xref: /petsc/src/mat/impls/maij/maij.c (revision d8d19677bbccf95218448bee62e6b87f4513e133)

/*
    Defines the basic matrix operations for the MAIJ  matrix storage format.
  This format is used for restriction and interpolation operations for
  multicomponent problems. It interpolates each component the same way
  independently.

     We provide:
         MatMult()
         MatMultTranspose()
         MatMultTransposeAdd()
         MatMultAdd()
          and
         MatCreateMAIJ(Mat,dof,Mat*)

     This single directory handles both the sequential and parallel codes
*/

#include <../src/mat/impls/maij/maij.h> /*I "petscmat.h" I*/
#include <../src/mat/utils/freespace.h>

/*@
   MatMAIJGetAIJ - Get the AIJ matrix describing the blockwise action of the MAIJ matrix

   Not Collective, but if the MAIJ matrix is parallel, the AIJ matrix is also parallel

   Input Parameter:
.  A - the MAIJ matrix

   Output Parameter:
.  B - the AIJ matrix

   Level: advanced

   Notes:
    The reference count on the AIJ matrix is not increased so you should not destroy it.

.seealso: MatCreateMAIJ()
@*/
PetscErrorCode  MatMAIJGetAIJ(Mat A,Mat *B)
{
  PetscErrorCode ierr;
  PetscBool      ismpimaij,isseqmaij;

  PetscFunctionBegin;
  ierr = PetscObjectTypeCompare((PetscObject)A,MATMPIMAIJ,&ismpimaij);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)A,MATSEQMAIJ,&isseqmaij);CHKERRQ(ierr);
  if (ismpimaij) {
    Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;

    *B = b->A;
  } else if (isseqmaij) {
    Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;

    *B = b->AIJ;
  } else {
    *B = A;
  }
  PetscFunctionReturn(0);
}

/*@
   MatMAIJRedimension - Get an MAIJ matrix with the same action, but for a different block size

   Logically Collective

   Input Parameters:
+  A - the MAIJ matrix
-  dof - the block size for the new matrix

   Output Parameter:
.  B - the new MAIJ matrix

   Level: advanced

.seealso: MatCreateMAIJ()
@*/
PetscErrorCode  MatMAIJRedimension(Mat A,PetscInt dof,Mat *B)
{
  PetscErrorCode ierr;
  Mat            Aij = NULL;

  PetscFunctionBegin;
  PetscValidLogicalCollectiveInt(A,dof,2);
  ierr = MatMAIJGetAIJ(A,&Aij);CHKERRQ(ierr);
  ierr = MatCreateMAIJ(Aij,dof,B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroy_SeqMAIJ(Mat A)
{
  PetscErrorCode ierr;
  Mat_SeqMAIJ    *b = (Mat_SeqMAIJ*)A->data;

  PetscFunctionBegin;
  ierr = MatDestroy(&b->AIJ);CHKERRQ(ierr);
  ierr = PetscFree(A->data);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_seqmaij_seqaij_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_seqaij_seqmaij_C",NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatSetUp_MAIJ(Mat A)
{
  PetscFunctionBegin;
  SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"Must use MatCreateMAIJ() to create MAIJ matrices");
}

PetscErrorCode MatView_SeqMAIJ(Mat A,PetscViewer viewer)
{
  PetscErrorCode ierr;
  Mat            B;

  PetscFunctionBegin;
  ierr = MatConvert(A,MATSEQAIJ,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
  ierr = MatView(B,viewer);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatView_MPIMAIJ(Mat A,PetscViewer viewer)
{
  PetscErrorCode ierr;
  Mat            B;

  PetscFunctionBegin;
  ierr = MatConvert(A,MATMPIAIJ,MAT_INITIAL_MATRIX,&B);CHKERRQ(ierr);
  ierr = MatView(B,viewer);CHKERRQ(ierr);
  ierr = MatDestroy(&B);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatDestroy_MPIMAIJ(Mat A)
{
  PetscErrorCode ierr;
  Mat_MPIMAIJ    *b = (Mat_MPIMAIJ*)A->data;

  PetscFunctionBegin;
  ierr = MatDestroy(&b->AIJ);CHKERRQ(ierr);
  ierr = MatDestroy(&b->OAIJ);CHKERRQ(ierr);
  ierr = MatDestroy(&b->A);CHKERRQ(ierr);
  ierr = VecScatterDestroy(&b->ctx);CHKERRQ(ierr);
  ierr = VecDestroy(&b->w);CHKERRQ(ierr);
  ierr = PetscFree(A->data);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatConvert_mpimaij_mpiaij_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectComposeFunction((PetscObject)A,"MatProductSetFromOptions_mpiaij_mpimaij_C",NULL);CHKERRQ(ierr);
  ierr = PetscObjectChangeTypeName((PetscObject)A,NULL);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
  MATMAIJ - MATMAIJ = "maij" - A matrix type to be used for restriction and interpolation operations for
  multicomponent problems, interpolating or restricting each component the same way independently.
  The matrix type is based on MATSEQAIJ for sequential matrices, and MATMPIAIJ for distributed matrices.

  Operations provided:
+ MatMult
. MatMultTranspose
. MatMultAdd
- MatMultTransposeAdd

  Level: advanced

.seealso: MatMAIJGetAIJ(), MatMAIJRedimension(), MatCreateMAIJ()
M*/

PETSC_EXTERN PetscErrorCode MatCreate_MAIJ(Mat A)
{
  PetscErrorCode ierr;
  Mat_MPIMAIJ    *b;
  PetscMPIInt    size;

  PetscFunctionBegin;
  ierr     = PetscNewLog(A,&b);CHKERRQ(ierr);
  A->data  = (void*)b;

  ierr = PetscMemzero(A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);

  A->ops->setup = MatSetUp_MAIJ;

  b->AIJ  = NULL;
  b->dof  = 0;
  b->OAIJ = NULL;
  b->ctx  = NULL;
  b->w    = NULL;
  ierr    = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRMPI(ierr);
  if (size == 1) {
    ierr = PetscObjectChangeTypeName((PetscObject)A,MATSEQMAIJ);CHKERRQ(ierr);
  } else {
    ierr = PetscObjectChangeTypeName((PetscObject)A,MATMPIMAIJ);CHKERRQ(ierr);
  }
  A->preallocated  = PETSC_TRUE;
  A->assembled     = PETSC_TRUE;
  PetscFunctionReturn(0);
}

/* --------------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y, sum1, sum2;
  PetscErrorCode    ierr;
  PetscInt          nonzerorow=0,n,i,jrow,j;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[2*idx[jrow]];
      sum2 += v[jrow]*x[2*idx[jrow]+1];
      jrow++;
    }
    y[2*i]   = sum1;
    y[2*i+1] = sum2;
  }

  ierr = PetscLogFlops(4.0*a->nz - 2.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[2*i];
    alpha2 = x[2*i+1];
    while (n-->0) {
      y[2*(*idx)]   += alpha1*(*v);
      y[2*(*idx)+1] += alpha2*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(4.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2;
  PetscErrorCode    ierr;
  PetscInt          n,i,jrow,j;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[2*idx[jrow]];
      sum2 += v[jrow]*x[2*idx[jrow]+1];
      jrow++;
    }
    y[2*i]   += sum1;
    y[2*i+1] += sum2;
  }

  ierr = PetscLogFlops(4.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
PetscErrorCode MatMultTransposeAdd_SeqMAIJ_2(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[2*i];
    alpha2 = x[2*i+1];
    while (n-->0) {
      y[2*(*idx)]   += alpha1*(*v);
      y[2*(*idx)+1] += alpha2*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(4.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* --------------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_3(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3;
  PetscErrorCode    ierr;
  PetscInt          nonzerorow=0,n,i,jrow,j;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[3*idx[jrow]];
      sum2 += v[jrow]*x[3*idx[jrow]+1];
      sum3 += v[jrow]*x[3*idx[jrow]+2];
      jrow++;
     }
    y[3*i]   = sum1;
    y[3*i+1] = sum2;
    y[3*i+2] = sum3;
  }

  ierr = PetscLogFlops(6.0*a->nz - 3.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_3(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[3*i];
    alpha2 = x[3*i+1];
    alpha3 = x[3*i+2];
    while (n-->0) {
      y[3*(*idx)]   += alpha1*(*v);
      y[3*(*idx)+1] += alpha2*(*v);
      y[3*(*idx)+2] += alpha3*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(6.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3;
  PetscErrorCode    ierr;
  PetscInt          n,i,jrow,j;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[3*idx[jrow]];
      sum2 += v[jrow]*x[3*idx[jrow]+1];
      sum3 += v[jrow]*x[3*idx[jrow]+2];
      jrow++;
    }
    y[3*i]   += sum1;
    y[3*i+1] += sum2;
    y[3*i+2] += sum3;
  }

  ierr = PetscLogFlops(6.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
PetscErrorCode MatMultTransposeAdd_SeqMAIJ_3(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[3*i];
    alpha2 = x[3*i+1];
    alpha3 = x[3*i+2];
    while (n-->0) {
      y[3*(*idx)]   += alpha1*(*v);
      y[3*(*idx)+1] += alpha2*(*v);
      y[3*(*idx)+2] += alpha3*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(6.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_4(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4;
  PetscErrorCode    ierr;
  PetscInt          nonzerorow=0,n,i,jrow,j;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow        = ii[i];
    n           = ii[i+1] - jrow;
    sum1        = 0.0;
    sum2        = 0.0;
    sum3        = 0.0;
    sum4        = 0.0;
    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[4*idx[jrow]];
      sum2 += v[jrow]*x[4*idx[jrow]+1];
      sum3 += v[jrow]*x[4*idx[jrow]+2];
      sum4 += v[jrow]*x[4*idx[jrow]+3];
      jrow++;
    }
    y[4*i]   = sum1;
    y[4*i+1] = sum2;
    y[4*i+2] = sum3;
    y[4*i+3] = sum4;
  }

  ierr = PetscLogFlops(8.0*a->nz - 4.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_4(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[4*i];
    alpha2 = x[4*i+1];
    alpha3 = x[4*i+2];
    alpha4 = x[4*i+3];
    while (n-->0) {
      y[4*(*idx)]   += alpha1*(*v);
      y[4*(*idx)+1] += alpha2*(*v);
      y[4*(*idx)+2] += alpha3*(*v);
      y[4*(*idx)+3] += alpha4*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(8.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4;
  PetscErrorCode    ierr;
  PetscInt          n,i,jrow,j;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[4*idx[jrow]];
      sum2 += v[jrow]*x[4*idx[jrow]+1];
      sum3 += v[jrow]*x[4*idx[jrow]+2];
      sum4 += v[jrow]*x[4*idx[jrow]+3];
      jrow++;
    }
    y[4*i]   += sum1;
    y[4*i+1] += sum2;
    y[4*i+2] += sum3;
    y[4*i+3] += sum4;
  }

  ierr = PetscLogFlops(8.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
PetscErrorCode MatMultTransposeAdd_SeqMAIJ_4(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[4*i];
    alpha2 = x[4*i+1];
    alpha3 = x[4*i+2];
    alpha4 = x[4*i+3];
    while (n-->0) {
      y[4*(*idx)]   += alpha1*(*v);
      y[4*(*idx)+1] += alpha2*(*v);
      y[4*(*idx)+2] += alpha3*(*v);
      y[4*(*idx)+3] += alpha4*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(8.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* ------------------------------------------------------------------------------*/

PetscErrorCode MatMult_SeqMAIJ_5(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5;
  PetscErrorCode    ierr;
  PetscInt          nonzerorow=0,n,i,jrow,j;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[5*idx[jrow]];
      sum2 += v[jrow]*x[5*idx[jrow]+1];
      sum3 += v[jrow]*x[5*idx[jrow]+2];
      sum4 += v[jrow]*x[5*idx[jrow]+3];
      sum5 += v[jrow]*x[5*idx[jrow]+4];
      jrow++;
    }
    y[5*i]   = sum1;
    y[5*i+1] = sum2;
    y[5*i+2] = sum3;
    y[5*i+3] = sum4;
    y[5*i+4] = sum5;
  }

  ierr = PetscLogFlops(10.0*a->nz - 5.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_5(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[5*i];
    alpha2 = x[5*i+1];
    alpha3 = x[5*i+2];
    alpha4 = x[5*i+3];
    alpha5 = x[5*i+4];
    while (n-->0) {
      y[5*(*idx)]   += alpha1*(*v);
      y[5*(*idx)+1] += alpha2*(*v);
      y[5*(*idx)+2] += alpha3*(*v);
      y[5*(*idx)+3] += alpha4*(*v);
      y[5*(*idx)+4] += alpha5*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(10.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5;
  PetscErrorCode    ierr;
  PetscInt          n,i,jrow,j;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    sum5 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[5*idx[jrow]];
      sum2 += v[jrow]*x[5*idx[jrow]+1];
      sum3 += v[jrow]*x[5*idx[jrow]+2];
      sum4 += v[jrow]*x[5*idx[jrow]+3];
      sum5 += v[jrow]*x[5*idx[jrow]+4];
      jrow++;
    }
    y[5*i]   += sum1;
    y[5*i+1] += sum2;
    y[5*i+2] += sum3;
    y[5*i+3] += sum4;
    y[5*i+4] += sum5;
  }

  ierr = PetscLogFlops(10.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_5(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[5*i];
    alpha2 = x[5*i+1];
    alpha3 = x[5*i+2];
    alpha4 = x[5*i+3];
    alpha5 = x[5*i+4];
    while (n-->0) {
      y[5*(*idx)]   += alpha1*(*v);
      y[5*(*idx)+1] += alpha2*(*v);
      y[5*(*idx)+2] += alpha3*(*v);
      y[5*(*idx)+3] += alpha4*(*v);
      y[5*(*idx)+4] += alpha5*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(10.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_6(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6;
  PetscErrorCode    ierr;
  PetscInt          nonzerorow=0,n,i,jrow,j;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[6*idx[jrow]];
      sum2 += v[jrow]*x[6*idx[jrow]+1];
      sum3 += v[jrow]*x[6*idx[jrow]+2];
      sum4 += v[jrow]*x[6*idx[jrow]+3];
      sum5 += v[jrow]*x[6*idx[jrow]+4];
      sum6 += v[jrow]*x[6*idx[jrow]+5];
      jrow++;
    }
    y[6*i]   = sum1;
    y[6*i+1] = sum2;
    y[6*i+2] = sum3;
    y[6*i+3] = sum4;
    y[6*i+4] = sum5;
    y[6*i+5] = sum6;
  }

  ierr = PetscLogFlops(12.0*a->nz - 6.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_6(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[6*i];
    alpha2 = x[6*i+1];
    alpha3 = x[6*i+2];
    alpha4 = x[6*i+3];
    alpha5 = x[6*i+4];
    alpha6 = x[6*i+5];
    while (n-->0) {
      y[6*(*idx)]   += alpha1*(*v);
      y[6*(*idx)+1] += alpha2*(*v);
      y[6*(*idx)+2] += alpha3*(*v);
      y[6*(*idx)+3] += alpha4*(*v);
      y[6*(*idx)+4] += alpha5*(*v);
      y[6*(*idx)+5] += alpha6*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(12.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6;
  PetscErrorCode    ierr;
  PetscInt          n,i,jrow,j;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    sum5 = 0.0;
    sum6 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[6*idx[jrow]];
      sum2 += v[jrow]*x[6*idx[jrow]+1];
      sum3 += v[jrow]*x[6*idx[jrow]+2];
      sum4 += v[jrow]*x[6*idx[jrow]+3];
      sum5 += v[jrow]*x[6*idx[jrow]+4];
      sum6 += v[jrow]*x[6*idx[jrow]+5];
      jrow++;
    }
    y[6*i]   += sum1;
    y[6*i+1] += sum2;
    y[6*i+2] += sum3;
    y[6*i+3] += sum4;
    y[6*i+4] += sum5;
    y[6*i+5] += sum6;
  }

  ierr = PetscLogFlops(12.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_6(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6;
  PetscErrorCode    ierr;
  PetscInt          n,i;
  const PetscInt    m = b->AIJ->rmap->n,*idx;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[6*i];
    alpha2 = x[6*i+1];
    alpha3 = x[6*i+2];
    alpha4 = x[6*i+3];
    alpha5 = x[6*i+4];
    alpha6 = x[6*i+5];
    while (n-->0) {
      y[6*(*idx)]   += alpha1*(*v);
      y[6*(*idx)+1] += alpha2*(*v);
      y[6*(*idx)+2] += alpha3*(*v);
      y[6*(*idx)+3] += alpha4*(*v);
      y[6*(*idx)+4] += alpha5*(*v);
      y[6*(*idx)+5] += alpha6*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(12.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_7(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[7*idx[jrow]];
      sum2 += v[jrow]*x[7*idx[jrow]+1];
      sum3 += v[jrow]*x[7*idx[jrow]+2];
      sum4 += v[jrow]*x[7*idx[jrow]+3];
      sum5 += v[jrow]*x[7*idx[jrow]+4];
      sum6 += v[jrow]*x[7*idx[jrow]+5];
      sum7 += v[jrow]*x[7*idx[jrow]+6];
      jrow++;
    }
    y[7*i]   = sum1;
    y[7*i+1] = sum2;
    y[7*i+2] = sum3;
    y[7*i+3] = sum4;
    y[7*i+4] = sum5;
    y[7*i+5] = sum6;
    y[7*i+6] = sum7;
  }

  ierr = PetscLogFlops(14.0*a->nz - 7.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_7(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[7*i];
    alpha2 = x[7*i+1];
    alpha3 = x[7*i+2];
    alpha4 = x[7*i+3];
    alpha5 = x[7*i+4];
    alpha6 = x[7*i+5];
    alpha7 = x[7*i+6];
    while (n-->0) {
      y[7*(*idx)]   += alpha1*(*v);
      y[7*(*idx)+1] += alpha2*(*v);
      y[7*(*idx)+2] += alpha3*(*v);
      y[7*(*idx)+3] += alpha4*(*v);
      y[7*(*idx)+4] += alpha5*(*v);
      y[7*(*idx)+5] += alpha6*(*v);
      y[7*(*idx)+6] += alpha7*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(14.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    sum5 = 0.0;
    sum6 = 0.0;
    sum7 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[7*idx[jrow]];
      sum2 += v[jrow]*x[7*idx[jrow]+1];
      sum3 += v[jrow]*x[7*idx[jrow]+2];
      sum4 += v[jrow]*x[7*idx[jrow]+3];
      sum5 += v[jrow]*x[7*idx[jrow]+4];
      sum6 += v[jrow]*x[7*idx[jrow]+5];
      sum7 += v[jrow]*x[7*idx[jrow]+6];
      jrow++;
    }
    y[7*i]   += sum1;
    y[7*i+1] += sum2;
    y[7*i+2] += sum3;
    y[7*i+3] += sum4;
    y[7*i+4] += sum5;
    y[7*i+5] += sum6;
    y[7*i+6] += sum7;
  }

  ierr = PetscLogFlops(14.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_7(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[7*i];
    alpha2 = x[7*i+1];
    alpha3 = x[7*i+2];
    alpha4 = x[7*i+3];
    alpha5 = x[7*i+4];
    alpha6 = x[7*i+5];
    alpha7 = x[7*i+6];
    while (n-->0) {
      y[7*(*idx)]   += alpha1*(*v);
      y[7*(*idx)+1] += alpha2*(*v);
      y[7*(*idx)+2] += alpha3*(*v);
      y[7*(*idx)+3] += alpha4*(*v);
      y[7*(*idx)+4] += alpha5*(*v);
      y[7*(*idx)+5] += alpha6*(*v);
      y[7*(*idx)+6] += alpha7*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(14.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMult_SeqMAIJ_8(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[8*idx[jrow]];
      sum2 += v[jrow]*x[8*idx[jrow]+1];
      sum3 += v[jrow]*x[8*idx[jrow]+2];
      sum4 += v[jrow]*x[8*idx[jrow]+3];
      sum5 += v[jrow]*x[8*idx[jrow]+4];
      sum6 += v[jrow]*x[8*idx[jrow]+5];
      sum7 += v[jrow]*x[8*idx[jrow]+6];
      sum8 += v[jrow]*x[8*idx[jrow]+7];
      jrow++;
    }
    y[8*i]   = sum1;
    y[8*i+1] = sum2;
    y[8*i+2] = sum3;
    y[8*i+3] = sum4;
    y[8*i+4] = sum5;
    y[8*i+5] = sum6;
    y[8*i+6] = sum7;
    y[8*i+7] = sum8;
  }

  ierr = PetscLogFlops(16.0*a->nz - 8.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_8(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[8*i];
    alpha2 = x[8*i+1];
    alpha3 = x[8*i+2];
    alpha4 = x[8*i+3];
    alpha5 = x[8*i+4];
    alpha6 = x[8*i+5];
    alpha7 = x[8*i+6];
    alpha8 = x[8*i+7];
    while (n-->0) {
      y[8*(*idx)]   += alpha1*(*v);
      y[8*(*idx)+1] += alpha2*(*v);
      y[8*(*idx)+2] += alpha3*(*v);
      y[8*(*idx)+3] += alpha4*(*v);
      y[8*(*idx)+4] += alpha5*(*v);
      y[8*(*idx)+5] += alpha6*(*v);
      y[8*(*idx)+6] += alpha7*(*v);
      y[8*(*idx)+7] += alpha8*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(16.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_8(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    sum5 = 0.0;
    sum6 = 0.0;
    sum7 = 0.0;
    sum8 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[8*idx[jrow]];
      sum2 += v[jrow]*x[8*idx[jrow]+1];
      sum3 += v[jrow]*x[8*idx[jrow]+2];
      sum4 += v[jrow]*x[8*idx[jrow]+3];
      sum5 += v[jrow]*x[8*idx[jrow]+4];
      sum6 += v[jrow]*x[8*idx[jrow]+5];
      sum7 += v[jrow]*x[8*idx[jrow]+6];
      sum8 += v[jrow]*x[8*idx[jrow]+7];
      jrow++;
    }
    y[8*i]   += sum1;
    y[8*i+1] += sum2;
    y[8*i+2] += sum3;
    y[8*i+3] += sum4;
    y[8*i+4] += sum5;
    y[8*i+5] += sum6;
    y[8*i+6] += sum7;
    y[8*i+7] += sum8;
  }

  ierr = PetscLogFlops(16.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_8(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[8*i];
    alpha2 = x[8*i+1];
    alpha3 = x[8*i+2];
    alpha4 = x[8*i+3];
    alpha5 = x[8*i+4];
    alpha6 = x[8*i+5];
    alpha7 = x[8*i+6];
    alpha8 = x[8*i+7];
    while (n-->0) {
      y[8*(*idx)]   += alpha1*(*v);
      y[8*(*idx)+1] += alpha2*(*v);
      y[8*(*idx)+2] += alpha3*(*v);
      y[8*(*idx)+3] += alpha4*(*v);
      y[8*(*idx)+4] += alpha5*(*v);
      y[8*(*idx)+5] += alpha6*(*v);
      y[8*(*idx)+6] += alpha7*(*v);
      y[8*(*idx)+7] += alpha8*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(16.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_9(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[9*idx[jrow]];
      sum2 += v[jrow]*x[9*idx[jrow]+1];
      sum3 += v[jrow]*x[9*idx[jrow]+2];
      sum4 += v[jrow]*x[9*idx[jrow]+3];
      sum5 += v[jrow]*x[9*idx[jrow]+4];
      sum6 += v[jrow]*x[9*idx[jrow]+5];
      sum7 += v[jrow]*x[9*idx[jrow]+6];
      sum8 += v[jrow]*x[9*idx[jrow]+7];
      sum9 += v[jrow]*x[9*idx[jrow]+8];
      jrow++;
    }
    y[9*i]   = sum1;
    y[9*i+1] = sum2;
    y[9*i+2] = sum3;
    y[9*i+3] = sum4;
    y[9*i+4] = sum5;
    y[9*i+5] = sum6;
    y[9*i+6] = sum7;
    y[9*i+7] = sum8;
    y[9*i+8] = sum9;
  }

  ierr = PetscLogFlops(18.0*a->nz - 9*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/

PetscErrorCode MatMultTranspose_SeqMAIJ_9(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[9*i];
    alpha2 = x[9*i+1];
    alpha3 = x[9*i+2];
    alpha4 = x[9*i+3];
    alpha5 = x[9*i+4];
    alpha6 = x[9*i+5];
    alpha7 = x[9*i+6];
    alpha8 = x[9*i+7];
    alpha9 = x[9*i+8];
    while (n-->0) {
      y[9*(*idx)]   += alpha1*(*v);
      y[9*(*idx)+1] += alpha2*(*v);
      y[9*(*idx)+2] += alpha3*(*v);
      y[9*(*idx)+3] += alpha4*(*v);
      y[9*(*idx)+4] += alpha5*(*v);
      y[9*(*idx)+5] += alpha6*(*v);
      y[9*(*idx)+6] += alpha7*(*v);
      y[9*(*idx)+7] += alpha8*(*v);
      y[9*(*idx)+8] += alpha9*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(18.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_9(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sum1 = 0.0;
    sum2 = 0.0;
    sum3 = 0.0;
    sum4 = 0.0;
    sum5 = 0.0;
    sum6 = 0.0;
    sum7 = 0.0;
    sum8 = 0.0;
    sum9 = 0.0;
    for (j=0; j<n; j++) {
      sum1 += v[jrow]*x[9*idx[jrow]];
      sum2 += v[jrow]*x[9*idx[jrow]+1];
      sum3 += v[jrow]*x[9*idx[jrow]+2];
      sum4 += v[jrow]*x[9*idx[jrow]+3];
      sum5 += v[jrow]*x[9*idx[jrow]+4];
      sum6 += v[jrow]*x[9*idx[jrow]+5];
      sum7 += v[jrow]*x[9*idx[jrow]+6];
      sum8 += v[jrow]*x[9*idx[jrow]+7];
      sum9 += v[jrow]*x[9*idx[jrow]+8];
      jrow++;
    }
    y[9*i]   += sum1;
    y[9*i+1] += sum2;
    y[9*i+2] += sum3;
    y[9*i+3] += sum4;
    y[9*i+4] += sum5;
    y[9*i+5] += sum6;
    y[9*i+6] += sum7;
    y[9*i+7] += sum8;
    y[9*i+8] += sum9;
  }

  ierr = PetscLogFlops(18.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_9(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i];
    v      = a->a + a->i[i];
    n      = a->i[i+1] - a->i[i];
    alpha1 = x[9*i];
    alpha2 = x[9*i+1];
    alpha3 = x[9*i+2];
    alpha4 = x[9*i+3];
    alpha5 = x[9*i+4];
    alpha6 = x[9*i+5];
    alpha7 = x[9*i+6];
    alpha8 = x[9*i+7];
    alpha9 = x[9*i+8];
    while (n-->0) {
      y[9*(*idx)]   += alpha1*(*v);
      y[9*(*idx)+1] += alpha2*(*v);
      y[9*(*idx)+2] += alpha3*(*v);
      y[9*(*idx)+3] += alpha4*(*v);
      y[9*(*idx)+4] += alpha5*(*v);
      y[9*(*idx)+5] += alpha6*(*v);
      y[9*(*idx)+6] += alpha7*(*v);
      y[9*(*idx)+7] += alpha8*(*v);
      y[9*(*idx)+8] += alpha9*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(18.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
PetscErrorCode MatMult_SeqMAIJ_10(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9, sum10;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[10*idx[jrow]];
      sum2  += v[jrow]*x[10*idx[jrow]+1];
      sum3  += v[jrow]*x[10*idx[jrow]+2];
      sum4  += v[jrow]*x[10*idx[jrow]+3];
      sum5  += v[jrow]*x[10*idx[jrow]+4];
      sum6  += v[jrow]*x[10*idx[jrow]+5];
      sum7  += v[jrow]*x[10*idx[jrow]+6];
      sum8  += v[jrow]*x[10*idx[jrow]+7];
      sum9  += v[jrow]*x[10*idx[jrow]+8];
      sum10 += v[jrow]*x[10*idx[jrow]+9];
      jrow++;
    }
    y[10*i]   = sum1;
    y[10*i+1] = sum2;
    y[10*i+2] = sum3;
    y[10*i+3] = sum4;
    y[10*i+4] = sum5;
    y[10*i+5] = sum6;
    y[10*i+6] = sum7;
    y[10*i+7] = sum8;
    y[10*i+8] = sum9;
    y[10*i+9] = sum10;
  }

  ierr = PetscLogFlops(20.0*a->nz - 10.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_10(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9, sum10;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[10*idx[jrow]];
      sum2  += v[jrow]*x[10*idx[jrow]+1];
      sum3  += v[jrow]*x[10*idx[jrow]+2];
      sum4  += v[jrow]*x[10*idx[jrow]+3];
      sum5  += v[jrow]*x[10*idx[jrow]+4];
      sum6  += v[jrow]*x[10*idx[jrow]+5];
      sum7  += v[jrow]*x[10*idx[jrow]+6];
      sum8  += v[jrow]*x[10*idx[jrow]+7];
      sum9  += v[jrow]*x[10*idx[jrow]+8];
      sum10 += v[jrow]*x[10*idx[jrow]+9];
      jrow++;
    }
    y[10*i]   += sum1;
    y[10*i+1] += sum2;
    y[10*i+2] += sum3;
    y[10*i+3] += sum4;
    y[10*i+4] += sum5;
    y[10*i+5] += sum6;
    y[10*i+6] += sum7;
    y[10*i+7] += sum8;
    y[10*i+8] += sum9;
    y[10*i+9] += sum10;
  }

  ierr = PetscLogFlops(20.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_10(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[10*i];
    alpha2  = x[10*i+1];
    alpha3  = x[10*i+2];
    alpha4  = x[10*i+3];
    alpha5  = x[10*i+4];
    alpha6  = x[10*i+5];
    alpha7  = x[10*i+6];
    alpha8  = x[10*i+7];
    alpha9  = x[10*i+8];
    alpha10 = x[10*i+9];
    while (n-->0) {
      y[10*(*idx)]   += alpha1*(*v);
      y[10*(*idx)+1] += alpha2*(*v);
      y[10*(*idx)+2] += alpha3*(*v);
      y[10*(*idx)+3] += alpha4*(*v);
      y[10*(*idx)+4] += alpha5*(*v);
      y[10*(*idx)+5] += alpha6*(*v);
      y[10*(*idx)+6] += alpha7*(*v);
      y[10*(*idx)+7] += alpha8*(*v);
      y[10*(*idx)+8] += alpha9*(*v);
      y[10*(*idx)+9] += alpha10*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(20.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_10(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[10*i];
    alpha2  = x[10*i+1];
    alpha3  = x[10*i+2];
    alpha4  = x[10*i+3];
    alpha5  = x[10*i+4];
    alpha6  = x[10*i+5];
    alpha7  = x[10*i+6];
    alpha8  = x[10*i+7];
    alpha9  = x[10*i+8];
    alpha10 = x[10*i+9];
    while (n-->0) {
      y[10*(*idx)]   += alpha1*(*v);
      y[10*(*idx)+1] += alpha2*(*v);
      y[10*(*idx)+2] += alpha3*(*v);
      y[10*(*idx)+3] += alpha4*(*v);
      y[10*(*idx)+4] += alpha5*(*v);
      y[10*(*idx)+5] += alpha6*(*v);
      y[10*(*idx)+6] += alpha7*(*v);
      y[10*(*idx)+7] += alpha8*(*v);
      y[10*(*idx)+8] += alpha9*(*v);
      y[10*(*idx)+9] += alpha10*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(20.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*--------------------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_11(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9, sum10, sum11;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[11*idx[jrow]];
      sum2  += v[jrow]*x[11*idx[jrow]+1];
      sum3  += v[jrow]*x[11*idx[jrow]+2];
      sum4  += v[jrow]*x[11*idx[jrow]+3];
      sum5  += v[jrow]*x[11*idx[jrow]+4];
      sum6  += v[jrow]*x[11*idx[jrow]+5];
      sum7  += v[jrow]*x[11*idx[jrow]+6];
      sum8  += v[jrow]*x[11*idx[jrow]+7];
      sum9  += v[jrow]*x[11*idx[jrow]+8];
      sum10 += v[jrow]*x[11*idx[jrow]+9];
      sum11 += v[jrow]*x[11*idx[jrow]+10];
      jrow++;
    }
    y[11*i]    = sum1;
    y[11*i+1]  = sum2;
    y[11*i+2]  = sum3;
    y[11*i+3]  = sum4;
    y[11*i+4]  = sum5;
    y[11*i+5]  = sum6;
    y[11*i+6]  = sum7;
    y[11*i+7]  = sum8;
    y[11*i+8]  = sum9;
    y[11*i+9]  = sum10;
    y[11*i+10] = sum11;
  }

  ierr = PetscLogFlops(22.0*a->nz - 11*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_11(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8, sum9, sum10, sum11;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[11*idx[jrow]];
      sum2  += v[jrow]*x[11*idx[jrow]+1];
      sum3  += v[jrow]*x[11*idx[jrow]+2];
      sum4  += v[jrow]*x[11*idx[jrow]+3];
      sum5  += v[jrow]*x[11*idx[jrow]+4];
      sum6  += v[jrow]*x[11*idx[jrow]+5];
      sum7  += v[jrow]*x[11*idx[jrow]+6];
      sum8  += v[jrow]*x[11*idx[jrow]+7];
      sum9  += v[jrow]*x[11*idx[jrow]+8];
      sum10 += v[jrow]*x[11*idx[jrow]+9];
      sum11 += v[jrow]*x[11*idx[jrow]+10];
      jrow++;
    }
    y[11*i]    += sum1;
    y[11*i+1]  += sum2;
    y[11*i+2]  += sum3;
    y[11*i+3]  += sum4;
    y[11*i+4]  += sum5;
    y[11*i+5]  += sum6;
    y[11*i+6]  += sum7;
    y[11*i+7]  += sum8;
    y[11*i+8]  += sum9;
    y[11*i+9]  += sum10;
    y[11*i+10] += sum11;
  }

  ierr = PetscLogFlops(22.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_11(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10,alpha11;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[11*i];
    alpha2  = x[11*i+1];
    alpha3  = x[11*i+2];
    alpha4  = x[11*i+3];
    alpha5  = x[11*i+4];
    alpha6  = x[11*i+5];
    alpha7  = x[11*i+6];
    alpha8  = x[11*i+7];
    alpha9  = x[11*i+8];
    alpha10 = x[11*i+9];
    alpha11 = x[11*i+10];
    while (n-->0) {
      y[11*(*idx)]    += alpha1*(*v);
      y[11*(*idx)+1]  += alpha2*(*v);
      y[11*(*idx)+2]  += alpha3*(*v);
      y[11*(*idx)+3]  += alpha4*(*v);
      y[11*(*idx)+4]  += alpha5*(*v);
      y[11*(*idx)+5]  += alpha6*(*v);
      y[11*(*idx)+6]  += alpha7*(*v);
      y[11*(*idx)+7]  += alpha8*(*v);
      y[11*(*idx)+8]  += alpha9*(*v);
      y[11*(*idx)+9]  += alpha10*(*v);
      y[11*(*idx)+10] += alpha11*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(22.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_11(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8,alpha9,alpha10,alpha11;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[11*i];
    alpha2  = x[11*i+1];
    alpha3  = x[11*i+2];
    alpha4  = x[11*i+3];
    alpha5  = x[11*i+4];
    alpha6  = x[11*i+5];
    alpha7  = x[11*i+6];
    alpha8  = x[11*i+7];
    alpha9  = x[11*i+8];
    alpha10 = x[11*i+9];
    alpha11 = x[11*i+10];
    while (n-->0) {
      y[11*(*idx)]    += alpha1*(*v);
      y[11*(*idx)+1]  += alpha2*(*v);
      y[11*(*idx)+2]  += alpha3*(*v);
      y[11*(*idx)+3]  += alpha4*(*v);
      y[11*(*idx)+4]  += alpha5*(*v);
      y[11*(*idx)+5]  += alpha6*(*v);
      y[11*(*idx)+6]  += alpha7*(*v);
      y[11*(*idx)+7]  += alpha8*(*v);
      y[11*(*idx)+8]  += alpha9*(*v);
      y[11*(*idx)+9]  += alpha10*(*v);
      y[11*(*idx)+10] += alpha11*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(22.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*--------------------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_16(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscScalar       sum9, sum10, sum11, sum12, sum13, sum14, sum15, sum16;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;
    sum12 = 0.0;
    sum13 = 0.0;
    sum14 = 0.0;
    sum15 = 0.0;
    sum16 = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[16*idx[jrow]];
      sum2  += v[jrow]*x[16*idx[jrow]+1];
      sum3  += v[jrow]*x[16*idx[jrow]+2];
      sum4  += v[jrow]*x[16*idx[jrow]+3];
      sum5  += v[jrow]*x[16*idx[jrow]+4];
      sum6  += v[jrow]*x[16*idx[jrow]+5];
      sum7  += v[jrow]*x[16*idx[jrow]+6];
      sum8  += v[jrow]*x[16*idx[jrow]+7];
      sum9  += v[jrow]*x[16*idx[jrow]+8];
      sum10 += v[jrow]*x[16*idx[jrow]+9];
      sum11 += v[jrow]*x[16*idx[jrow]+10];
      sum12 += v[jrow]*x[16*idx[jrow]+11];
      sum13 += v[jrow]*x[16*idx[jrow]+12];
      sum14 += v[jrow]*x[16*idx[jrow]+13];
      sum15 += v[jrow]*x[16*idx[jrow]+14];
      sum16 += v[jrow]*x[16*idx[jrow]+15];
      jrow++;
    }
    y[16*i]    = sum1;
    y[16*i+1]  = sum2;
    y[16*i+2]  = sum3;
    y[16*i+3]  = sum4;
    y[16*i+4]  = sum5;
    y[16*i+5]  = sum6;
    y[16*i+6]  = sum7;
    y[16*i+7]  = sum8;
    y[16*i+8]  = sum9;
    y[16*i+9]  = sum10;
    y[16*i+10] = sum11;
    y[16*i+11] = sum12;
    y[16*i+12] = sum13;
    y[16*i+13] = sum14;
    y[16*i+14] = sum15;
    y[16*i+15] = sum16;
  }

  ierr = PetscLogFlops(32.0*a->nz - 16.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_16(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscScalar       alpha9,alpha10,alpha11,alpha12,alpha13,alpha14,alpha15,alpha16;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[16*i];
    alpha2  = x[16*i+1];
    alpha3  = x[16*i+2];
    alpha4  = x[16*i+3];
    alpha5  = x[16*i+4];
    alpha6  = x[16*i+5];
    alpha7  = x[16*i+6];
    alpha8  = x[16*i+7];
    alpha9  = x[16*i+8];
    alpha10 = x[16*i+9];
    alpha11 = x[16*i+10];
    alpha12 = x[16*i+11];
    alpha13 = x[16*i+12];
    alpha14 = x[16*i+13];
    alpha15 = x[16*i+14];
    alpha16 = x[16*i+15];
    while (n-->0) {
      y[16*(*idx)]    += alpha1*(*v);
      y[16*(*idx)+1]  += alpha2*(*v);
      y[16*(*idx)+2]  += alpha3*(*v);
      y[16*(*idx)+3]  += alpha4*(*v);
      y[16*(*idx)+4]  += alpha5*(*v);
      y[16*(*idx)+5]  += alpha6*(*v);
      y[16*(*idx)+6]  += alpha7*(*v);
      y[16*(*idx)+7]  += alpha8*(*v);
      y[16*(*idx)+8]  += alpha9*(*v);
      y[16*(*idx)+9]  += alpha10*(*v);
      y[16*(*idx)+10] += alpha11*(*v);
      y[16*(*idx)+11] += alpha12*(*v);
      y[16*(*idx)+12] += alpha13*(*v);
      y[16*(*idx)+13] += alpha14*(*v);
      y[16*(*idx)+14] += alpha15*(*v);
      y[16*(*idx)+15] += alpha16*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(32.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_16(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscScalar       sum9, sum10, sum11, sum12, sum13, sum14, sum15, sum16;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;
    sum12 = 0.0;
    sum13 = 0.0;
    sum14 = 0.0;
    sum15 = 0.0;
    sum16 = 0.0;
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[16*idx[jrow]];
      sum2  += v[jrow]*x[16*idx[jrow]+1];
      sum3  += v[jrow]*x[16*idx[jrow]+2];
      sum4  += v[jrow]*x[16*idx[jrow]+3];
      sum5  += v[jrow]*x[16*idx[jrow]+4];
      sum6  += v[jrow]*x[16*idx[jrow]+5];
      sum7  += v[jrow]*x[16*idx[jrow]+6];
      sum8  += v[jrow]*x[16*idx[jrow]+7];
      sum9  += v[jrow]*x[16*idx[jrow]+8];
      sum10 += v[jrow]*x[16*idx[jrow]+9];
      sum11 += v[jrow]*x[16*idx[jrow]+10];
      sum12 += v[jrow]*x[16*idx[jrow]+11];
      sum13 += v[jrow]*x[16*idx[jrow]+12];
      sum14 += v[jrow]*x[16*idx[jrow]+13];
      sum15 += v[jrow]*x[16*idx[jrow]+14];
      sum16 += v[jrow]*x[16*idx[jrow]+15];
      jrow++;
    }
    y[16*i]    += sum1;
    y[16*i+1]  += sum2;
    y[16*i+2]  += sum3;
    y[16*i+3]  += sum4;
    y[16*i+4]  += sum5;
    y[16*i+5]  += sum6;
    y[16*i+6]  += sum7;
    y[16*i+7]  += sum8;
    y[16*i+8]  += sum9;
    y[16*i+9]  += sum10;
    y[16*i+10] += sum11;
    y[16*i+11] += sum12;
    y[16*i+12] += sum13;
    y[16*i+13] += sum14;
    y[16*i+14] += sum15;
    y[16*i+15] += sum16;
  }

  ierr = PetscLogFlops(32.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_16(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscScalar       alpha9,alpha10,alpha11,alpha12,alpha13,alpha14,alpha15,alpha16;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[16*i];
    alpha2  = x[16*i+1];
    alpha3  = x[16*i+2];
    alpha4  = x[16*i+3];
    alpha5  = x[16*i+4];
    alpha6  = x[16*i+5];
    alpha7  = x[16*i+6];
    alpha8  = x[16*i+7];
    alpha9  = x[16*i+8];
    alpha10 = x[16*i+9];
    alpha11 = x[16*i+10];
    alpha12 = x[16*i+11];
    alpha13 = x[16*i+12];
    alpha14 = x[16*i+13];
    alpha15 = x[16*i+14];
    alpha16 = x[16*i+15];
    while (n-->0) {
      y[16*(*idx)]    += alpha1*(*v);
      y[16*(*idx)+1]  += alpha2*(*v);
      y[16*(*idx)+2]  += alpha3*(*v);
      y[16*(*idx)+3]  += alpha4*(*v);
      y[16*(*idx)+4]  += alpha5*(*v);
      y[16*(*idx)+5]  += alpha6*(*v);
      y[16*(*idx)+6]  += alpha7*(*v);
      y[16*(*idx)+7]  += alpha8*(*v);
      y[16*(*idx)+8]  += alpha9*(*v);
      y[16*(*idx)+9]  += alpha10*(*v);
      y[16*(*idx)+10] += alpha11*(*v);
      y[16*(*idx)+11] += alpha12*(*v);
      y[16*(*idx)+12] += alpha13*(*v);
      y[16*(*idx)+13] += alpha14*(*v);
      y[16*(*idx)+14] += alpha15*(*v);
      y[16*(*idx)+15] += alpha16*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(32.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*--------------------------------------------------------------------------------------------*/
PetscErrorCode MatMult_SeqMAIJ_18(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscScalar       sum9, sum10, sum11, sum12, sum13, sum14, sum15, sum16, sum17, sum18;
  PetscErrorCode    ierr;
  const PetscInt    m         = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          nonzerorow=0,n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;
    sum12 = 0.0;
    sum13 = 0.0;
    sum14 = 0.0;
    sum15 = 0.0;
    sum16 = 0.0;
    sum17 = 0.0;
    sum18 = 0.0;

    nonzerorow += (n>0);
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[18*idx[jrow]];
      sum2  += v[jrow]*x[18*idx[jrow]+1];
      sum3  += v[jrow]*x[18*idx[jrow]+2];
      sum4  += v[jrow]*x[18*idx[jrow]+3];
      sum5  += v[jrow]*x[18*idx[jrow]+4];
      sum6  += v[jrow]*x[18*idx[jrow]+5];
      sum7  += v[jrow]*x[18*idx[jrow]+6];
      sum8  += v[jrow]*x[18*idx[jrow]+7];
      sum9  += v[jrow]*x[18*idx[jrow]+8];
      sum10 += v[jrow]*x[18*idx[jrow]+9];
      sum11 += v[jrow]*x[18*idx[jrow]+10];
      sum12 += v[jrow]*x[18*idx[jrow]+11];
      sum13 += v[jrow]*x[18*idx[jrow]+12];
      sum14 += v[jrow]*x[18*idx[jrow]+13];
      sum15 += v[jrow]*x[18*idx[jrow]+14];
      sum16 += v[jrow]*x[18*idx[jrow]+15];
      sum17 += v[jrow]*x[18*idx[jrow]+16];
      sum18 += v[jrow]*x[18*idx[jrow]+17];
      jrow++;
    }
    y[18*i]    = sum1;
    y[18*i+1]  = sum2;
    y[18*i+2]  = sum3;
    y[18*i+3]  = sum4;
    y[18*i+4]  = sum5;
    y[18*i+5]  = sum6;
    y[18*i+6]  = sum7;
    y[18*i+7]  = sum8;
    y[18*i+8]  = sum9;
    y[18*i+9]  = sum10;
    y[18*i+10] = sum11;
    y[18*i+11] = sum12;
    y[18*i+12] = sum13;
    y[18*i+13] = sum14;
    y[18*i+14] = sum15;
    y[18*i+15] = sum16;
    y[18*i+16] = sum17;
    y[18*i+17] = sum18;
  }

  ierr = PetscLogFlops(36.0*a->nz - 18.0*nonzerorow);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_SeqMAIJ_18(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscScalar       alpha9,alpha10,alpha11,alpha12,alpha13,alpha14,alpha15,alpha16,alpha17,alpha18;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);

  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[18*i];
    alpha2  = x[18*i+1];
    alpha3  = x[18*i+2];
    alpha4  = x[18*i+3];
    alpha5  = x[18*i+4];
    alpha6  = x[18*i+5];
    alpha7  = x[18*i+6];
    alpha8  = x[18*i+7];
    alpha9  = x[18*i+8];
    alpha10 = x[18*i+9];
    alpha11 = x[18*i+10];
    alpha12 = x[18*i+11];
    alpha13 = x[18*i+12];
    alpha14 = x[18*i+13];
    alpha15 = x[18*i+14];
    alpha16 = x[18*i+15];
    alpha17 = x[18*i+16];
    alpha18 = x[18*i+17];
    while (n-->0) {
      y[18*(*idx)]    += alpha1*(*v);
      y[18*(*idx)+1]  += alpha2*(*v);
      y[18*(*idx)+2]  += alpha3*(*v);
      y[18*(*idx)+3]  += alpha4*(*v);
      y[18*(*idx)+4]  += alpha5*(*v);
      y[18*(*idx)+5]  += alpha6*(*v);
      y[18*(*idx)+6]  += alpha7*(*v);
      y[18*(*idx)+7]  += alpha8*(*v);
      y[18*(*idx)+8]  += alpha9*(*v);
      y[18*(*idx)+9]  += alpha10*(*v);
      y[18*(*idx)+10] += alpha11*(*v);
      y[18*(*idx)+11] += alpha12*(*v);
      y[18*(*idx)+12] += alpha13*(*v);
      y[18*(*idx)+13] += alpha14*(*v);
      y[18*(*idx)+14] += alpha15*(*v);
      y[18*(*idx)+15] += alpha16*(*v);
      y[18*(*idx)+16] += alpha17*(*v);
      y[18*(*idx)+17] += alpha18*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(36.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_SeqMAIJ_18(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,sum1, sum2, sum3, sum4, sum5, sum6, sum7, sum8;
  PetscScalar       sum9, sum10, sum11, sum12, sum13, sum14, sum15, sum16, sum17, sum18;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow  = ii[i];
    n     = ii[i+1] - jrow;
    sum1  = 0.0;
    sum2  = 0.0;
    sum3  = 0.0;
    sum4  = 0.0;
    sum5  = 0.0;
    sum6  = 0.0;
    sum7  = 0.0;
    sum8  = 0.0;
    sum9  = 0.0;
    sum10 = 0.0;
    sum11 = 0.0;
    sum12 = 0.0;
    sum13 = 0.0;
    sum14 = 0.0;
    sum15 = 0.0;
    sum16 = 0.0;
    sum17 = 0.0;
    sum18 = 0.0;
    for (j=0; j<n; j++) {
      sum1  += v[jrow]*x[18*idx[jrow]];
      sum2  += v[jrow]*x[18*idx[jrow]+1];
      sum3  += v[jrow]*x[18*idx[jrow]+2];
      sum4  += v[jrow]*x[18*idx[jrow]+3];
      sum5  += v[jrow]*x[18*idx[jrow]+4];
      sum6  += v[jrow]*x[18*idx[jrow]+5];
      sum7  += v[jrow]*x[18*idx[jrow]+6];
      sum8  += v[jrow]*x[18*idx[jrow]+7];
      sum9  += v[jrow]*x[18*idx[jrow]+8];
      sum10 += v[jrow]*x[18*idx[jrow]+9];
      sum11 += v[jrow]*x[18*idx[jrow]+10];
      sum12 += v[jrow]*x[18*idx[jrow]+11];
      sum13 += v[jrow]*x[18*idx[jrow]+12];
      sum14 += v[jrow]*x[18*idx[jrow]+13];
      sum15 += v[jrow]*x[18*idx[jrow]+14];
      sum16 += v[jrow]*x[18*idx[jrow]+15];
      sum17 += v[jrow]*x[18*idx[jrow]+16];
      sum18 += v[jrow]*x[18*idx[jrow]+17];
      jrow++;
    }
    y[18*i]    += sum1;
    y[18*i+1]  += sum2;
    y[18*i+2]  += sum3;
    y[18*i+3]  += sum4;
    y[18*i+4]  += sum5;
    y[18*i+5]  += sum6;
    y[18*i+6]  += sum7;
    y[18*i+7]  += sum8;
    y[18*i+8]  += sum9;
    y[18*i+9]  += sum10;
    y[18*i+10] += sum11;
    y[18*i+11] += sum12;
    y[18*i+12] += sum13;
    y[18*i+13] += sum14;
    y[18*i+14] += sum15;
    y[18*i+15] += sum16;
    y[18*i+16] += sum17;
    y[18*i+17] += sum18;
  }

  ierr = PetscLogFlops(36.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_18(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,alpha1,alpha2,alpha3,alpha4,alpha5,alpha6,alpha7,alpha8;
  PetscScalar       alpha9,alpha10,alpha11,alpha12,alpha13,alpha14,alpha15,alpha16,alpha17,alpha18;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx;
  PetscInt          n,i;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx     = a->j + a->i[i];
    v       = a->a + a->i[i];
    n       = a->i[i+1] - a->i[i];
    alpha1  = x[18*i];
    alpha2  = x[18*i+1];
    alpha3  = x[18*i+2];
    alpha4  = x[18*i+3];
    alpha5  = x[18*i+4];
    alpha6  = x[18*i+5];
    alpha7  = x[18*i+6];
    alpha8  = x[18*i+7];
    alpha9  = x[18*i+8];
    alpha10 = x[18*i+9];
    alpha11 = x[18*i+10];
    alpha12 = x[18*i+11];
    alpha13 = x[18*i+12];
    alpha14 = x[18*i+13];
    alpha15 = x[18*i+14];
    alpha16 = x[18*i+15];
    alpha17 = x[18*i+16];
    alpha18 = x[18*i+17];
    while (n-->0) {
      y[18*(*idx)]    += alpha1*(*v);
      y[18*(*idx)+1]  += alpha2*(*v);
      y[18*(*idx)+2]  += alpha3*(*v);
      y[18*(*idx)+3]  += alpha4*(*v);
      y[18*(*idx)+4]  += alpha5*(*v);
      y[18*(*idx)+5]  += alpha6*(*v);
      y[18*(*idx)+6]  += alpha7*(*v);
      y[18*(*idx)+7]  += alpha8*(*v);
      y[18*(*idx)+8]  += alpha9*(*v);
      y[18*(*idx)+9]  += alpha10*(*v);
      y[18*(*idx)+10] += alpha11*(*v);
      y[18*(*idx)+11] += alpha12*(*v);
      y[18*(*idx)+12] += alpha13*(*v);
      y[18*(*idx)+13] += alpha14*(*v);
      y[18*(*idx)+14] += alpha15*(*v);
      y[18*(*idx)+15] += alpha16*(*v);
      y[18*(*idx)+16] += alpha17*(*v);
      y[18*(*idx)+17] += alpha18*(*v);
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(36.0*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMult_SeqMAIJ_N(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,*sums;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j,dof = b->dof,k;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sums = y + dof*i;
    for (j=0; j<n; j++) {
      for (k=0; k<dof; k++) {
        sums[k] += v[jrow]*x[dof*idx[jrow]+k];
      }
      jrow++;
    }
  }

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

PetscErrorCode MatMultAdd_SeqMAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v;
  PetscScalar       *y,*sums;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,*ii;
  PetscInt          n,i,jrow,j,dof = b->dof,k;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    sums = y + dof*i;
    for (j=0; j<n; j++) {
      for (k=0; k<dof; k++) {
        sums[k] += v[jrow]*x[dof*idx[jrow]+k];
      }
      jrow++;
    }
  }

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

PetscErrorCode MatMultTranspose_SeqMAIJ_N(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v,*alpha;
  PetscScalar       *y;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,dof = b->dof;
  PetscInt          n,i,k;

  PetscFunctionBegin;
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecSet(yy,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx   = a->j + a->i[i];
    v     = a->a + a->i[i];
    n     = a->i[i+1] - a->i[i];
    alpha = x + dof*i;
    while (n-->0) {
      for (k=0; k<dof; k++) {
        y[dof*(*idx)+k] += alpha[k]*(*v);
      }
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(2.0*dof*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_SeqMAIJ_N(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_SeqMAIJ       *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ        *a = (Mat_SeqAIJ*)b->AIJ->data;
  const PetscScalar *x,*v,*alpha;
  PetscScalar       *y;
  PetscErrorCode    ierr;
  const PetscInt    m = b->AIJ->rmap->n,*idx,dof = b->dof;
  PetscInt          n,i,k;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    idx   = a->j + a->i[i];
    v     = a->a + a->i[i];
    n     = a->i[i+1] - a->i[i];
    alpha = x + dof*i;
    while (n-->0) {
      for (k=0; k<dof; k++) {
        y[dof*(*idx)+k] += alpha[k]*(*v);
      }
      idx++; v++;
    }
  }
  ierr = PetscLogFlops(2.0*dof*a->nz);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*===================================================================================*/
PetscErrorCode MatMult_MPIMAIJ_dof(Mat A,Vec xx,Vec yy)
{
  Mat_MPIMAIJ    *b = (Mat_MPIMAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* start the scatter */
  ierr = VecScatterBegin(b->ctx,xx,b->w,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->mult)(b->AIJ,xx,yy);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->ctx,xx,b->w,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = (*b->OAIJ->ops->multadd)(b->OAIJ,b->w,yy,yy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTranspose_MPIMAIJ_dof(Mat A,Vec xx,Vec yy)
{
  Mat_MPIMAIJ    *b = (Mat_MPIMAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = (*b->OAIJ->ops->multtranspose)(b->OAIJ,xx,b->w);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->multtranspose)(b->AIJ,xx,yy);CHKERRQ(ierr);
  ierr = VecScatterBegin(b->ctx,b->w,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->ctx,b->w,yy,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultAdd_MPIMAIJ_dof(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIMAIJ    *b = (Mat_MPIMAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  /* start the scatter */
  ierr = VecScatterBegin(b->ctx,xx,b->w,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->multadd)(b->AIJ,xx,yy,zz);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->ctx,xx,b->w,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  ierr = (*b->OAIJ->ops->multadd)(b->OAIJ,b->w,zz,zz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatMultTransposeAdd_MPIMAIJ_dof(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIMAIJ    *b = (Mat_MPIMAIJ*)A->data;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = (*b->OAIJ->ops->multtranspose)(b->OAIJ,xx,b->w);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->multtransposeadd)(b->AIJ,xx,yy,zz);CHKERRQ(ierr);
  ierr = VecScatterBegin(b->ctx,b->w,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->ctx,b->w,zz,ADD_VALUES,SCATTER_REVERSE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
PetscErrorCode MatProductSetFromOptions_SeqAIJ_SeqMAIJ(Mat C)
{
  Mat_Product    *product = C->product;

  PetscFunctionBegin;
  if (product->type == MATPRODUCT_PtAP) {
    C->ops->productsymbolic = MatProductSymbolic_PtAP_SeqAIJ_SeqMAIJ;
  } else SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat Product type %s is not supported for SeqAIJ and SeqMAIJ matrices",MatProductTypes[product->type]);
  PetscFunctionReturn(0);
}

PetscErrorCode MatProductSetFromOptions_MPIAIJ_MPIMAIJ(Mat C)
{
  PetscErrorCode ierr;
  Mat_Product    *product = C->product;
  PetscBool      flg = PETSC_FALSE;
  Mat            A=product->A,P=product->B;
  PetscInt       alg=1; /* set default algorithm */
#if !defined(PETSC_HAVE_HYPRE)
  const char     *algTypes[4] = {"scalable","nonscalable","allatonce","allatonce_merged"};
  PetscInt       nalg=4;
#else
  const char     *algTypes[5] = {"scalable","nonscalable","allatonce","allatonce_merged","hypre"};
  PetscInt       nalg=5;
#endif

  PetscFunctionBegin;
  if (product->type != MATPRODUCT_PtAP) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_SUP,"Mat Product type %s is not supported for MPIAIJ and MPIMAIJ matrices",MatProductTypes[product->type]);

  /* PtAP */
  /* Check matrix local sizes */
  if (A->rmap->rstart != P->rmap->rstart || A->rmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Arow (%D, %D) != Prow (%D,%D)",A->rmap->rstart,A->rmap->rend,P->rmap->rstart,P->rmap->rend);
  if (A->cmap->rstart != P->rmap->rstart || A->cmap->rend != P->rmap->rend) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Matrix local dimensions are incompatible, Acol (%D, %D) != Prow (%D,%D)",A->cmap->rstart,A->cmap->rend,P->rmap->rstart,P->rmap->rend);

  /* Set the default algorithm */
  ierr = PetscStrcmp(C->product->alg,"default",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
  }

  /* Get runtime option */
  ierr = PetscOptionsBegin(PetscObjectComm((PetscObject)C),((PetscObject)C)->prefix,"MatProduct_PtAP","Mat");CHKERRQ(ierr);
  ierr = PetscOptionsEList("-matproduct_ptap_via","Algorithmic approach","MatPtAP",algTypes,nalg,algTypes[alg],&alg,&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatProductSetAlgorithm(C,(MatProductAlgorithm)algTypes[alg]);CHKERRQ(ierr);
  }
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  ierr = PetscStrcmp(C->product->alg,"allatonce",&flg);CHKERRQ(ierr);
  if (flg) {
    C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIMAIJ;
    PetscFunctionReturn(0);
  }

  ierr = PetscStrcmp(C->product->alg,"allatonce_merged",&flg);CHKERRQ(ierr);
  if (flg) {
    C->ops->productsymbolic = MatProductSymbolic_PtAP_MPIAIJ_MPIMAIJ;
    PetscFunctionReturn(0);
  }

  /* Convert P from MAIJ to AIJ matrix since implementation not available for MAIJ */
  ierr = PetscInfo((PetscObject)A,"Converting from MAIJ to AIJ matrix since implementation not available for MAIJ\n");CHKERRQ(ierr);
  ierr = MatConvert(P,MATMPIAIJ,MAT_INPLACE_MATRIX,&P);CHKERRQ(ierr);
  ierr = MatProductSetFromOptions(C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ----------------------------------------------------------------*/
PetscErrorCode MatPtAPSymbolic_SeqAIJ_SeqMAIJ(Mat A,Mat PP,PetscReal fill,Mat C)
{
  PetscErrorCode     ierr;
  PetscFreeSpaceList free_space=NULL,current_space=NULL;
  Mat_SeqMAIJ        *pp       =(Mat_SeqMAIJ*)PP->data;
  Mat                P         =pp->AIJ;
  Mat_SeqAIJ         *a        =(Mat_SeqAIJ*)A->data,*p=(Mat_SeqAIJ*)P->data,*c;
  PetscInt           *pti,*ptj,*ptJ;
  PetscInt           *ci,*cj,*ptadenserow,*ptasparserow,*denserow,*sparserow,*ptaj;
  const PetscInt     an=A->cmap->N,am=A->rmap->N,pn=P->cmap->N,pm=P->rmap->N,ppdof=pp->dof;
  PetscInt           i,j,k,dof,pshift,ptnzi,arow,anzj,ptanzi,prow,pnzj,cnzi,cn;
  MatScalar          *ca;
  const PetscInt     *pi = p->i,*pj = p->j,*pjj,*ai=a->i,*aj=a->j,*ajj;

  PetscFunctionBegin;
  /* Get ij structure of P^T */
  ierr = MatGetSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);

  cn = pn*ppdof;
  /* Allocate ci array, arrays for fill computation and */
  /* free space for accumulating nonzero column info */
  ierr  = PetscMalloc1(cn+1,&ci);CHKERRQ(ierr);
  ci[0] = 0;

  /* Work arrays for rows of P^T*A */
  ierr = PetscMalloc4(an,&ptadenserow,an,&ptasparserow,cn,&denserow,cn,&sparserow);CHKERRQ(ierr);
  ierr = PetscArrayzero(ptadenserow,an);CHKERRQ(ierr);
  ierr = PetscArrayzero(denserow,cn);CHKERRQ(ierr);

  /* Set initial free space to be nnz(A) scaled by aspect ratio of P. */
  /* This should be reasonable if sparsity of PtAP is similar to that of A. */
  /* Note, aspect ratio of P is the same as the aspect ratio of SeqAIJ inside P */
  ierr          = PetscFreeSpaceGet(PetscIntMultTruncate(ai[am]/pm,pn),&free_space);CHKERRQ(ierr);
  current_space = free_space;

  /* Determine symbolic info for each row of C: */
  for (i=0; i<pn; i++) {
    ptnzi = pti[i+1] - pti[i];
    ptJ   = ptj + pti[i];
    for (dof=0; dof<ppdof; dof++) {
      ptanzi = 0;
      /* Determine symbolic row of PtA: */
      for (j=0; j<ptnzi; j++) {
        /* Expand ptJ[j] by block size and shift by dof to get the right row of A */
        arow = ptJ[j]*ppdof + dof;
        /* Nonzeros of P^T*A will be in same locations as any element of A in that row */
        anzj = ai[arow+1] - ai[arow];
        ajj  = aj + ai[arow];
        for (k=0; k<anzj; k++) {
          if (!ptadenserow[ajj[k]]) {
            ptadenserow[ajj[k]]    = -1;
            ptasparserow[ptanzi++] = ajj[k];
          }
        }
      }
      /* Using symbolic info for row of PtA, determine symbolic info for row of C: */
      ptaj = ptasparserow;
      cnzi = 0;
      for (j=0; j<ptanzi; j++) {
        /* Get offset within block of P */
        pshift = *ptaj%ppdof;
        /* Get block row of P */
        prow = (*ptaj++)/ppdof; /* integer division */
        /* P has same number of nonzeros per row as the compressed form */
        pnzj = pi[prow+1] - pi[prow];
        pjj  = pj + pi[prow];
        for (k=0;k<pnzj;k++) {
          /* Locations in C are shifted by the offset within the block */
          /* Note: we cannot use PetscLLAdd here because of the additional offset for the write location */
          if (!denserow[pjj[k]*ppdof+pshift]) {
            denserow[pjj[k]*ppdof+pshift] = -1;
            sparserow[cnzi++]             = pjj[k]*ppdof+pshift;
          }
        }
      }

      /* sort sparserow */
      ierr = PetscSortInt(cnzi,sparserow);CHKERRQ(ierr);

      /* If free space is not available, make more free space */
      /* Double the amount of total space in the list */
      if (current_space->local_remaining<cnzi) {
        ierr = PetscFreeSpaceGet(PetscIntSumTruncate(cnzi,current_space->total_array_size),&current_space);CHKERRQ(ierr);
      }

      /* Copy data into free space, and zero out denserows */
      ierr = PetscArraycpy(current_space->array,sparserow,cnzi);CHKERRQ(ierr);

      current_space->array           += cnzi;
      current_space->local_used      += cnzi;
      current_space->local_remaining -= cnzi;

      for (j=0; j<ptanzi; j++) ptadenserow[ptasparserow[j]] = 0;
      for (j=0; j<cnzi; j++) denserow[sparserow[j]] = 0;

      /* Aside: Perhaps we should save the pta info for the numerical factorization. */
      /*        For now, we will recompute what is needed. */
      ci[i*ppdof+1+dof] = ci[i*ppdof+dof] + cnzi;
    }
  }
  /* nnz is now stored in ci[ptm], column indices are in the list of free space */
  /* Allocate space for cj, initialize cj, and */
  /* destroy list of free space and other temporary array(s) */
  ierr = PetscMalloc1(ci[cn]+1,&cj);CHKERRQ(ierr);
  ierr = PetscFreeSpaceContiguous(&free_space,cj);CHKERRQ(ierr);
  ierr = PetscFree4(ptadenserow,ptasparserow,denserow,sparserow);CHKERRQ(ierr);

  /* Allocate space for ca */
  ierr = PetscCalloc1(ci[cn]+1,&ca);CHKERRQ(ierr);

  /* put together the new matrix */
  ierr = MatSetSeqAIJWithArrays_private(PetscObjectComm((PetscObject)A),cn,cn,ci,cj,ca,NULL,C);CHKERRQ(ierr);
  ierr = MatSetBlockSize(C,pp->dof);CHKERRQ(ierr);

  /* MatCreateSeqAIJWithArrays flags matrix so PETSc doesn't free the user's arrays. */
  /* Since these are PETSc arrays, change flags to free them as necessary. */
  c          = (Mat_SeqAIJ*)(C->data);
  c->free_a  = PETSC_TRUE;
  c->free_ij = PETSC_TRUE;
  c->nonew   = 0;

  C->ops->ptapnumeric    = MatPtAPNumeric_SeqAIJ_SeqMAIJ;
  C->ops->productnumeric = MatProductNumeric_PtAP;

  /* Clean up. */
  ierr = MatRestoreSymbolicTranspose_SeqAIJ(P,&pti,&ptj);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatPtAPNumeric_SeqAIJ_SeqMAIJ(Mat A,Mat PP,Mat C)
{
  /* This routine requires testing -- first draft only */
  PetscErrorCode  ierr;
  Mat_SeqMAIJ     *pp=(Mat_SeqMAIJ*)PP->data;
  Mat             P  =pp->AIJ;
  Mat_SeqAIJ      *a = (Mat_SeqAIJ*) A->data;
  Mat_SeqAIJ      *p = (Mat_SeqAIJ*) P->data;
  Mat_SeqAIJ      *c = (Mat_SeqAIJ*) C->data;
  const PetscInt  *ai=a->i,*aj=a->j,*pi=p->i,*pj=p->j,*pJ,*pjj;
  const PetscInt  *ci=c->i,*cj=c->j,*cjj;
  const PetscInt  am =A->rmap->N,cn=C->cmap->N,cm=C->rmap->N,ppdof=pp->dof;
  PetscInt        i,j,k,pshift,poffset,anzi,pnzi,apnzj,nextap,pnzj,prow,crow,*apj,*apjdense;
  const MatScalar *aa=a->a,*pa=p->a,*pA,*paj;
  MatScalar       *ca=c->a,*caj,*apa;

  PetscFunctionBegin;
  /* Allocate temporary array for storage of one row of A*P */
  ierr = PetscCalloc3(cn,&apa,cn,&apj,cn,&apjdense);CHKERRQ(ierr);

  /* Clear old values in C */
  ierr = PetscArrayzero(ca,ci[cm]);CHKERRQ(ierr);

  for (i=0; i<am; i++) {
    /* Form sparse row of A*P */
    anzi  = ai[i+1] - ai[i];
    apnzj = 0;
    for (j=0; j<anzi; j++) {
      /* Get offset within block of P */
      pshift = *aj%ppdof;
      /* Get block row of P */
      prow = *aj++/ppdof;   /* integer division */
      pnzj = pi[prow+1] - pi[prow];
      pjj  = pj + pi[prow];
      paj  = pa + pi[prow];
      for (k=0; k<pnzj; k++) {
        poffset = pjj[k]*ppdof+pshift;
        if (!apjdense[poffset]) {
          apjdense[poffset] = -1;
          apj[apnzj++]      = poffset;
        }
        apa[poffset] += (*aa)*paj[k];
      }
      ierr = PetscLogFlops(2.0*pnzj);CHKERRQ(ierr);
      aa++;
    }

    /* Sort the j index array for quick sparse axpy. */
    /* Note: a array does not need sorting as it is in dense storage locations. */
    ierr = PetscSortInt(apnzj,apj);CHKERRQ(ierr);

    /* Compute P^T*A*P using outer product (P^T)[:,j]*(A*P)[j,:]. */
    prow    = i/ppdof; /* integer division */
    pshift  = i%ppdof;
    poffset = pi[prow];
    pnzi    = pi[prow+1] - poffset;
    /* Reset pJ and pA so we can traverse the same row of P 'dof' times. */
    pJ = pj+poffset;
    pA = pa+poffset;
    for (j=0; j<pnzi; j++) {
      crow = (*pJ)*ppdof+pshift;
      cjj  = cj + ci[crow];
      caj  = ca + ci[crow];
      pJ++;
      /* Perform sparse axpy operation.  Note cjj includes apj. */
      for (k=0,nextap=0; nextap<apnzj; k++) {
        if (cjj[k] == apj[nextap]) caj[k] += (*pA)*apa[apj[nextap++]];
      }
      ierr = PetscLogFlops(2.0*apnzj);CHKERRQ(ierr);
      pA++;
    }

    /* Zero the current row info for A*P */
    for (j=0; j<apnzj; j++) {
      apa[apj[j]]      = 0.;
      apjdense[apj[j]] = 0;
    }
  }

  /* Assemble the final matrix and clean up */
  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = PetscFree3(apa,apj,apjdense);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatProductSymbolic_PtAP_SeqAIJ_SeqMAIJ(Mat C)
{
  PetscErrorCode      ierr;
  Mat_Product         *product = C->product;
  Mat                 A=product->A,P=product->B;

  PetscFunctionBegin;
  ierr = MatPtAPSymbolic_SeqAIJ_SeqMAIJ(A,P,product->fill,C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIMAIJ(Mat A,Mat PP,PetscReal fill,Mat *C)
{
  PetscFunctionBegin;
  SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatPtAPSymbolic is not implemented for MPIMAIJ matrix yet");
}

PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIMAIJ(Mat A,Mat PP,Mat C)
{
  PetscFunctionBegin;
  SETERRQ(PetscObjectComm((PetscObject)A),PETSC_ERR_SUP,"MatPtAPNumeric is not implemented for MPIMAIJ matrix yet");
}

PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIXAIJ_allatonce(Mat,Mat,PetscInt,Mat);

PETSC_INTERN PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIMAIJ_allatonce(Mat A,Mat P,Mat C)
{
  Mat_MPIMAIJ     *maij = (Mat_MPIMAIJ*)P->data;
  PetscErrorCode  ierr;

  PetscFunctionBegin;

  ierr = MatPtAPNumeric_MPIAIJ_MPIXAIJ_allatonce(A,maij->A,maij->dof,C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIXAIJ_allatonce(Mat,Mat,PetscInt,PetscReal,Mat);

PETSC_INTERN PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIMAIJ_allatonce(Mat A,Mat P,PetscReal fill,Mat C)
{
  Mat_MPIMAIJ     *maij = (Mat_MPIMAIJ*)P->data;
  PetscErrorCode  ierr;

  PetscFunctionBegin;
  ierr = MatPtAPSymbolic_MPIAIJ_MPIXAIJ_allatonce(A,maij->A,maij->dof,fill,C);CHKERRQ(ierr);
  C->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIMAIJ_allatonce;
  PetscFunctionReturn(0);
}

PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIXAIJ_allatonce_merged(Mat,Mat,PetscInt,Mat);

PETSC_INTERN PetscErrorCode MatPtAPNumeric_MPIAIJ_MPIMAIJ_allatonce_merged(Mat A,Mat P,Mat C)
{
  Mat_MPIMAIJ     *maij = (Mat_MPIMAIJ*)P->data;
  PetscErrorCode  ierr;

  PetscFunctionBegin;

  ierr = MatPtAPNumeric_MPIAIJ_MPIXAIJ_allatonce_merged(A,maij->A,maij->dof,C);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIXAIJ_allatonce_merged(Mat,Mat,PetscInt,PetscReal,Mat);

PETSC_INTERN PetscErrorCode MatPtAPSymbolic_MPIAIJ_MPIMAIJ_allatonce_merged(Mat A,Mat P,PetscReal fill,Mat C)
{
  Mat_MPIMAIJ     *maij = (Mat_MPIMAIJ*)P->data;
  PetscErrorCode  ierr;

  PetscFunctionBegin;

  ierr = MatPtAPSymbolic_MPIAIJ_MPIXAIJ_allatonce_merged(A,maij->A,maij->dof,fill,C);CHKERRQ(ierr);
  C->ops->ptapnumeric = MatPtAPNumeric_MPIAIJ_MPIMAIJ_allatonce_merged;
  PetscFunctionReturn(0);
}

PETSC_INTERN PetscErrorCode MatProductSymbolic_PtAP_MPIAIJ_MPIMAIJ(Mat C)
{
  PetscErrorCode      ierr;
  Mat_Product         *product = C->product;
  Mat                 A=product->A,P=product->B;
  PetscBool           flg;

  PetscFunctionBegin;
  ierr = PetscStrcmp(product->alg,"allatonce",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatPtAPSymbolic_MPIAIJ_MPIMAIJ_allatonce(A,P,product->fill,C);CHKERRQ(ierr);
    C->ops->productnumeric = MatProductNumeric_PtAP;
    PetscFunctionReturn(0);
  }

  ierr = PetscStrcmp(product->alg,"allatonce_merged",&flg);CHKERRQ(ierr);
  if (flg) {
    ierr = MatPtAPSymbolic_MPIAIJ_MPIMAIJ_allatonce_merged(A,P,product->fill,C);CHKERRQ(ierr);
    C->ops->productnumeric = MatProductNumeric_PtAP;
    PetscFunctionReturn(0);
  }

  SETERRQ(PetscObjectComm((PetscObject)C),PETSC_ERR_SUP,"Mat Product Algorithm is not supported");
}

PETSC_INTERN PetscErrorCode MatConvert_SeqMAIJ_SeqAIJ(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
{
  Mat_SeqMAIJ    *b   = (Mat_SeqMAIJ*)A->data;
  Mat            a    = b->AIJ,B;
  Mat_SeqAIJ     *aij = (Mat_SeqAIJ*)a->data;
  PetscErrorCode ierr;
  PetscInt       m,n,i,ncols,*ilen,nmax = 0,*icols,j,k,ii,dof = b->dof;
  PetscInt       *cols;
  PetscScalar    *vals;

  PetscFunctionBegin;
  ierr = MatGetSize(a,&m,&n);CHKERRQ(ierr);
  ierr = PetscMalloc1(dof*m,&ilen);CHKERRQ(ierr);
  for (i=0; i<m; i++) {
    nmax = PetscMax(nmax,aij->ilen[i]);
    for (j=0; j<dof; j++) ilen[dof*i+j] = aij->ilen[i];
  }
  ierr = MatCreate(PETSC_COMM_SELF,&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,dof*m,dof*n,dof*m,dof*n);CHKERRQ(ierr);
  ierr = MatSetType(B,newtype);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(B,0,ilen);CHKERRQ(ierr);
  ierr = PetscFree(ilen);CHKERRQ(ierr);
  ierr = PetscMalloc1(nmax,&icols);CHKERRQ(ierr);
  ii   = 0;
  for (i=0; i<m; i++) {
    ierr = MatGetRow_SeqAIJ(a,i,&ncols,&cols,&vals);CHKERRQ(ierr);
    for (j=0; j<dof; j++) {
      for (k=0; k<ncols; k++) icols[k] = dof*cols[k]+j;
      ierr = MatSetValues_SeqAIJ(B,1,&ii,ncols,icols,vals,INSERT_VALUES);CHKERRQ(ierr);
      ii++;
    }
    ierr = MatRestoreRow_SeqAIJ(a,i,&ncols,&cols,&vals);CHKERRQ(ierr);
  }
  ierr = PetscFree(icols);CHKERRQ(ierr);
  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  if (reuse == MAT_INPLACE_MATRIX) {
    ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(0);
}

#include <../src/mat/impls/aij/mpi/mpiaij.h>

PETSC_INTERN PetscErrorCode MatConvert_MPIMAIJ_MPIAIJ(Mat A, MatType newtype,MatReuse reuse,Mat *newmat)
{
  Mat_MPIMAIJ    *maij   = (Mat_MPIMAIJ*)A->data;
  Mat            MatAIJ  = ((Mat_SeqMAIJ*)maij->AIJ->data)->AIJ,B;
  Mat            MatOAIJ = ((Mat_SeqMAIJ*)maij->OAIJ->data)->AIJ;
  Mat_SeqAIJ     *AIJ    = (Mat_SeqAIJ*) MatAIJ->data;
  Mat_SeqAIJ     *OAIJ   =(Mat_SeqAIJ*) MatOAIJ->data;
  Mat_MPIAIJ     *mpiaij = (Mat_MPIAIJ*) maij->A->data;
  PetscInt       dof     = maij->dof,i,j,*dnz = NULL,*onz = NULL,nmax = 0,onmax = 0;
  PetscInt       *oicols = NULL,*icols = NULL,ncols,*cols = NULL,oncols,*ocols = NULL;
  PetscInt       rstart,cstart,*garray,ii,k;
  PetscErrorCode ierr;
  PetscScalar    *vals,*ovals;

  PetscFunctionBegin;
  ierr = PetscMalloc2(A->rmap->n,&dnz,A->rmap->n,&onz);CHKERRQ(ierr);
  for (i=0; i<A->rmap->n/dof; i++) {
    nmax  = PetscMax(nmax,AIJ->ilen[i]);
    onmax = PetscMax(onmax,OAIJ->ilen[i]);
    for (j=0; j<dof; j++) {
      dnz[dof*i+j] = AIJ->ilen[i];
      onz[dof*i+j] = OAIJ->ilen[i];
    }
  }
  ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
  ierr = MatSetSizes(B,A->rmap->n,A->cmap->n,A->rmap->N,A->cmap->N);CHKERRQ(ierr);
  ierr = MatSetType(B,newtype);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(B,0,dnz,0,onz);CHKERRQ(ierr);
  ierr = MatSetBlockSize(B,dof);CHKERRQ(ierr);
  ierr = PetscFree2(dnz,onz);CHKERRQ(ierr);

  ierr   = PetscMalloc2(nmax,&icols,onmax,&oicols);CHKERRQ(ierr);
  rstart = dof*maij->A->rmap->rstart;
  cstart = dof*maij->A->cmap->rstart;
  garray = mpiaij->garray;

  ii = rstart;
  for (i=0; i<A->rmap->n/dof; i++) {
    ierr = MatGetRow_SeqAIJ(MatAIJ,i,&ncols,&cols,&vals);CHKERRQ(ierr);
    ierr = MatGetRow_SeqAIJ(MatOAIJ,i,&oncols,&ocols,&ovals);CHKERRQ(ierr);
    for (j=0; j<dof; j++) {
      for (k=0; k<ncols; k++) {
        icols[k] = cstart + dof*cols[k]+j;
      }
      for (k=0; k<oncols; k++) {
        oicols[k] = dof*garray[ocols[k]]+j;
      }
      ierr = MatSetValues_MPIAIJ(B,1,&ii,ncols,icols,vals,INSERT_VALUES);CHKERRQ(ierr);
      ierr = MatSetValues_MPIAIJ(B,1,&ii,oncols,oicols,ovals,INSERT_VALUES);CHKERRQ(ierr);
      ii++;
    }
    ierr = MatRestoreRow_SeqAIJ(MatAIJ,i,&ncols,&cols,&vals);CHKERRQ(ierr);
    ierr = MatRestoreRow_SeqAIJ(MatOAIJ,i,&oncols,&ocols,&ovals);CHKERRQ(ierr);
  }
  ierr = PetscFree2(icols,oicols);CHKERRQ(ierr);

  ierr = MatAssemblyBegin(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(B,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  if (reuse == MAT_INPLACE_MATRIX) {
    PetscInt refct = ((PetscObject)A)->refct; /* save ((PetscObject)A)->refct */
    ((PetscObject)A)->refct = 1;

    ierr = MatHeaderReplace(A,&B);CHKERRQ(ierr);

    ((PetscObject)A)->refct = refct; /* restore ((PetscObject)A)->refct */
  } else {
    *newmat = B;
  }
  PetscFunctionReturn(0);
}

PetscErrorCode MatCreateSubMatrix_MAIJ(Mat mat,IS isrow,IS iscol,MatReuse cll,Mat *newmat)
{
  PetscErrorCode ierr;
  Mat            A;

  PetscFunctionBegin;
  ierr = MatConvert(mat,MATAIJ,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
  ierr = MatCreateSubMatrix(A,isrow,iscol,cll,newmat);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

PetscErrorCode MatCreateSubMatrices_MAIJ(Mat mat,PetscInt n,const IS irow[],const IS icol[],MatReuse scall,Mat *submat[])
{
  PetscErrorCode ierr;
  Mat            A;

  PetscFunctionBegin;
  ierr = MatConvert(mat,MATAIJ,MAT_INITIAL_MATRIX,&A);CHKERRQ(ierr);
  ierr = MatCreateSubMatrices(A,n,irow,icol,scall,submat);CHKERRQ(ierr);
  ierr = MatDestroy(&A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ---------------------------------------------------------------------------------- */
/*@
  MatCreateMAIJ - Creates a matrix type providing restriction and interpolation
  operations for multicomponent problems.  It interpolates each component the same
  way independently.  The matrix type is based on MATSEQAIJ for sequential matrices,
  and MATMPIAIJ for distributed matrices.

  Collective

  Input Parameters:
+ A - the AIJ matrix describing the action on blocks
- dof - the block size (number of components per node)

  Output Parameter:
. maij - the new MAIJ matrix

  Operations provided:
+ MatMult
. MatMultTranspose
. MatMultAdd
. MatMultTransposeAdd
- MatView

  Level: advanced

.seealso: MatMAIJGetAIJ(), MatMAIJRedimension(), MATMAIJ
@*/
PetscErrorCode  MatCreateMAIJ(Mat A,PetscInt dof,Mat *maij)
{
  PetscErrorCode ierr;
  PetscMPIInt    size;
  PetscInt       n;
  Mat            B;
#if defined(PETSC_HAVE_CUDA)
  /* hack to prevent conversion to AIJ format for CUDA when used inside a parallel MAIJ */
  PetscBool      convert = dof < 0 ? PETSC_FALSE : PETSC_TRUE;
#endif

  PetscFunctionBegin;
  dof  = PetscAbs(dof);
  ierr = PetscObjectReference((PetscObject)A);CHKERRQ(ierr);

  if (dof == 1) *maij = A;
  else {
    ierr = MatCreate(PetscObjectComm((PetscObject)A),&B);CHKERRQ(ierr);
    /* propagate vec type */
    ierr = MatSetVecType(B,A->defaultvectype);CHKERRQ(ierr);
    ierr = MatSetSizes(B,dof*A->rmap->n,dof*A->cmap->n,dof*A->rmap->N,dof*A->cmap->N);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(B->rmap,dof);CHKERRQ(ierr);
    ierr = PetscLayoutSetBlockSize(B->cmap,dof);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(B->rmap);CHKERRQ(ierr);
    ierr = PetscLayoutSetUp(B->cmap);CHKERRQ(ierr);

    B->assembled = PETSC_TRUE;

    ierr = MPI_Comm_size(PetscObjectComm((PetscObject)A),&size);CHKERRMPI(ierr);
    if (size == 1) {
      Mat_SeqMAIJ *b;

      ierr = MatSetType(B,MATSEQMAIJ);CHKERRQ(ierr);

      B->ops->setup   = NULL;
      B->ops->destroy = MatDestroy_SeqMAIJ;
      B->ops->view    = MatView_SeqMAIJ;

      b               = (Mat_SeqMAIJ*)B->data;
      b->dof          = dof;
      b->AIJ          = A;

      if (dof == 2) {
        B->ops->mult             = MatMult_SeqMAIJ_2;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_2;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_2;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_2;
      } else if (dof == 3) {
        B->ops->mult             = MatMult_SeqMAIJ_3;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_3;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_3;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_3;
      } else if (dof == 4) {
        B->ops->mult             = MatMult_SeqMAIJ_4;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_4;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_4;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_4;
      } else if (dof == 5) {
        B->ops->mult             = MatMult_SeqMAIJ_5;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_5;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_5;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_5;
      } else if (dof == 6) {
        B->ops->mult             = MatMult_SeqMAIJ_6;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_6;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_6;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_6;
      } else if (dof == 7) {
        B->ops->mult             = MatMult_SeqMAIJ_7;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_7;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_7;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_7;
      } else if (dof == 8) {
        B->ops->mult             = MatMult_SeqMAIJ_8;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_8;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_8;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_8;
      } else if (dof == 9) {
        B->ops->mult             = MatMult_SeqMAIJ_9;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_9;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_9;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_9;
      } else if (dof == 10) {
        B->ops->mult             = MatMult_SeqMAIJ_10;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_10;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_10;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_10;
      } else if (dof == 11) {
        B->ops->mult             = MatMult_SeqMAIJ_11;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_11;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_11;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_11;
      } else if (dof == 16) {
        B->ops->mult             = MatMult_SeqMAIJ_16;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_16;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_16;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_16;
      } else if (dof == 18) {
        B->ops->mult             = MatMult_SeqMAIJ_18;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_18;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_18;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_18;
      } else {
        B->ops->mult             = MatMult_SeqMAIJ_N;
        B->ops->multadd          = MatMultAdd_SeqMAIJ_N;
        B->ops->multtranspose    = MatMultTranspose_SeqMAIJ_N;
        B->ops->multtransposeadd = MatMultTransposeAdd_SeqMAIJ_N;
      }
#if defined(PETSC_HAVE_CUDA)
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqmaij_seqaijcusparse_C",MatConvert_SeqMAIJ_SeqAIJ);CHKERRQ(ierr);
#endif
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_seqmaij_seqaij_C",MatConvert_SeqMAIJ_SeqAIJ);CHKERRQ(ierr);
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_seqaij_seqmaij_C",MatProductSetFromOptions_SeqAIJ_SeqMAIJ);CHKERRQ(ierr);
    } else {
      Mat_MPIAIJ  *mpiaij = (Mat_MPIAIJ*)A->data;
      Mat_MPIMAIJ *b;
      IS          from,to;
      Vec         gvec;

      ierr = MatSetType(B,MATMPIMAIJ);CHKERRQ(ierr);

      B->ops->setup            = NULL;
      B->ops->destroy          = MatDestroy_MPIMAIJ;
      B->ops->view             = MatView_MPIMAIJ;

      b      = (Mat_MPIMAIJ*)B->data;
      b->dof = dof;
      b->A   = A;

      ierr = MatCreateMAIJ(mpiaij->A,-dof,&b->AIJ);CHKERRQ(ierr);
      ierr = MatCreateMAIJ(mpiaij->B,-dof,&b->OAIJ);CHKERRQ(ierr);

      ierr = VecGetSize(mpiaij->lvec,&n);CHKERRQ(ierr);
      ierr = VecCreate(PETSC_COMM_SELF,&b->w);CHKERRQ(ierr);
      ierr = VecSetSizes(b->w,n*dof,n*dof);CHKERRQ(ierr);
      ierr = VecSetBlockSize(b->w,dof);CHKERRQ(ierr);
      ierr = VecSetType(b->w,VECSEQ);CHKERRQ(ierr);

      /* create two temporary Index sets for build scatter gather */
      ierr = ISCreateBlock(PetscObjectComm((PetscObject)A),dof,n,mpiaij->garray,PETSC_COPY_VALUES,&from);CHKERRQ(ierr);
      ierr = ISCreateStride(PETSC_COMM_SELF,n*dof,0,1,&to);CHKERRQ(ierr);

      /* create temporary global vector to generate scatter context */
      ierr = VecCreateMPIWithArray(PetscObjectComm((PetscObject)A),dof,dof*A->cmap->n,dof*A->cmap->N,NULL,&gvec);CHKERRQ(ierr);

      /* generate the scatter context */
      ierr = VecScatterCreate(gvec,from,b->w,to,&b->ctx);CHKERRQ(ierr);

      ierr = ISDestroy(&from);CHKERRQ(ierr);
      ierr = ISDestroy(&to);CHKERRQ(ierr);
      ierr = VecDestroy(&gvec);CHKERRQ(ierr);

      B->ops->mult             = MatMult_MPIMAIJ_dof;
      B->ops->multtranspose    = MatMultTranspose_MPIMAIJ_dof;
      B->ops->multadd          = MatMultAdd_MPIMAIJ_dof;
      B->ops->multtransposeadd = MatMultTransposeAdd_MPIMAIJ_dof;

#if defined(PETSC_HAVE_CUDA)
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpimaij_mpiaijcusparse_C",MatConvert_MPIMAIJ_MPIAIJ);CHKERRQ(ierr);
#endif
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatConvert_mpimaij_mpiaij_C",MatConvert_MPIMAIJ_MPIAIJ);CHKERRQ(ierr);
      ierr = PetscObjectComposeFunction((PetscObject)B,"MatProductSetFromOptions_mpiaij_mpimaij_C",MatProductSetFromOptions_MPIAIJ_MPIMAIJ);CHKERRQ(ierr);
    }
    B->ops->createsubmatrix   = MatCreateSubMatrix_MAIJ;
    B->ops->createsubmatrices = MatCreateSubMatrices_MAIJ;
    ierr = MatSetUp(B);CHKERRQ(ierr);
#if defined(PETSC_HAVE_CUDA)
    /* temporary until we have CUDA implementation of MAIJ */
    {
      PetscBool flg;
      if (convert) {
        ierr = PetscObjectTypeCompareAny((PetscObject)A,&flg,MATSEQAIJCUSPARSE,MATMPIAIJCUSPARSE,MATAIJCUSPARSE,"");CHKERRQ(ierr);
        if (flg) {
          ierr = MatConvert(B,((PetscObject)A)->type_name,MAT_INPLACE_MATRIX,&B);CHKERRQ(ierr);
        }
      }
    }
#endif
    *maij = B;
  }
  PetscFunctionReturn(0);
}