AI[AM] + CHUNKSIZE, len, *new_i = NULL, *new_j = NULL; \
\
    PetscCheck(NONEW != -2, PETSC_COMM_SELF, PETSC_ERR_ARG_OUTOFRANGE, "New nonzero at (%" PetscInt_FMT ",%" PetscInt_FMT ") caused a malloc\nUse MatSetOption(A, MAT_NEW_NONZERO_ALLOCATION_ERR, PETSC_FALSE) to turn off this check", ROW, COL); \
    /* malloc new storage space */ \
    PetscCall(PetscMalloc1(new_nz, &new_j)); \
    PetscCall(PetscMalloc1(AM + 1, &new_i)); \
\
    /* copy over old data into new slots */ \
    for (ii = 0; ii < ROW + 1; ii++) new_i[ii] = AI[ii]; \
    for (ii = ROW + 1; ii < AM + 1; ii++) new_i[ii] = AI[ii] + CHUNKSIZE; \
    PetscCall(PetscArraycpy(new_j, AJ, AI[ROW] + NROW)); \
    len = (new_nz - CHUNKSIZE - AI[ROW] - NROW); \
    PetscCall(PetscArraycpy(new_j + AI[ROW] + NROW + CHUNKSIZE, AJ + AI[ROW] + NROW, len)); \
\
    /* free up old matrix storage */ \
    PetscCall(MatSeqXAIJFreeAIJ(A, &Ain->a, &Ain->j, &Ain->i)); \
    Ain->a = NULL; \
    AI = Ain->i = new_i; \
    AJ = Ain->j       = new_j; \
    Ain->singlemalloc = PETSC_FALSE; \
    Ain->free_a       = PETSC_FALSE; \
\
    RP   = AJ + AI[ROW]; \
    RMAX = AIMAX[ROW] = AIMAX[ROW] + CHUNKSIZE; \
    Ain->maxnz += BS2 * CHUNKSIZE; \
    Ain->reallocs++; \
  }

PETSC_INTERN PetscErrorCode MatSeqAIJSetPreallocation_SeqAIJ(Mat, PetscInt, const PetscInt *);
PETSC_INTERN PetscErrorCode MatSetPreallocationCOO_SeqAIJ(Mat, PetscCount, PetscInt[], PetscInt[]);
PETSC_INTERN PetscErrorCode MatResetPreallocationCOO_SeqAIJ(Mat);

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

PETSC_INTERN PetscErrorCode MatICCFactorSymbolic_SeqAIJ(Mat, Mat, IS, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatCholeskyFactorSymbolic_SeqAIJ(Mat, Mat, IS, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ_inplace(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatCholeskyFactorNumeric_SeqAIJ(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatDuplicate_SeqAIJ(Mat, MatDuplicateOption, Mat *);
PETSC_INTERN PetscErrorCode MatCopy_SeqAIJ(Mat, Mat, MatStructure);
PETSC_INTERN PetscErrorCode MatMissingDiagonal_SeqAIJ(Mat, PetscBool *, PetscInt *);
PETSC_INTERN PetscErrorCode MatMarkDiagonal_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatFindZeroDiagonals_SeqAIJ_Private(Mat, PetscInt *, PetscInt **);

PETSC_INTERN PetscErrorCode MatMult_SeqAIJ(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMult_SeqAIJ_Inode(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMultAdd_SeqAIJ(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMultAdd_SeqAIJ_Inode(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMultTranspose_SeqAIJ(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMultTransposeAdd_SeqAIJ(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSOR_SeqAIJ(Mat, Vec, PetscReal, MatSORType, PetscReal, PetscInt, PetscInt, Vec);
PETSC_INTERN PetscErrorCode MatSOR_SeqAIJ_Inode(Mat, Vec, PetscReal, MatSORType, PetscReal, PetscInt, PetscInt, Vec);

PETSC_INTERN PetscErrorCode MatSetOption_SeqAIJ(Mat, MatOption, PetscBool);

PETSC_INTERN PetscErrorCode MatGetSymbolicTranspose_SeqAIJ(Mat, PetscInt *[], PetscInt *[]);
PETSC_INTERN PetscErrorCode MatRestoreSymbolicTranspose_SeqAIJ(Mat, PetscInt *[], PetscInt *[]);
PETSC_INTERN PetscErrorCode MatGetSymbolicTransposeReduced_SeqAIJ(Mat, PetscInt, PetscInt, PetscInt *[], PetscInt *[]);
PETSC_INTERN PetscErrorCode MatTransposeSymbolic_SeqAIJ(Mat, Mat *);
PETSC_INTERN PetscErrorCode MatTranspose_SeqAIJ(Mat, MatReuse, Mat *);

PETSC_INTERN PetscErrorCode MatToSymmetricIJ_SeqAIJ(PetscInt, PetscInt *, PetscInt *, PetscBool, PetscInt, PetscInt, PetscInt **, PetscInt **);
PETSC_INTERN PetscErrorCode MatLUFactorSymbolic_SeqAIJ(Mat, Mat, IS, IS, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_inplace(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatLUFactorNumeric_SeqAIJ_InplaceWithPerm(Mat, Mat, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatLUFactor_SeqAIJ(Mat, IS, IS, const MatFactorInfo *);
PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_inplace(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_Inode(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolve_SeqAIJ_NaturalOrdering(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolveAdd_SeqAIJ(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolveTranspose_SeqAIJ_inplace(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolveTranspose_SeqAIJ(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolveTransposeAdd_SeqAIJ_inplace(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatSolveTransposeAdd_SeqAIJ(Mat, Vec, Vec, Vec);
PETSC_INTERN PetscErrorCode MatMatSolve_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatEqual_SeqAIJ(Mat, Mat, PetscBool *);
PETSC_INTERN PetscErrorCode MatFDColoringCreate_SeqXAIJ(Mat, ISColoring, MatFDColoring);
PETSC_INTERN PetscErrorCode MatFDColoringSetUp_SeqXAIJ(Mat, ISColoring, MatFDColoring);
PETSC_INTERN PetscErrorCode MatFDColoringSetUpBlocked_AIJ_Private(Mat, MatFDColoring, PetscInt);
PETSC_INTERN PetscErrorCode MatLoad_AIJ_HDF5(Mat, PetscViewer);
PETSC_INTERN PetscErrorCode MatLoad_SeqAIJ_Binary(Mat, PetscViewer);
PETSC_INTERN PetscErrorCode MatLoad_SeqAIJ(Mat, PetscViewer);
PETSC_INTERN PetscErrorCode RegisterApplyPtAPRoutines_Private(Mat);

#if defined(PETSC_HAVE_HYPRE)
PETSC_INTERN PetscErrorCode MatProductSetFromOptions_Transpose_AIJ_AIJ(Mat);
#endif
PETSC_INTERN PetscErrorCode MatProductSetFromOptions_SeqAIJ(Mat);

PETSC_INTERN PetscErrorCode MatProductSymbolic_SeqAIJ_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatProductSymbolic_RARt_SeqAIJ_SeqAIJ(Mat);

PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Sorted(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqDense_SeqAIJ(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Scalable_fast(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_Heap(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_BTHeap(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_RowMerge(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_SeqAIJ_SeqAIJ_LLCondensed(Mat, Mat, PetscReal, Mat);
#if defined(PETSC_HAVE_HYPRE)
PETSC_INTERN PetscErrorCode MatMatMultSymbolic_AIJ_AIJ_wHYPRE(Mat, Mat, PetscReal, Mat);
#endif

PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Sorted(Mat, Mat, Mat);

PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqDense_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatMatMultNumeric_SeqAIJ_SeqAIJ_Scalable(Mat, Mat, Mat);

PETSC_INTERN PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqAIJ_SparseAxpy(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqAIJ_SparseAxpy(Mat, Mat, Mat);

PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_matmattransposemult(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatRARtSymbolic_SeqAIJ_SeqAIJ_colorrart(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_matmattransposemult(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatRARtNumeric_SeqAIJ_SeqAIJ_colorrart(Mat, Mat, Mat);

PETSC_INTERN PetscErrorCode MatTransposeMatMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatTransposeMatMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ_MatTransMatMult(void *);

PETSC_INTERN PetscErrorCode MatMatTransposeMultSymbolic_SeqAIJ_SeqAIJ(Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatTransposeMultNumeric_SeqAIJ_SeqAIJ(Mat, Mat, Mat);
PETSC_INTERN PetscErrorCode MatTransposeColoringCreate_SeqAIJ(Mat, ISColoring, MatTransposeColoring);
PETSC_INTERN PetscErrorCode MatTransColoringApplySpToDen_SeqAIJ(MatTransposeColoring, Mat, Mat);
PETSC_INTERN PetscErrorCode MatTransColoringApplyDenToSp_SeqAIJ(MatTransposeColoring, Mat, Mat);

PETSC_INTERN PetscErrorCode MatMatMatMultSymbolic_SeqAIJ_SeqAIJ_SeqAIJ(Mat, Mat, Mat, PetscReal, Mat);
PETSC_INTERN PetscErrorCode MatMatMatMultNumeric_SeqAIJ_SeqAIJ_SeqAIJ(Mat, Mat, Mat, Mat);

PETSC_INTERN PetscErrorCode MatSetRandomSkipColumnRange_SeqAIJ_Private(Mat, PetscInt, PetscInt, PetscRandom);
PETSC_INTERN PetscErrorCode MatSetValues_SeqAIJ(Mat, PetscInt, const PetscInt[], PetscInt, const PetscInt[], const PetscScalar[], InsertMode);
PETSC_INTERN PetscErrorCode MatGetRow_SeqAIJ(Mat, PetscInt, PetscInt *, PetscInt **, PetscScalar **);
PETSC_INTERN PetscErrorCode MatRestoreRow_SeqAIJ(Mat, PetscInt, PetscInt *, PetscInt **, PetscScalar **);
PETSC_INTERN PetscErrorCode MatScale_SeqAIJ(Mat, PetscScalar);
PETSC_INTERN PetscErrorCode MatDiagonalScale_SeqAIJ(Mat, Vec, Vec);
PETSC_INTERN PetscErrorCode MatDiagonalSet_SeqAIJ(Mat, Vec, InsertMode);
PETSC_INTERN PetscErrorCode MatAXPY_SeqAIJ(Mat, PetscScalar, Mat, MatStructure);
PETSC_INTERN PetscErrorCode MatGetRowIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatRestoreRowIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatGetColumnIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatRestoreColumnIJ_SeqAIJ(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatGetColumnIJ_SeqAIJ_Color(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatRestoreColumnIJ_SeqAIJ_Color(Mat, PetscInt, PetscBool, PetscBool, PetscInt *, const PetscInt *[], const PetscInt *[], PetscInt *[], PetscBool *);
PETSC_INTERN PetscErrorCode MatDestroy_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatView_SeqAIJ(Mat, PetscViewer);

PETSC_INTERN PetscErrorCode MatSeqAIJInvalidateDiagonal(Mat);
PETSC_INTERN PetscErrorCode MatSeqAIJInvalidateDiagonal_Inode(Mat);
PETSC_INTERN PetscErrorCode MatSeqAIJCheckInode(Mat);
PETSC_INTERN PetscErrorCode MatSeqAIJCheckInode_FactorLU(Mat);

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

#if defined(PETSC_HAVE_MATLAB)
PETSC_EXTERN PetscErrorCode MatlabEnginePut_SeqAIJ(PetscObject, void *);
PETSC_EXTERN PetscErrorCode MatlabEngineGet_SeqAIJ(PetscObject, void *);
#endif
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqSBAIJ(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqBAIJ(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqDense(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJCRL(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_Elemental(Mat, MatType, MatReuse, Mat *);
#if defined(PETSC_HAVE_SCALAPACK)
PETSC_INTERN PetscErrorCode MatConvert_AIJ_ScaLAPACK(Mat, MatType, MatReuse, Mat *);
#endif
PETSC_INTERN PetscErrorCode MatConvert_AIJ_HYPRE(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJPERM(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJSELL(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJMKL(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJViennaCL(Mat, MatType, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatReorderForNonzeroDiagonal_SeqAIJ(Mat, PetscReal, IS, IS);
PETSC_INTERN PetscErrorCode MatRARt_SeqAIJ_SeqAIJ(Mat, Mat, MatReuse, PetscReal, Mat *);
PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat, MatAssemblyType);
PETSC_EXTERN PetscErrorCode MatZeroEntries_SeqAIJ(Mat);

PETSC_INTERN PetscErrorCode MatAXPYGetPreallocation_SeqX_private(PetscInt, const PetscInt *, const PetscInt *, const PetscInt *, const PetscInt *, PetscInt *);
PETSC_INTERN PetscErrorCode MatCreateMPIMatConcatenateSeqMat_SeqAIJ(MPI_Comm, Mat, PetscInt, MatReuse, Mat *);
PETSC_INTERN PetscErrorCode MatCreateMPIMatConcatenateSeqMat_MPIAIJ(MPI_Comm, Mat, PetscInt, MatReuse, Mat *);

PETSC_INTERN PetscErrorCode MatSetSeqMat_SeqAIJ(Mat, IS, IS, MatStructure, Mat);
PETSC_INTERN PetscErrorCode MatEliminateZeros_SeqAIJ(Mat A);
PETSC_INTERN PetscErrorCode MatDestroySubMatrix_Private(Mat_SubSppt *);
PETSC_INTERN PetscErrorCode MatDestroySubMatrix_SeqAIJ(Mat);
PETSC_INTERN PetscErrorCode MatDestroySubMatrix_Dummy(Mat);
PETSC_INTERN PetscErrorCode MatDestroySubMatrices_Dummy(PetscInt, Mat *[]);
PETSC_INTERN PetscErrorCode MatCreateSubMatrix_SeqAIJ(Mat, IS, IS, PetscInt, MatReuse, Mat *);

PETSC_INTERN PetscErrorCode MatSeqAIJCompactOutExtraColumns_SeqAIJ(Mat, ISLocalToGlobalMapping *);
PETSC_INTERN PetscErrorCode MatSetSeqAIJWithArrays_private(MPI_Comm, PetscInt, PetscInt, PetscInt[], PetscInt[], PetscScalar[], MatType, Mat);

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

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

  Output Parameter:
.  sum - negative the sum of results

  PETSc compile flags:
+   PETSC_KERNEL_USE_UNROLL_4
-   PETSC_KERNEL_USE_UNROLL_2

  Developer Note:
    The macro changes sum but not other parameters

.seealso: `PetscSparseDensePlusDot()`
*/
#if defined(PETSC_KERNEL_USE_UNROLL_4)
  #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    { \
      if (nnz > 0) { \
        PetscInt nnz2 = nnz, rem = nnz & 0x3; \
        switch (rem) { \
        case 3: \
          sum -= *xv++ * r[*xi++]; \
        case 2: \
          sum -= *xv++ * r[*xi++]; \
        case 1: \
          sum -= *xv++ * r[*xi++]; \
          nnz2 -= rem; \
        } \
        while (nnz2 > 0) { \
          sum -= xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
          xv += 4; \
          xi += 4; \
          nnz2 -= 4; \
        } \
        xv -= nnz; \
        xi -= nnz; \
      } \
    }

#elif defined(PETSC_KERNEL_USE_UNROLL_2)
  #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    { \
      PetscInt __i, __i1, __i2; \
      for (__i = 0; __i < nnz - 1; __i += 2) { \
        __i1 = xi[__i]; \
        __i2 = xi[__i + 1]; \
        sum -= (xv[__i] * r[__i1] + xv[__i + 1] * r[__i2]); \
      } \
      if (nnz & 0x1) sum -= xv[__i] * r[xi[__i]]; \
    }

#else
  #define PetscSparseDenseMinusDot(sum, r, xv, xi, nnz) \
    { \
      PetscInt __i; \
      for (__i = 0; __i < nnz; __i++) sum -= xv[__i] * r[xi[__i]]; \
    }
#endif

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

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

  Output Parameter:
.  sum - the sum of results

  PETSc compile flags:
+   PETSC_KERNEL_USE_UNROLL_4
-   PETSC_KERNEL_USE_UNROLL_2

  Developer Note:
    The macro changes sum but not other parameters

.seealso: `PetscSparseDenseMinusDot()`
*/
#if defined(PETSC_KERNEL_USE_UNROLL_4)
  #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    { \
      if (nnz > 0) { \
        PetscInt nnz2 = nnz, rem = nnz & 0x3; \
        switch (rem) { \
        case 3: \
          sum += *xv++ * r[*xi++]; \
        case 2: \
          sum += *xv++ * r[*xi++]; \
        case 1: \
          sum += *xv++ * r[*xi++]; \
          nnz2 -= rem; \
        } \
        while (nnz2 > 0) { \
          sum += xv[0] * r[xi[0]] + xv[1] * r[xi[1]] + xv[2] * r[xi[2]] + xv[3] * r[xi[3]]; \
          xv += 4; \
          xi += 4; \
          nnz2 -= 4; \
        } \
        xv -= nnz; \
        xi -= nnz; \
      } \
    }

#elif defined(PETSC_KERNEL_USE_UNROLL_2)
  #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    { \
      PetscInt __i, __i1, __i2; \
      for (__i = 0; __i < nnz - 1; __i += 2) { \
        __i1 = xi[__i]; \
        __i2 = xi[__i + 1]; \
        sum += (xv[__i] * r[__i1] + xv[__i + 1] * r[__i2]); \
      } \
      if (nnz & 0x1) sum += xv[__i] * r[xi[__i]]; \
    }

#elif 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)
  #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) PetscSparseDensePlusDot_AVX512_Private(&(sum), (r), (xv), (xi), (nnz))

#else
  #define PetscSparseDensePlusDot(sum, r, xv, xi, nnz) \
    { \
      PetscInt __i; \
      for (__i = 0; __i < nnz; __i++) sum += xv[__i] * r[xi[__i]]; \
    }
#endif

#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)
  #include <immintrin.h>
  #if !defined(_MM_SCALE_8)
    #define _MM_SCALE_8 8
  #endif

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

  vec_y = _mm512_setzero_pd();
  for (j = 0; j < (n >> 3); j++) {
    vec_idx  = _mm256_loadu_si256((__m256i const *)aj);
    vec_vals = _mm512_loadu_pd(aa);
    vec_x    = _mm512_i32gather_pd(vec_idx, x, _MM_SCALE_8);
    vec_y    = _mm512_fmadd_pd(vec_x, vec_vals, vec_y);
    aj += 8;
    aa += 8;
  }
  #if defined(__AVX512VL__)
  /* masked load requires avx512vl, which is not supported by KNL */
  if (n & 0x07) {
    __mmask8 mask;
    mask     = (__mmask8)(0xff >> (8 - (n & 0x07)));
    vec_idx  = _mm256_mask_loadu_epi32(vec_idx, mask, aj);
    vec_vals = _mm512_mask_loadu_pd(vec_vals, mask, aa);
    vec_x    = _mm512_mask_i32gather_pd(vec_x, mask, vec_idx, x, _MM_SCALE_8);
    vec_y    = _mm512_mask3_fmadd_pd(vec_x, vec_vals, vec_y, mask);
  }
  *sum += _mm512_reduce_add_pd(vec_y);
  #else
  *sum += _mm512_reduce_add_pd(vec_y);
  for (j = 0; j < (n & 0x07); j++) *sum += aa[j] * x[aj[j]];
  #endif
}
#endif

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

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

  Output Parameter:
.  max - the max of results

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

/*
 Add column indices into table for counting the max nonzeros of merged rows
 */
#define MatRowMergeMax_SeqAIJ(mat, nrows, ta) \
  do { \
    if ((mat)) { \
      for (PetscInt _row = 0; _row < (nrows); _row++) { \
        const PetscInt _nz = (mat)->i[_row + 1] - (mat)->i[_row]; \
        for (PetscInt _j = 0; _j < _nz; _j++) { \
          PetscInt *_col = _j + (mat)->j + (mat)->i[_row]; \
          PetscCall(PetscHMapISet((ta), *_col + 1, 1)); \
        } \
      } \
    } \
  } while (0)

/*
 Add column indices into table for counting the nonzeros of merged rows
 */
#define MatMergeRows_SeqAIJ(mat, nrows, rows, ta) \
  do { \
    for (PetscInt _i = 0; _i < (nrows); _i++) { \
      const PetscInt _row = (rows)[_i]; \
      const PetscInt _nz  = (mat)->i[_row + 1] - (mat)->i[_row]; \
      for (PetscInt _j = 0; _j < _nz; _j++) { \
        PetscInt *_col = _j + (mat)->j + (mat)->i[_row]; \
        PetscCall(PetscHMapISetWithMode((ta), *_col + 1, 1, INSERT_VALUES)); \
      } \
    } \
  } while (0)

#endif