xref: /petsc/src/mat/impls/maij/maij.c (revision d72c5c086a9ad2ca28c7153cd0684f41320be008)

/*$Id: maij.c,v 1.6 2000/06/27 17:46:45 bsmith Exp bsmith $*/
/*
    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/aij/mpi/mpiaij.h"

typedef struct {
  int        dof;         /* number of components */
  Mat        AIJ;        /* representation of interpolation for one component */
} Mat_SeqMAIJ;

typedef struct {
  int        dof;         /* number of components */
  Mat        AIJ,OAIJ;    /* representation of interpolation for one component */
  Mat        A;
  VecScatter ctx;         /* update ghost points for parallel case */
  Vec        w;           /* work space for ghost values for parallel case */
} Mat_MPIMAIJ;

#undef __FUNC__
#define __FUNC__ /*<a name="MatDestroy_SeqMAIJ"></a>*/"MatDestroy_SeqMAIJ"
int MatDestroy_SeqMAIJ(Mat A)
{
  int         ierr;
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;

  PetscFunctionBegin;
  if (b->AIJ) {
    ierr = MatDestroy(b->AIJ);CHKERRQ(ierr);
  }
  ierr = PetscFree(b);CHKERRQ(ierr);
  PetscHeaderDestroy(A);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatDestroy_MPIMAIJ"></a>*/"MatDestroy_MPIMAIJ"
int MatDestroy_MPIMAIJ(Mat A)
{
  int         ierr;
  Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;

  PetscFunctionBegin;
  if (b->A) {
    ierr = MatDestroy(b->A);CHKERRQ(ierr);
  }
  if (b->AIJ) {
    ierr = MatDestroy(b->AIJ);CHKERRQ(ierr);
  }
  if (b->OAIJ) {
    ierr = MatDestroy(b->OAIJ);CHKERRQ(ierr);
  }
  if (b->ctx) {
    ierr = VecScatterDestroy(b->ctx);CHKERRQ(ierr);
  }
  if (b->w) {
    ierr = VecDestroy(b->w);CHKERRQ(ierr);
  }
  ierr = PetscFree(b);CHKERRQ(ierr);
  PetscHeaderDestroy(A);
  PetscFunctionReturn(0);
}

EXTERN_C_BEGIN
#undef __FUNC__
#define __FUNC__ /*<a name="MatCreate_MAIJ"></a>*/"MatCreate_MAIJ"
int MatCreate_MAIJ(Mat A)
{
  int         ierr;
  Mat_MPIMAIJ *b;

  PetscFunctionBegin;
  A->data             = (void*)(b = PetscNew(Mat_MPIMAIJ));CHKPTRQ(b);
  ierr = PetscMemzero(b,sizeof(Mat_MPIMAIJ));CHKERRQ(ierr);
  ierr = PetscMemzero(A->ops,sizeof(struct _MatOps));CHKERRQ(ierr);
  A->factor           = 0;
  A->mapping          = 0;

  b->AIJ  = 0;
  b->dof  = 0;
  b->OAIJ = 0;
  b->ctx  = 0;
  b->w    = 0;
  PetscFunctionReturn(0);
}
EXTERN_C_END

/* --------------------------------------------------------------------------------------*/
#undef __FUNC__
#define __FUNC__ /*<a name="MatMult_SeqMAIJ_2"></a>*/"MatMult_SeqMAIJ_2"
int MatMult_SeqMAIJ_2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,sum1, sum2;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(4*a->nz - 2*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTranspose_SeqMAIJ_2"></a>*/"MatMultTranspose_SeqMAIJ_2"
int MatMultTranspose_SeqMAIJ_2(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,alpha1,alpha2,zero = 0.0;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  ierr = VecSet(&zero,yy);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;}
  }
  PLogFlops(4*a->nz - 2*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultAdd_SeqMAIJ_2"></a>*/"MatMultAdd_SeqMAIJ_2"
int 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;
  Scalar      *x,*y,*v,sum1, sum2;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(4*a->nz - 2*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTransposeAdd_SeqMAIJ_2"></a>*/"MatMultTransposeAdd_SeqMAIJ_2"
int 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;
  Scalar      *x,*y,*v,alpha1,alpha2;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx   = a->j + a->i[i] + shift;
    v     = a->a + a->i[i] + shift;
    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++;}
  }
  PLogFlops(4*a->nz - 2*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
/* --------------------------------------------------------------------------------------*/
#undef __FUNC__
#define __FUNC__ /*<a name="MatMult_SeqMAIJ_3"></a>*/"MatMult_SeqMAIJ_3"
int MatMult_SeqMAIJ_3(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,sum1, sum2, sum3;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(6*a->nz - 3*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTranspose_SeqMAIJ_3"></a>*/"MatMultTranspose_SeqMAIJ_3"
int MatMultTranspose_SeqMAIJ_3(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3,zero = 0.0;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  ierr = VecSet(&zero,yy);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(6*a->nz - 3*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultAdd_SeqMAIJ_3"></a>*/"MatMultAdd_SeqMAIJ_3"
int 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;
  Scalar      *x,*y,*v,sum1, sum2, sum3;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(6*a->nz);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTransposeAdd_SeqMAIJ_3"></a>*/"MatMultTransposeAdd_SeqMAIJ_3"
int 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;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(6*a->nz);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ------------------------------------------------------------------------------*/
#undef __FUNC__
#define __FUNC__ /*<a name="MatMult_SeqMAIJ_4"></a>*/"MatMult_SeqMAIJ_4"
int MatMult_SeqMAIJ_4(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,sum1, sum2, sum3, sum4;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(8*a->nz - 4*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTranspose_SeqMAIJ_4"></a>*/"MatMultTranspose_SeqMAIJ_4"
int MatMultTranspose_SeqMAIJ_4(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3,alpha4,zero = 0.0;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  ierr = VecSet(&zero,yy);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(8*a->nz - 4*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultAdd_SeqMAIJ_4"></a>*/"MatMultAdd_SeqMAIJ_4"
int 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;
  Scalar      *x,*y,*v,sum1, sum2, sum3, sum4;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(8*a->nz - 4*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTransposeAdd_SeqMAIJ_4"></a>*/"MatMultTransposeAdd_SeqMAIJ_4"
int 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;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3,alpha4;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(8*a->nz - 4*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);

}

/* ------------------------------------------------------------------------------*/
#undef __FUNC__
#define __FUNC__ /*<a name="MatMult_SeqMAIJ_5"></a>*/"MatMult_SeqMAIJ_5"
int MatMult_SeqMAIJ_5(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,sum1, sum2, sum3, sum4, sum5;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(10*a->nz - 5*m);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTranspose_SeqMAIJ_5"></a>*/"MatMultTranspose_SeqMAIJ_5"
int MatMultTranspose_SeqMAIJ_5(Mat A,Vec xx,Vec yy)
{
  Mat_SeqMAIJ *b = (Mat_SeqMAIJ*)A->data;
  Mat_SeqAIJ  *a = (Mat_SeqAIJ*)b->AIJ->data;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3,alpha4,alpha5,zero = 0.0;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  ierr = VecSet(&zero,yy);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(yy,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(10*a->nz - 5*a->n);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(yy,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultAdd_SeqMAIJ_5"></a>*/"MatMultAdd_SeqMAIJ_5"
int 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;
  Scalar      *x,*y,*v,sum1, sum2, sum3, sum4, sum5;
  int         ierr,m = a->m,*idx,shift = a->indexshift,*ii;
  int         n,i,jrow,j;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  x    = x + shift;    /* shift for Fortran start by 1 indexing */
  idx  = a->j;
  v    = a->a;
  ii   = a->i;

  v    += shift; /* shift for Fortran start by 1 indexing */
  idx  += shift;
  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;
  }

  PLogFlops(10*a->nz);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTransposeAdd_SeqMAIJ_5"></a>*/"MatMultTransposeAdd_SeqMAIJ_5"
int 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;
  Scalar      *x,*y,*v,alpha1,alpha2,alpha3,alpha4,alpha5;
  int         ierr,m = a->m,n,i,*idx,shift = a->indexshift;

  PetscFunctionBegin;
  if (yy != zz) {ierr = VecCopy(yy,zz);CHKERRQ(ierr);}
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArray(zz,&y);CHKERRQ(ierr);
  y = y + shift; /* shift for Fortran start by 1 indexing */
  for (i=0; i<m; i++) {
    idx    = a->j + a->i[i] + shift;
    v      = a->a + a->i[i] + shift;
    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++;
    }
  }
  PLogFlops(10*a->nz);
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArray(zz,&y);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*===================================================================================*/
#undef __FUNC__
#define __FUNC__ /*<a name="MatMult_MPIMAIJ_dof"></a>*/"MatMult_MPIMAIJ_dof"
int MatMult_MPIMAIJ_dof(Mat A,Vec xx,Vec yy)
{
  Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;
  int         ierr;
  PetscFunctionBegin;

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

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTranspose_MPIMAIJ_dof"></a>*/"MatMultTranspose_MPIMAIJ_dof"
int MatMultTranspose_MPIMAIJ_dof(Mat A,Vec xx,Vec yy)
{
  Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;
  int         ierr;
  PetscFunctionBegin;
  ierr = (*b->OAIJ->ops->multtranspose)(b->OAIJ,xx,b->w);CHKERRQ(ierr);
  ierr = VecScatterBegin(b->w,yy,ADD_VALUES,SCATTER_REVERSE,b->ctx);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->multtranspose)(b->AIJ,xx,yy);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->w,yy,ADD_VALUES,SCATTER_REVERSE,b->ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultAdd_MPIMAIJ_dof"></a>*/"MatMultAdd_MPIMAIJ_dof"
int MatMultAdd_MPIMAIJ_dof(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;
  int         ierr;
  PetscFunctionBegin;

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

#undef __FUNC__
#define __FUNC__ /*<a name="MatMultTransposeAdd_MPIMAIJ_dof"></a>*/"MatMultTransposeAdd_MPIMAIJ_dof"
int MatMultTransposeAdd_MPIMAIJ_dof(Mat A,Vec xx,Vec yy,Vec zz)
{
  Mat_MPIMAIJ *b = (Mat_MPIMAIJ*)A->data;
  int         ierr;
  PetscFunctionBegin;
  ierr = (*b->OAIJ->ops->multtranspose)(b->OAIJ,xx,b->w);CHKERRQ(ierr);
  ierr = VecScatterBegin(b->w,zz,ADD_VALUES,SCATTER_REVERSE,b->ctx);CHKERRQ(ierr);
  ierr = (*b->AIJ->ops->multtransposeadd)(b->AIJ,xx,yy,zz);CHKERRQ(ierr);
  ierr = VecScatterEnd(b->w,zz,ADD_VALUES,SCATTER_REVERSE,b->ctx);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/* ---------------------------------------------------------------------------------- */
#undef __FUNC__
#define __FUNC__ /*<a name="MatCreateMAIJ"></a>*/"MatCreateMAIJ"
int MatCreateMAIJ(Mat A,int dof,Mat *maij)
{
  int         ierr,size,n;
  Mat_MPIMAIJ *b;
  Mat         B;

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

  if (dof == 1) {
    *maij = A;
  } else {
    ierr = MATCreate(A->comm,dof*A->m,dof*A->n,dof*A->M,dof*A->N,&B);CHKERRQ(ierr);
    ierr = MatSetType(B,MATMAIJ);CHKERRQ(ierr);
    B->assembled    = PETSC_TRUE;
    b = (Mat_MPIMAIJ*)B->data;
    b->dof = dof;

    ierr = MPI_Comm_size(A->comm,&size);CHKERRQ(ierr);
    if (size == 1) {
      B->ops->destroy = MatDestroy_SeqMAIJ;
      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 {
        SETERRQ1(1,1,"Cannot handle a dof of %d\n",dof);
      }
    } else {
      Mat_MPIAIJ *mpiaij = (Mat_MPIAIJ *)A->data;
      IS         from,to;
      Vec        gvec;
      int        *garray,i;

      b->A = A;
      B->ops->destroy = MatDestroy_MPIMAIJ;
      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 = VecCreateSeq(PETSC_COMM_SELF,n*dof,&b->w);CHKERRQ(ierr);

      /* create two temporary Index sets for build scatter gather */
      garray = (int*)PetscMalloc((n+1)*sizeof(int));CHKPTRQ(garray);
      for (i=0; i<n; i++) garray[i] = dof*mpiaij->garray[i];
      ierr = ISCreateBlock(A->comm,dof,n,garray,&from);CHKERRQ(ierr);
      ierr = PetscFree(garray);CHKERRQ(ierr);
      ierr = ISCreateStride(PETSC_COMM_SELF,n*dof,0,1,&to);CHKERRQ(ierr);

      /* create temporary global vector to generate scatter context */
      ierr = VecCreateMPI(A->comm,dof*A->n,dof*A->N,&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;
    }
    *maij = B;
  }
  PetscFunctionReturn(0);
}