seq/aijmkl/aijmkl.c

/*
  Defines basic operations for the MATSEQAIJMKL matrix class.
  This class is derived from the MATSEQAIJ class and retains the
  compressed row storage (aka Yale sparse matrix format) but uses
  sparse BLAS operations from the Intel Math Kernel Library (MKL)
  wherever possible.
*/

#include <../src/mat/impls/aij/seq/aij.h>
#include <../src/mat/impls/aij/seq/aijmkl/aijmkl.h>

/* MKL include files. */
#include <mkl_spblas.h>  /* Sparse BLAS */

typedef struct {
  PetscBool no_SpMV2;  /* If PETSC_TRUE, then don't use the MKL SpMV2 inspector-executor routines. */
  PetscBool eager_inspection; /* If PETSC_TRUE, then call mkl_sparse_optimize() in MatDuplicate()/MatAssemblyEnd(). */
  PetscBool sparse_optimized; /* If PETSC_TRUE, then mkl_sparse_optimize() has been called. */
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  sparse_matrix_t csrA; /* "Handle" used by SpMV2 inspector-executor routines. */
  struct matrix_descr descr;
#endif
} Mat_SeqAIJMKL;

extern PetscErrorCode MatAssemblyEnd_SeqAIJ(Mat,MatAssemblyType);

PETSC_INTERN PetscErrorCode MatConvert_SeqAIJMKL_SeqAIJ(Mat A,MatType type,MatReuse reuse,Mat *newmat)
{
  /* This routine is only called to convert a MATAIJMKL to its base PETSc type, */
  /* so we will ignore 'MatType type'. */
  PetscErrorCode ierr;
  Mat            B       = *newmat;
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  Mat_SeqAIJMKL  *aijmkl=(Mat_SeqAIJMKL*)A->spptr;
#endif

  PetscFunctionBegin;
  if (reuse == MAT_INITIAL_MATRIX) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
  }

  /* Reset the original function pointers. */
  B->ops->duplicate        = MatDuplicate_SeqAIJ;
  B->ops->assemblyend      = MatAssemblyEnd_SeqAIJ;
  B->ops->destroy          = MatDestroy_SeqAIJ;
  B->ops->mult             = MatMult_SeqAIJ;
  B->ops->multtranspose    = MatMultTranspose_SeqAIJ;
  B->ops->multadd          = MatMultAdd_SeqAIJ;
  B->ops->multtransposeadd = MatMultTransposeAdd_SeqAIJ;
  B->ops->matmult          = MatMatMult_SeqAIJ_SeqAIJ;
  B->ops->scale            = MatScale_SeqAIJ;
  B->ops->diagonalscale    = MatDiagonalScale_SeqAIJ;
  B->ops->diagonalset      = MatDiagonalSet_SeqAIJ;
  B->ops->axpy             = MatAXPY_SeqAIJ;

  ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaijmkl_seqaij_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaijmkl_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaijmkl_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaijmkl_C",NULL);CHKERRQ(ierr);
  if(!aijmkl->no_SpMV2) {
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
    ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqaijmkl_seqaijmkl_C",NULL);CHKERRQ(ierr);
#endif
  }

  /* Free everything in the Mat_SeqAIJMKL data structure. Currently, this
   * simply involves destroying the MKL sparse matrix handle and then freeing
   * the spptr pointer. */
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  if (reuse == MAT_INITIAL_MATRIX) aijmkl = (Mat_SeqAIJMKL*)B->spptr;

  if (aijmkl->sparse_optimized) {
    sparse_status_t stat;
    stat = mkl_sparse_destroy(aijmkl->csrA);
    if (stat != SPARSE_STATUS_SUCCESS) {
      PetscFunctionReturn(PETSC_ERR_LIB);
    }
  }
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */
  ierr = PetscFree(B->spptr);CHKERRQ(ierr);

  /* Change the type of B to MATSEQAIJ. */
  ierr = PetscObjectChangeTypeName((PetscObject)B, MATSEQAIJ);CHKERRQ(ierr);

  *newmat = B;
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroy_SeqAIJMKL(Mat A)
{
  PetscErrorCode ierr;
  Mat_SeqAIJMKL *aijmkl = (Mat_SeqAIJMKL*) A->spptr;

  PetscFunctionBegin;

  /* If MatHeaderMerge() was used, then this SeqAIJMKL matrix will not have an
   * spptr pointer. */
  if (aijmkl) {
    /* Clean up everything in the Mat_SeqAIJMKL data structure, then free A->spptr. */
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
    if (aijmkl->sparse_optimized) {
      sparse_status_t stat = SPARSE_STATUS_SUCCESS;
      stat = mkl_sparse_destroy(aijmkl->csrA);
      if (stat != SPARSE_STATUS_SUCCESS) {
        PetscFunctionReturn(PETSC_ERR_LIB);
      }
    }
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */
    ierr = PetscFree(A->spptr);CHKERRQ(ierr);
  }

  /* Change the type of A back to SEQAIJ and use MatDestroy_SeqAIJ()
   * to destroy everything that remains. */
  ierr = PetscObjectChangeTypeName((PetscObject)A, MATSEQAIJ);CHKERRQ(ierr);
  /* Note that I don't call MatSetType().  I believe this is because that
   * is only to be called when *building* a matrix.  I could be wrong, but
   * that is how things work for the SuperLU matrix class. */
  ierr = MatDestroy_SeqAIJ(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* MatSeqAIJKL_create_mkl_handle(), if called with an AIJMKL matrix that has not had mkl_sparse_optimize() called for it,
 * creates an MKL sparse matrix handle from the AIJ arrays and calls mkl_sparse_optimize().
 * If called with an AIJMKL matrix for which aijmkl->sparse_optimized == PETSC_TRUE, then it destroys the old matrix
 * handle, creates a new one, and then calls mkl_sparse_optimize().
 * Although in normal MKL usage it is possible to have a valid matrix handle on which mkl_sparse_optimize() has not been
 * called, for AIJMKL the handle creation and optimization step always occur together, so we don't handle the case of
 * an unoptimized matrix handle here. */
PETSC_INTERN PetscErrorCode MatSeqAIJMKL_create_mkl_handle(Mat A)
{
#ifndef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  /* If the MKL library does not have mkl_sparse_optimize(), then this routine
   * does nothing. We make it callable anyway in this case because it cuts
   * down on littering the code with #ifdefs. */
  PetscFunctionBegin;
  PetscFunctionReturn(0);
#else
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL   *aijmkl = (Mat_SeqAIJMKL*)A->spptr;
  PetscInt        m,n;
  MatScalar       *aa;
  PetscInt        *aj,*ai;
  sparse_status_t stat;

  PetscFunctionBegin;
  if (aijmkl->no_SpMV2) PetscFunctionReturn(0);

  if (aijmkl->sparse_optimized) {
    /* Matrix has been previously assembled and optimized. Must destroy old
     * matrix handle before running the optimization step again. */
    stat = mkl_sparse_destroy(aijmkl->csrA);
    if (stat != SPARSE_STATUS_SUCCESS) {
      PetscFunctionReturn(PETSC_ERR_LIB);
    }
  }
  aijmkl->sparse_optimized = PETSC_FALSE;

  /* Now perform the SpMV2 setup and matrix optimization. */
  aijmkl->descr.type        = SPARSE_MATRIX_TYPE_GENERAL;
  aijmkl->descr.mode        = SPARSE_FILL_MODE_LOWER;
  aijmkl->descr.diag        = SPARSE_DIAG_NON_UNIT;
  m = A->rmap->n;
  n = A->cmap->n;
  aj   = a->j;  /* aj[k] gives column index for element aa[k]. */
  aa   = a->a;  /* Nonzero elements stored row-by-row. */
  ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */
  if ((a->nz!=0) & !(A->structure_only)) {
    /* Create a new, optimized sparse matrix handle only if the matrix has nonzero entries.
     * The MKL sparse-inspector executor routines don't like being passed an empty matrix. */
    stat = mkl_sparse_x_create_csr(&aijmkl->csrA,SPARSE_INDEX_BASE_ZERO,m,n,ai,ai+1,aj,aa);
    stat = mkl_sparse_set_mv_hint(aijmkl->csrA,SPARSE_OPERATION_NON_TRANSPOSE,aijmkl->descr,1000);
    stat = mkl_sparse_set_memory_hint(aijmkl->csrA,SPARSE_MEMORY_AGGRESSIVE);
    stat = mkl_sparse_optimize(aijmkl->csrA);
    if (stat != SPARSE_STATUS_SUCCESS) {
      SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Intel MKL error: unable to create matrix handle/complete mkl_sparse_optimize");
      PetscFunctionReturn(PETSC_ERR_LIB);
    }
    aijmkl->sparse_optimized = PETSC_TRUE;
  }

  PetscFunctionReturn(0);
#endif
}

/* MatSeqAIJMKL_create_from_mkl_handle() creates a sequential AIJMKL matrix from an MKL sparse matrix handle.
 * We need this to implement MatMatMult() using the MKL inspector-executor routines, which return an (unoptimized)
 * matrix handle. */
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PETSC_INTERN PetscErrorCode MatSeqAIJMKL_create_from_mkl_handle(MPI_Comm comm,sparse_matrix_t csrA,Mat *mat)
{
  PetscErrorCode ierr;
  sparse_status_t stat;
  sparse_index_base_t indexing;
  PetscInt nrows, ncols;
  PetscInt *aj,*ai,*dummy;
  MatScalar *aa;
  Mat A;
  Mat_SeqAIJMKL *aijmkl;

  /* Note: Must pass in &dummy below since MKL can't accept NULL for this output array we don't actually want. */
  stat = mkl_sparse_x_export_csr(csrA,&indexing,&nrows,&ncols,&ai,&dummy,&aj,&aa);
  if (stat != SPARSE_STATUS_SUCCESS) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Intel MKL error: unable to complete mkl_sparse_x_export_csr()");
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  ierr = MatCreate(comm,&A);CHKERRQ(ierr);
  ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
  ierr = MatSetSizes(A,PETSC_DECIDE,PETSC_DECIDE,nrows,ncols);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocationCSR(A,ai,aj,aa);CHKERRQ(ierr);

  /* We now have an assembled sequential AIJ matrix created from copies of the exported arrays from the MKL matrix handle.
   * Now turn it into a MATSEQAIJMKL. */
  ierr = MatConvert_SeqAIJ_SeqAIJMKL(A,MATSEQAIJMKL,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
  aijmkl = (Mat_SeqAIJMKL*) A->spptr;
  aijmkl->csrA = csrA;
  /* The below code duplicates much of what is in MatSeqAIJKL_create_mkl_handle(). I dislike this code duplication, but
   * MatSeqAIJMKL_create_mkl_handle() cannot be used because we don't need to create a handle -- we've already got one,
   * and just need to be able to run the MKL optimization step. */
  stat = mkl_sparse_set_mv_hint(aijmkl->csrA,SPARSE_OPERATION_NON_TRANSPOSE,aijmkl->descr,1000);
  stat = mkl_sparse_set_memory_hint(aijmkl->csrA,SPARSE_MEMORY_AGGRESSIVE);
  stat = mkl_sparse_optimize(aijmkl->csrA);
  if (stat != SPARSE_STATUS_SUCCESS) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Intel MKL error: unable to set hints/complete mkl_sparse_optimize");
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  aijmkl->sparse_optimized = PETSC_TRUE;

  *mat = A;
  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

PetscErrorCode MatDuplicate_SeqAIJMKL(Mat A, MatDuplicateOption op, Mat *M)
{
  PetscErrorCode ierr;
  Mat_SeqAIJMKL *aijmkl;
  Mat_SeqAIJMKL *aijmkl_dest;

  PetscFunctionBegin;
  ierr = MatDuplicate_SeqAIJ(A,op,M);CHKERRQ(ierr);
  aijmkl      = (Mat_SeqAIJMKL*) A->spptr;
  aijmkl_dest = (Mat_SeqAIJMKL*) (*M)->spptr;
  ierr = PetscMemcpy(aijmkl_dest,aijmkl,sizeof(Mat_SeqAIJMKL));CHKERRQ(ierr);
  aijmkl_dest->sparse_optimized = PETSC_FALSE;
  if (aijmkl->eager_inspection) {
    ierr = MatSeqAIJMKL_create_mkl_handle(A);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatAssemblyEnd_SeqAIJMKL(Mat A, MatAssemblyType mode)
{
  PetscErrorCode  ierr;
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL *aijmkl;

  PetscFunctionBegin;
  if (mode == MAT_FLUSH_ASSEMBLY) PetscFunctionReturn(0);

  /* Since a MATSEQAIJMKL matrix is really just a MATSEQAIJ with some
   * extra information and some different methods, call the AssemblyEnd
   * routine for a MATSEQAIJ.
   * I'm not sure if this is the best way to do this, but it avoids
   * a lot of code duplication. */
  a->inode.use = PETSC_FALSE;  /* Must disable: otherwise the MKL routines won't get used. */
  ierr = MatAssemblyEnd_SeqAIJ(A, mode);CHKERRQ(ierr);

  /* If the user has requested "eager" inspection, create the optimized MKL sparse handle (if needed; the function checks).
   * (The default is to do "lazy" inspection, deferring this until something like MatMult() is called.) */
  aijmkl = (Mat_SeqAIJMKL*) A->spptr;
  if (aijmkl->eager_inspection) {
    ierr = MatSeqAIJMKL_create_mkl_handle(A);CHKERRQ(ierr);
  }

  PetscFunctionReturn(0);
}

PetscErrorCode MatMult_SeqAIJMKL(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *x;
  PetscScalar       *y;
  const MatScalar   *aa;
  PetscErrorCode    ierr;
  PetscInt          m=A->rmap->n;
  PetscInt          n=A->cmap->n;
  PetscScalar       alpha = 1.0;
  PetscScalar       beta = 0.0;
  const PetscInt    *aj,*ai;
  char              matdescra[6];


  /* Variables not in MatMult_SeqAIJ. */
  char transa = 'n';  /* Used to indicate to MKL that we are not computing the transpose product. */

  PetscFunctionBegin;
  matdescra[0] = 'g';  /* Indicates to MKL that we using a general CSR matrix. */
  matdescra[3] = 'c';  /* Indicates to MKL that we use C-style (0-based) indexing. */
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  aj   = a->j;  /* aj[k] gives column index for element aa[k]. */
  aa   = a->a;  /* Nonzero elements stored row-by-row. */
  ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */

  /* Call MKL sparse BLAS routine to do the MatMult. */
  mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,y);

  ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PetscErrorCode MatMult_SeqAIJMKL_SpMV2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL     *aijmkl=(Mat_SeqAIJMKL*)A->spptr;
  const PetscScalar *x;
  PetscScalar       *y;
  PetscErrorCode    ierr;
  sparse_status_t stat = SPARSE_STATUS_SUCCESS;

  PetscFunctionBegin;

  /* If there are no nonzero entries, zero yy and return immediately. */
  if(!a->nz) {
    PetscInt i;
    PetscInt m=A->rmap->n;
    ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      y[i] = 0.0;
    }
    ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  /* In some cases, we get to this point without mkl_sparse_optimize() having been called, so we check and then call
   * it if needed. Eventually, when everything in PETSc is properly updating the matrix state, we should probably
   * take a "lazy" approach to creation/updating of the MKL matrix handle and plan to always do it here (when needed). */
  if (!aijmkl->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(A);
  }

  /* Call MKL SpMV2 executor routine to do the MatMult. */
  stat = mkl_sparse_x_mv(SPARSE_OPERATION_NON_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,0.0,y);

  ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  if (stat != SPARSE_STATUS_SUCCESS) {
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

PetscErrorCode MatMultTranspose_SeqAIJMKL(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *x;
  PetscScalar       *y;
  const MatScalar   *aa;
  PetscErrorCode    ierr;
  PetscInt          m=A->rmap->n;
  PetscInt          n=A->cmap->n;
  PetscScalar       alpha = 1.0;
  PetscScalar       beta = 0.0;
  const PetscInt    *aj,*ai;
  char              matdescra[6];

  /* Variables not in MatMultTranspose_SeqAIJ. */
  char transa = 't';  /* Used to indicate to MKL that we are computing the transpose product. */

  PetscFunctionBegin;
  matdescra[0] = 'g';  /* Indicates to MKL that we using a general CSR matrix. */
  matdescra[3] = 'c';  /* Indicates to MKL that we use C-style (0-based) indexing. */
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  aj   = a->j;  /* aj[k] gives column index for element aa[k]. */
  aa   = a->a;  /* Nonzero elements stored row-by-row. */
  ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */

  /* Call MKL sparse BLAS routine to do the MatMult. */
  mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,y);

  ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PetscErrorCode MatMultTranspose_SeqAIJMKL_SpMV2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL     *aijmkl=(Mat_SeqAIJMKL*)A->spptr;
  const PetscScalar *x;
  PetscScalar       *y;
  PetscErrorCode    ierr;
  sparse_status_t   stat;

  PetscFunctionBegin;

  /* If there are no nonzero entries, zero yy and return immediately. */
  if(!a->nz) {
    PetscInt i;
    PetscInt n=A->cmap->n;
    ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      y[i] = 0.0;
    }
    ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  /* In some cases, we get to this point without mkl_sparse_optimize() having been called, so we check and then call
   * it if needed. Eventually, when everything in PETSc is properly updating the matrix state, we should probably
   * take a "lazy" approach to creation/updating of the MKL matrix handle and plan to always do it here (when needed). */
  if (!aijmkl->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(A);
  }

  /* Call MKL SpMV2 executor routine to do the MatMultTranspose. */
  stat = mkl_sparse_x_mv(SPARSE_OPERATION_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,0.0,y);

  ierr = PetscLogFlops(2.0*a->nz - a->nonzerorowcnt);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  if (stat != SPARSE_STATUS_SUCCESS) {
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

PetscErrorCode MatMultAdd_SeqAIJMKL(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *x;
  PetscScalar       *y,*z;
  const MatScalar   *aa;
  PetscErrorCode    ierr;
  PetscInt          m=A->rmap->n;
  PetscInt          n=A->cmap->n;
  const PetscInt    *aj,*ai;
  PetscInt          i;

  /* Variables not in MatMultAdd_SeqAIJ. */
  char transa = 'n';  /* Used to indicate to MKL that we are not computing the transpose product. */
  PetscScalar       alpha = 1.0;
  PetscScalar       beta;
  char              matdescra[6];

  PetscFunctionBegin;
  matdescra[0] = 'g';  /* Indicates to MKL that we using a general CSR matrix. */
  matdescra[3] = 'c';  /* Indicates to MKL that we use C-style (0-based) indexing. */

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  aj   = a->j;  /* aj[k] gives column index for element aa[k]. */
  aa   = a->a;  /* Nonzero elements stored row-by-row. */
  ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */

  /* Call MKL sparse BLAS routine to do the MatMult. */
  if (zz == yy) {
    /* If zz and yy are the same vector, we can use MKL's mkl_xcsrmv(), which calculates y = alpha*A*x + beta*y. */
    beta = 1.0;
    mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,z);
  } else {
    /* zz and yy are different vectors, so call MKL's mkl_xcsrmv() with beta=0, then add the result to z.
     * MKL sparse BLAS does not have a MatMultAdd equivalent. */
    beta = 0.0;
    mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,z);
    for (i=0; i<m; i++) {
      z[i] += y[i];
    }
  }

  ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PetscErrorCode MatMultAdd_SeqAIJMKL_SpMV2(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL     *aijmkl=(Mat_SeqAIJMKL*)A->spptr;
  const PetscScalar *x;
  PetscScalar       *y,*z;
  PetscErrorCode    ierr;
  PetscInt          m=A->rmap->n;
  PetscInt          i;

  /* Variables not in MatMultAdd_SeqAIJ. */
  sparse_status_t stat = SPARSE_STATUS_SUCCESS;

  PetscFunctionBegin;

  /* If there are no nonzero entries, set zz = yy and return immediately. */
  if(!a->nz) {
    PetscInt i;
    ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
    for (i=0; i<m; i++) {
      z[i] = y[i];
    }
    ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);

  /* In some cases, we get to this point without mkl_sparse_optimize() having been called, so we check and then call
   * it if needed. Eventually, when everything in PETSc is properly updating the matrix state, we should probably
   * take a "lazy" approach to creation/updating of the MKL matrix handle and plan to always do it here (when needed). */
  if (!aijmkl->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(A);
  }

  /* Call MKL sparse BLAS routine to do the MatMult. */
  if (zz == yy) {
    /* If zz and yy are the same vector, we can use mkl_sparse_x_mv, which calculates y = alpha*A*x + beta*y,
     * with alpha and beta both set to 1.0. */
    stat = mkl_sparse_x_mv(SPARSE_OPERATION_NON_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,1.0,z);
  } else {
    /* zz and yy are different vectors, so we call mkl_sparse_x_mv with alpha=1.0 and beta=0.0, and then
     * we add the contents of vector yy to the result; MKL sparse BLAS does not have a MatMultAdd equivalent. */
    stat = mkl_sparse_x_mv(SPARSE_OPERATION_NON_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,0.0,z);
    for (i=0; i<m; i++) {
      z[i] += y[i];
    }
  }

  ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  if (stat != SPARSE_STATUS_SUCCESS) {
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

PetscErrorCode MatMultTransposeAdd_SeqAIJMKL(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  const PetscScalar *x;
  PetscScalar       *y,*z;
  const MatScalar   *aa;
  PetscErrorCode    ierr;
  PetscInt          m=A->rmap->n;
  PetscInt          n=A->cmap->n;
  const PetscInt    *aj,*ai;
  PetscInt          i;

  /* Variables not in MatMultTransposeAdd_SeqAIJ. */
  char transa = 't';  /* Used to indicate to MKL that we are computing the transpose product. */
  PetscScalar       alpha = 1.0;
  PetscScalar       beta;
  char              matdescra[6];

  PetscFunctionBegin;
  matdescra[0] = 'g';  /* Indicates to MKL that we using a general CSR matrix. */
  matdescra[3] = 'c';  /* Indicates to MKL that we use C-style (0-based) indexing. */

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  aj   = a->j;  /* aj[k] gives column index for element aa[k]. */
  aa   = a->a;  /* Nonzero elements stored row-by-row. */
  ai   = a->i;  /* ai[k] is the position in aa and aj where row k starts. */

  /* Call MKL sparse BLAS routine to do the MatMult. */
  if (zz == yy) {
    /* If zz and yy are the same vector, we can use MKL's mkl_xcsrmv(), which calculates y = alpha*A*x + beta*y. */
    beta = 1.0;
    mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,z);
  } else {
    /* zz and yy are different vectors, so call MKL's mkl_xcsrmv() with beta=0, then add the result to z.
     * MKL sparse BLAS does not have a MatMultAdd equivalent. */
    beta = 0.0;
    mkl_xcsrmv(&transa,&m,&n,&alpha,matdescra,aa,aj,ai,ai+1,x,&beta,z);
    for (i=0; i<n; i++) {
      z[i] += y[i];
    }
  }

  ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PetscErrorCode MatMultTransposeAdd_SeqAIJMKL_SpMV2(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)A->data;
  Mat_SeqAIJMKL     *aijmkl=(Mat_SeqAIJMKL*)A->spptr;
  const PetscScalar *x;
  PetscScalar       *y,*z;
  PetscErrorCode    ierr;
  PetscInt          n=A->cmap->n;
  PetscInt          i;

  /* Variables not in MatMultTransposeAdd_SeqAIJ. */
  sparse_status_t stat = SPARSE_STATUS_SUCCESS;

  PetscFunctionBegin;

  /* If there are no nonzero entries, set zz = yy and return immediately. */
  if(!a->nz) {
    PetscInt i;
    ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
    for (i=0; i<n; i++) {
      z[i] = y[i];
    }
    ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }

  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);

  /* In some cases, we get to this point without mkl_sparse_optimize() having been called, so we check and then call
   * it if needed. Eventually, when everything in PETSc is properly updating the matrix state, we should probably
   * take a "lazy" approach to creation/updating of the MKL matrix handle and plan to always do it here (when needed). */
  if (!aijmkl->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(A);
  }

  /* Call MKL sparse BLAS routine to do the MatMult. */
  if (zz == yy) {
    /* If zz and yy are the same vector, we can use mkl_sparse_x_mv, which calculates y = alpha*A*x + beta*y,
     * with alpha and beta both set to 1.0. */
    stat = mkl_sparse_x_mv(SPARSE_OPERATION_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,1.0,z);
  } else {
    /* zz and yy are different vectors, so we call mkl_sparse_x_mv with alpha=1.0 and beta=0.0, and then
     * we add the contents of vector yy to the result; MKL sparse BLAS does not have a MatMultAdd equivalent. */
    stat = mkl_sparse_x_mv(SPARSE_OPERATION_TRANSPOSE,1.0,aijmkl->csrA,aijmkl->descr,x,0.0,z);
    for (i=0; i<n; i++) {
      z[i] += y[i];
    }
  }

  ierr = PetscLogFlops(2.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayPair(yy,zz,&y,&z);CHKERRQ(ierr);
  if (stat != SPARSE_STATUS_SUCCESS) {
    PetscFunctionReturn(PETSC_ERR_LIB);
  }
  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
PetscErrorCode MatMatMult_SeqAIJMKL_SeqAIJMKL_SpMV2(Mat A,Mat B,MatReuse scall,PetscReal fill,Mat*C)
{
  Mat_SeqAIJMKL *a, *b;
  sparse_matrix_t csrA, csrB, csrC;
  PetscErrorCode ierr;
  sparse_status_t stat = SPARSE_STATUS_SUCCESS;

  PetscFunctionBegin;
  a = (Mat_SeqAIJMKL*)A->spptr;
  b = (Mat_SeqAIJMKL*)B->spptr;
  if (!a->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(A);
  }
  if (!b->sparse_optimized) {
    MatSeqAIJMKL_create_mkl_handle(B);
  }
  csrA = a->csrA;
  csrB = b->csrA;

  stat = mkl_sparse_spmm(SPARSE_OPERATION_NON_TRANSPOSE,csrA,csrB,&csrC);
  if (stat != SPARSE_STATUS_SUCCESS) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_LIB,"Intel MKL error: unable to complete sparse matrix-matrix multiply");
    PetscFunctionReturn(PETSC_ERR_LIB);
  }

  /* TODO: Make this handle MAT_REUSE_MATRIX sensibly; MKL has no notion of this, but we still need to do the right thing. */
  ierr = MatSeqAIJMKL_create_from_mkl_handle(PETSC_COMM_SELF,csrC,C);CHKERRQ(ierr);

  PetscFunctionReturn(0);
}
#endif /* PETSC_HAVE_MKL_SPARSE_OPTIMIZE */

PetscErrorCode MatScale_SeqAIJMKL(Mat inA,PetscScalar alpha)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatScale_SeqAIJ(inA,alpha);CHKERRQ(ierr);
  ierr = MatSeqAIJMKL_create_mkl_handle(inA);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDiagonalScale_SeqAIJMKL(Mat A,Vec ll,Vec rr)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatDiagonalScale_SeqAIJ(A,ll,rr);CHKERRQ(ierr);
  ierr = MatSeqAIJMKL_create_mkl_handle(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDiagonalSet_SeqAIJMKL(Mat Y,Vec D,InsertMode is)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatDiagonalSet_SeqAIJ(Y,D,is);CHKERRQ(ierr);
  ierr = MatSeqAIJMKL_create_mkl_handle(Y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatAXPY_SeqAIJMKL(Mat Y,PetscScalar a,Mat X,MatStructure str)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatAXPY_SeqAIJ(Y,a,X,str);CHKERRQ(ierr);
  if (str == SAME_NONZERO_PATTERN) {
    /* MatAssemblyEnd() is not called if SAME_NONZERO_PATTERN, so we need to force update of the MKL matrix handle. */
    ierr = MatSeqAIJMKL_create_mkl_handle(Y);CHKERRQ(ierr);
  }
  PetscFunctionReturn(0);
}

/* MatConvert_SeqAIJ_SeqAIJMKL converts a SeqAIJ matrix into a
 * SeqAIJMKL matrix.  This routine is called by the MatCreate_SeqMKLAIJ()
 * routine, but can also be used to convert an assembled SeqAIJ matrix
 * into a SeqAIJMKL one. */
PETSC_INTERN PetscErrorCode MatConvert_SeqAIJ_SeqAIJMKL(Mat A,MatType type,MatReuse reuse,Mat *newmat)
{
  PetscErrorCode ierr;
  Mat            B = *newmat;
  Mat_SeqAIJMKL  *aijmkl;
  PetscBool      set;
  PetscBool      sametype;

  PetscFunctionBegin;
  if (reuse == MAT_INITIAL_MATRIX) {
    ierr = MatDuplicate(A,MAT_COPY_VALUES,&B);CHKERRQ(ierr);
  }

  ierr = PetscObjectTypeCompare((PetscObject)A,type,&sametype);CHKERRQ(ierr);
  if (sametype) PetscFunctionReturn(0);

  ierr     = PetscNewLog(B,&aijmkl);CHKERRQ(ierr);
  B->spptr = (void*) aijmkl;

  /* Set function pointers for methods that we inherit from AIJ but override.
   * We also parse some command line options below, since those determine some of the methods we point to. */
  B->ops->duplicate        = MatDuplicate_SeqAIJMKL;
  B->ops->assemblyend      = MatAssemblyEnd_SeqAIJMKL;
  B->ops->destroy          = MatDestroy_SeqAIJMKL;

  aijmkl->sparse_optimized = PETSC_FALSE;
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  aijmkl->no_SpMV2 = PETSC_FALSE;  /* Default to using the SpMV2 routines if our MKL supports them. */
#else
  aijmkl->no_SpMV2 = PETSC_TRUE;
#endif
  aijmkl->eager_inspection = PETSC_FALSE;

  /* Parse command line options. */
  ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)A),((PetscObject)A)->prefix,"AIJMKL Options","Mat");CHKERRQ(ierr);
  ierr = PetscOptionsBool("-mat_aijmkl_no_spmv2","NoSPMV2","None",(PetscBool)aijmkl->no_SpMV2,(PetscBool*)&aijmkl->no_SpMV2,&set);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-mat_aijmkl_eager_inspection","Eager Inspection","None",(PetscBool)aijmkl->eager_inspection,(PetscBool*)&aijmkl->eager_inspection,&set);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();CHKERRQ(ierr);
#ifndef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
  if(!aijmkl->no_SpMV2) {
    ierr = PetscInfo(B,"User requested use of MKL SpMV2 routines, but MKL version does not support mkl_sparse_optimize();  defaulting to non-SpMV2 routines.\n");
    aijmkl->no_SpMV2 = PETSC_TRUE;
  }
#endif

  if(!aijmkl->no_SpMV2) {
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
    B->ops->mult             = MatMult_SeqAIJMKL_SpMV2;
    B->ops->multtranspose    = MatMultTranspose_SeqAIJMKL_SpMV2;
    B->ops->multadd          = MatMultAdd_SeqAIJMKL_SpMV2;
    B->ops->multtransposeadd = MatMultTransposeAdd_SeqAIJMKL_SpMV2;
    B->ops->matmult          = MatMatMult_SeqAIJMKL_SeqAIJMKL_SpMV2;
#endif
  } else {
    B->ops->mult             = MatMult_SeqAIJMKL;
    B->ops->multtranspose    = MatMultTranspose_SeqAIJMKL;
    B->ops->multadd          = MatMultAdd_SeqAIJMKL;
    B->ops->multtransposeadd = MatMultTransposeAdd_SeqAIJMKL;
  }

  B->ops->scale              = MatScale_SeqAIJMKL;
  B->ops->diagonalscale      = MatDiagonalScale_SeqAIJMKL;
  B->ops->diagonalset        = MatDiagonalSet_SeqAIJMKL;
  B->ops->axpy               = MatAXPY_SeqAIJMKL;

  ierr = PetscObjectComposeFunction((PetscObject)B,"MatScale_SeqAIJMKL_C",MatScale_SeqAIJMKL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqaijmkl_seqaij_C",MatConvert_SeqAIJMKL_SeqAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqdense_seqaijmkl_C",MatMatMult_SeqDense_SeqAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultSymbolic_seqdense_seqaijmkl_C",MatMatMultSymbolic_SeqDense_SeqAIJ);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMultNumeric_seqdense_seqaijmkl_C",MatMatMultNumeric_SeqDense_SeqAIJ);CHKERRQ(ierr);
  if(!aijmkl->no_SpMV2) {
#ifdef PETSC_HAVE_MKL_SPARSE_OPTIMIZE
    ierr = PetscObjectComposeFunction((PetscObject)B,"MatMatMult_seqaijmkl_seqaijmkl_C",MatMatMult_SeqAIJMKL_SeqAIJMKL_SpMV2);CHKERRQ(ierr);
#endif
  }

  ierr    = PetscObjectChangeTypeName((PetscObject)B,MATSEQAIJMKL);CHKERRQ(ierr);
  *newmat = B;
  PetscFunctionReturn(0);
}

/*@C
   MatCreateSeqAIJMKL - Creates a sparse matrix of type SEQAIJMKL.
   This type inherits from AIJ and is largely identical, but uses sparse BLAS
   routines from Intel MKL whenever possible.
   MatMult, MatMultAdd, MatMultTranspose, and MatMultTransposeAdd
   operations are currently supported.
   If the installed version of MKL supports the "SpMV2" sparse
   inspector-executor routines, then those are used by default.

   Collective on MPI_Comm

   Input Parameters:
+  comm - MPI communicator, set to PETSC_COMM_SELF
.  m - number of rows
.  n - number of columns
.  nz - number of nonzeros per row (same for all rows)
-  nnz - array containing the number of nonzeros in the various rows
         (possibly different for each row) or NULL

   Output Parameter:
.  A - the matrix

   Options Database Keys:
.  -mat_aijmkl_no_spmv2 - disables use of the SpMV2 inspector-executor routines

   Notes:
   If nnz is given then nz is ignored

   Level: intermediate

.keywords: matrix, MKL, sparse, parallel

.seealso: MatCreate(), MatCreateMPIAIJMKL(), MatSetValues()
@*/
PetscErrorCode  MatCreateSeqAIJMKL(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt nz,const PetscInt nnz[],Mat *A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate(comm,A);CHKERRQ(ierr);
  ierr = MatSetSizes(*A,m,n,m,n);CHKERRQ(ierr);
  ierr = MatSetType(*A,MATSEQAIJMKL);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation_SeqAIJ(*A,nz,nnz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_EXTERN PetscErrorCode MatCreate_SeqAIJMKL(Mat A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatSetType(A,MATSEQAIJ);CHKERRQ(ierr);
  ierr = MatConvert_SeqAIJ_SeqAIJMKL(A,MATSEQAIJMKL,MAT_INPLACE_MATRIX,&A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}