xref: /petsc/src/mat/impls/blockmat/seq/blockmat.c (revision dcca6d9d80ebd869fe6029bd05a3aa9faafef49e)

/*
   This provides a matrix that consists of Mats
*/

#include <petsc-private/matimpl.h>              /*I "petscmat.h" I*/
#include <../src/mat/impls/baij/seq/baij.h>    /* use the common AIJ data-structure */

typedef struct {
  SEQAIJHEADER(Mat);
  SEQBAIJHEADER;
  Mat *diags;

  Vec left,right,middle,workb;                 /* dummy vectors to perform local parts of product */
} Mat_BlockMat;

extern PetscErrorCode  MatBlockMatSetPreallocation(Mat,PetscInt,PetscInt,const PetscInt*);

#undef __FUNCT__
#define __FUNCT__ "MatSOR_BlockMat_Symmetric"
PetscErrorCode MatSOR_BlockMat_Symmetric(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
  Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
  PetscScalar       *x;
  const Mat         *v;
  const PetscScalar *b;
  PetscErrorCode    ierr;
  PetscInt          n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
  const PetscInt    *idx;
  IS                row,col;
  MatFactorInfo     info;
  Vec               left = a->left,right = a->right, middle = a->middle;
  Mat               *diag;

  PetscFunctionBegin;
  its = its*lits;
  if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
  if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
  if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
  if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");
  if ((flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) && !(flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP)) {
    SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Cannot do backward sweep without forward sweep");
  }

  if (!a->diags) {
    ierr = PetscMalloc(mbs*sizeof(Mat),&a->diags);CHKERRQ(ierr);
    ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
    for (i=0; i<mbs; i++) {
      ierr = MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);CHKERRQ(ierr);
      ierr = MatCholeskyFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,&info);CHKERRQ(ierr);
      ierr = MatCholeskyFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);CHKERRQ(ierr);
      ierr = ISDestroy(&row);CHKERRQ(ierr);
      ierr = ISDestroy(&col);CHKERRQ(ierr);
    }
    ierr = VecDuplicate(bb,&a->workb);CHKERRQ(ierr);
  }
  diag = a->diags;

  ierr = VecSet(xx,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  /* copy right hand side because it must be modified during iteration */
  ierr = VecCopy(bb,a->workb);CHKERRQ(ierr);
  ierr = VecGetArrayRead(a->workb,&b);CHKERRQ(ierr);

  /* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
  while (its--) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {

      for (i=0; i<mbs; i++) {
        n   = a->i[i+1] - a->i[i] - 1;
        idx = a->j + a->i[i] + 1;
        v   = a->a + a->i[i] + 1;

        ierr = VecSet(left,0.0);CHKERRQ(ierr);
        for (j=0; j<n; j++) {
          ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
          ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
          ierr = VecResetArray(right);CHKERRQ(ierr);
        }
        ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
        ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

        ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
        ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);

        /* now adjust right hand side, see MatSOR_SeqSBAIJ */
        for (j=0; j<n; j++) {
          ierr = MatMultTranspose(v[j],right,left);CHKERRQ(ierr);
          ierr = VecPlaceArray(middle,b + idx[j]*bs);CHKERRQ(ierr);
          ierr = VecAXPY(middle,-1.0,left);CHKERRQ(ierr);
          ierr = VecResetArray(middle);CHKERRQ(ierr);
        }
        ierr = VecResetArray(right);CHKERRQ(ierr);

      }
    }
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

      for (i=mbs-1; i>=0; i--) {
        n   = a->i[i+1] - a->i[i] - 1;
        idx = a->j + a->i[i] + 1;
        v   = a->a + a->i[i] + 1;

        ierr = VecSet(left,0.0);CHKERRQ(ierr);
        for (j=0; j<n; j++) {
          ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
          ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
          ierr = VecResetArray(right);CHKERRQ(ierr);
        }
        ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
        ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

        ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
        ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

      }
    }
  }
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(a->workb,&b);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSOR_BlockMat"
PetscErrorCode MatSOR_BlockMat(Mat A,Vec bb,PetscReal omega,MatSORType flag,PetscReal fshift,PetscInt its,PetscInt lits,Vec xx)
{
  Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
  PetscScalar       *x;
  const Mat         *v;
  const PetscScalar *b;
  PetscErrorCode    ierr;
  PetscInt          n = A->cmap->n,i,mbs = n/A->rmap->bs,j,bs = A->rmap->bs;
  const PetscInt    *idx;
  IS                row,col;
  MatFactorInfo     info;
  Vec               left = a->left,right = a->right;
  Mat               *diag;

  PetscFunctionBegin;
  its = its*lits;
  if (its <= 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONG,"Relaxation requires global its %D and local its %D both positive",its,lits);
  if (flag & SOR_EISENSTAT) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for Eisenstat");
  if (omega != 1.0) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for omega not equal to 1.0");
  if (fshift) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"No support yet for fshift");

  if (!a->diags) {
    ierr = PetscMalloc(mbs*sizeof(Mat),&a->diags);CHKERRQ(ierr);
    ierr = MatFactorInfoInitialize(&info);CHKERRQ(ierr);
    for (i=0; i<mbs; i++) {
      ierr = MatGetOrdering(a->a[a->diag[i]], MATORDERINGND,&row,&col);CHKERRQ(ierr);
      ierr = MatLUFactorSymbolic(a->diags[i],a->a[a->diag[i]],row,col,&info);CHKERRQ(ierr);
      ierr = MatLUFactorNumeric(a->diags[i],a->a[a->diag[i]],&info);CHKERRQ(ierr);
      ierr = ISDestroy(&row);CHKERRQ(ierr);
      ierr = ISDestroy(&col);CHKERRQ(ierr);
    }
  }
  diag = a->diags;

  ierr = VecSet(xx,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(xx,&x);CHKERRQ(ierr);
  ierr = VecGetArrayRead(bb,&b);CHKERRQ(ierr);

  /* need to add code for when initial guess is zero, see MatSOR_SeqAIJ */
  while (its--) {
    if (flag & SOR_FORWARD_SWEEP || flag & SOR_LOCAL_FORWARD_SWEEP) {

      for (i=0; i<mbs; i++) {
        n   = a->i[i+1] - a->i[i];
        idx = a->j + a->i[i];
        v   = a->a + a->i[i];

        ierr = VecSet(left,0.0);CHKERRQ(ierr);
        for (j=0; j<n; j++) {
          if (idx[j] != i) {
            ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
            ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
            ierr = VecResetArray(right);CHKERRQ(ierr);
          }
        }
        ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
        ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

        ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
        ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);
      }
    }
    if (flag & SOR_BACKWARD_SWEEP || flag & SOR_LOCAL_BACKWARD_SWEEP) {

      for (i=mbs-1; i>=0; i--) {
        n   = a->i[i+1] - a->i[i];
        idx = a->j + a->i[i];
        v   = a->a + a->i[i];

        ierr = VecSet(left,0.0);CHKERRQ(ierr);
        for (j=0; j<n; j++) {
          if (idx[j] != i) {
            ierr = VecPlaceArray(right,x + idx[j]*bs);CHKERRQ(ierr);
            ierr = MatMultAdd(v[j],right,left,left);CHKERRQ(ierr);
            ierr = VecResetArray(right);CHKERRQ(ierr);
          }
        }
        ierr = VecPlaceArray(right,b + i*bs);CHKERRQ(ierr);
        ierr = VecAYPX(left,-1.0,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

        ierr = VecPlaceArray(right,x + i*bs);CHKERRQ(ierr);
        ierr = MatSolve(diag[i],left,right);CHKERRQ(ierr);
        ierr = VecResetArray(right);CHKERRQ(ierr);

      }
    }
  }
  ierr = VecRestoreArray(xx,&x);CHKERRQ(ierr);
  ierr = VecRestoreArrayRead(bb,&b);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetValues_BlockMat"
PetscErrorCode MatSetValues_BlockMat(Mat A,PetscInt m,const PetscInt im[],PetscInt n,const PetscInt in[],const PetscScalar v[],InsertMode is)
{
  Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
  PetscInt       *rp,k,low,high,t,ii,row,nrow,i,col,l,rmax,N,lastcol = -1;
  PetscInt       *imax=a->imax,*ai=a->i,*ailen=a->ilen;
  PetscInt       *aj  =a->j,nonew=a->nonew,bs=A->rmap->bs,brow,bcol;
  PetscErrorCode ierr;
  PetscInt       ridx,cidx;
  PetscBool      roworiented=a->roworiented;
  MatScalar      value;
  Mat            *ap,*aa = a->a;

  PetscFunctionBegin;
  if (v) PetscValidScalarPointer(v,6);
  for (k=0; k<m; k++) { /* loop over added rows */
    row  = im[k];
    brow = row/bs;
    if (row < 0) continue;
#if defined(PETSC_USE_DEBUG)
    if (row >= A->rmap->N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Row too large: row %D max %D",row,A->rmap->N-1);
#endif
    rp   = aj + ai[brow];
    ap   = aa + ai[brow];
    rmax = imax[brow];
    nrow = ailen[brow];
    low  = 0;
    high = nrow;
    for (l=0; l<n; l++) { /* loop over added columns */
      if (in[l] < 0) continue;
#if defined(PETSC_USE_DEBUG)
      if (in[l] >= A->cmap->n) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Column too large: col %D max %D",in[l],A->cmap->n-1);
#endif
      col = in[l]; bcol = col/bs;
      if (A->symmetric && brow > bcol) continue;
      ridx = row % bs; cidx = col % bs;
      if (roworiented) value = v[l + k*n];
      else value = v[k + l*m];

      if (col <= lastcol) low = 0;
      else high = nrow;
      lastcol = col;
      while (high-low > 7) {
        t = (low+high)/2;
        if (rp[t] > bcol) high = t;
        else              low  = t;
      }
      for (i=low; i<high; i++) {
        if (rp[i] > bcol) break;
        if (rp[i] == bcol) goto noinsert1;
      }
      if (nonew == 1) goto noinsert1;
      if (nonew == -1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Inserting a new nonzero (%D, %D) in the matrix", row, col);
      MatSeqXAIJReallocateAIJ(A,a->mbs,1,nrow,brow,bcol,rmax,aa,ai,aj,rp,ap,imax,nonew,Mat);
      N = nrow++ - 1; high++;
      /* shift up all the later entries in this row */
      for (ii=N; ii>=i; ii--) {
        rp[ii+1] = rp[ii];
        ap[ii+1] = ap[ii];
      }
      if (N>=i) ap[i] = 0;
      rp[i] = bcol;
      a->nz++;
noinsert1:;
      if (!*(ap+i)) {
        ierr = MatCreateSeqAIJ(PETSC_COMM_SELF,bs,bs,0,0,ap+i);CHKERRQ(ierr);
      }
      ierr = MatSetValues(ap[i],1,&ridx,1,&cidx,&value,is);CHKERRQ(ierr);
      low  = i;
    }
    ailen[brow] = nrow;
  }
  A->same_nonzero = PETSC_FALSE;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatLoad_BlockMat"
PetscErrorCode MatLoad_BlockMat(Mat newmat, PetscViewer viewer)
{
  PetscErrorCode    ierr;
  Mat               tmpA;
  PetscInt          i,j,m,n,bs = 1,ncols,*lens,currentcol,mbs,**ii,*ilens,nextcol,*llens,cnt = 0;
  const PetscInt    *cols;
  const PetscScalar *values;
  PetscBool         flg = PETSC_FALSE,notdone;
  Mat_SeqAIJ        *a;
  Mat_BlockMat      *amat;

  PetscFunctionBegin;
  ierr = MatCreate(PETSC_COMM_SELF,&tmpA);CHKERRQ(ierr);
  ierr = MatSetType(tmpA,MATSEQAIJ);CHKERRQ(ierr);
  ierr = MatLoad_SeqAIJ(tmpA,viewer);CHKERRQ(ierr);

  ierr = MatGetLocalSize(tmpA,&m,&n);CHKERRQ(ierr);
  ierr = PetscOptionsBegin(PETSC_COMM_SELF,NULL,"Options for loading BlockMat matrix 1","Mat");CHKERRQ(ierr);
  ierr = PetscOptionsInt("-matload_block_size","Set the blocksize used to store the matrix","MatLoad",bs,&bs,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsBool("-matload_symmetric","Store the matrix as symmetric","MatLoad",flg,&flg,NULL);CHKERRQ(ierr);
  ierr = PetscOptionsEnd();CHKERRQ(ierr);

  /* Determine number of nonzero blocks for each block row */
  a    = (Mat_SeqAIJ*) tmpA->data;
  mbs  = m/bs;
  ierr = PetscMalloc3(mbs,&lens,bs,&ii,bs,&ilens);CHKERRQ(ierr);
  ierr = PetscMemzero(lens,mbs*sizeof(PetscInt));CHKERRQ(ierr);

  for (i=0; i<mbs; i++) {
    for (j=0; j<bs; j++) {
      ii[j]    = a->j + a->i[i*bs + j];
      ilens[j] = a->i[i*bs + j + 1] - a->i[i*bs + j];
    }

    currentcol = -1;
    notdone    = PETSC_TRUE;
    while (PETSC_TRUE) {
      notdone = PETSC_FALSE;
      nextcol = 1000000000;
      for (j=0; j<bs; j++) {
        while ((ilens[j] > 0 && ii[j][0]/bs <= currentcol)) {
          ii[j]++;
          ilens[j]--;
        }
        if (ilens[j] > 0) {
          notdone = PETSC_TRUE;
          nextcol = PetscMin(nextcol,ii[j][0]/bs);
        }
      }
      if (!notdone) break;
      if (!flg || (nextcol >= i)) lens[i]++;
      currentcol = nextcol;
    }
  }

  if (newmat->rmap->n < 0 && newmat->rmap->N < 0 && newmat->cmap->n < 0 && newmat->cmap->N < 0) {
    ierr = MatSetSizes(newmat,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  }
  ierr = MatBlockMatSetPreallocation(newmat,bs,0,lens);CHKERRQ(ierr);
  if (flg) {
    ierr = MatSetOption(newmat,MAT_SYMMETRIC,PETSC_TRUE);CHKERRQ(ierr);
  }
  amat = (Mat_BlockMat*)(newmat)->data;

  /* preallocate the submatrices */
  ierr = PetscMalloc(bs*sizeof(PetscInt),&llens);CHKERRQ(ierr);
  for (i=0; i<mbs; i++) { /* loops for block rows */
    for (j=0; j<bs; j++) {
      ii[j]    = a->j + a->i[i*bs + j];
      ilens[j] = a->i[i*bs + j + 1] - a->i[i*bs + j];
    }

    currentcol = 1000000000;
    for (j=0; j<bs; j++) { /* loop over rows in block finding first nonzero block */
      if (ilens[j] > 0) {
        currentcol = PetscMin(currentcol,ii[j][0]/bs);
      }
    }

    notdone = PETSC_TRUE;
    while (PETSC_TRUE) {  /* loops over blocks in block row */

      notdone = PETSC_FALSE;
      nextcol = 1000000000;
      ierr    = PetscMemzero(llens,bs*sizeof(PetscInt));CHKERRQ(ierr);
      for (j=0; j<bs; j++) { /* loop over rows in block */
        while ((ilens[j] > 0 && ii[j][0]/bs <= currentcol)) { /* loop over columns in row */
          ii[j]++;
          ilens[j]--;
          llens[j]++;
        }
        if (ilens[j] > 0) {
          notdone = PETSC_TRUE;
          nextcol = PetscMin(nextcol,ii[j][0]/bs);
        }
      }
      if (cnt >= amat->maxnz) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Number of blocks found greater than expected %D",cnt);
      if (!flg || currentcol >= i) {
        amat->j[cnt] = currentcol;
        ierr         = MatCreateSeqAIJ(PETSC_COMM_SELF,bs,bs,0,llens,amat->a+cnt++);CHKERRQ(ierr);
      }

      if (!notdone) break;
      currentcol = nextcol;
    }
    amat->ilen[i] = lens[i];
  }

  ierr = PetscFree3(lens,ii,ilens);CHKERRQ(ierr);
  ierr = PetscFree(llens);CHKERRQ(ierr);

  /* copy over the matrix, one row at a time */
  for (i=0; i<m; i++) {
    ierr = MatGetRow(tmpA,i,&ncols,&cols,&values);CHKERRQ(ierr);
    ierr = MatSetValues(newmat,1,&i,ncols,cols,values,INSERT_VALUES);CHKERRQ(ierr);
    ierr = MatRestoreRow(tmpA,i,&ncols,&cols,&values);CHKERRQ(ierr);
  }
  ierr = MatAssemblyBegin(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(newmat,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatView_BlockMat"
PetscErrorCode MatView_BlockMat(Mat A,PetscViewer viewer)
{
  Mat_BlockMat      *a = (Mat_BlockMat*)A->data;
  PetscErrorCode    ierr;
  const char        *name;
  PetscViewerFormat format;

  PetscFunctionBegin;
  ierr = PetscObjectGetName((PetscObject)A,&name);CHKERRQ(ierr);
  ierr = PetscViewerGetFormat(viewer,&format);CHKERRQ(ierr);
  if (format == PETSC_VIEWER_ASCII_FACTOR_INFO || format == PETSC_VIEWER_ASCII_INFO) {
    ierr = PetscViewerASCIIPrintf(viewer,"Nonzero block matrices = %D \n",a->nz);CHKERRQ(ierr);
    if (A->symmetric) {
      ierr = PetscViewerASCIIPrintf(viewer,"Only upper triangular part of symmetric matrix is stored\n");CHKERRQ(ierr);
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatDestroy_BlockMat"
PetscErrorCode MatDestroy_BlockMat(Mat mat)
{
  PetscErrorCode ierr;
  Mat_BlockMat   *bmat = (Mat_BlockMat*)mat->data;
  PetscInt       i;

  PetscFunctionBegin;
  ierr = VecDestroy(&bmat->right);CHKERRQ(ierr);
  ierr = VecDestroy(&bmat->left);CHKERRQ(ierr);
  ierr = VecDestroy(&bmat->middle);CHKERRQ(ierr);
  ierr = VecDestroy(&bmat->workb);CHKERRQ(ierr);
  if (bmat->diags) {
    for (i=0; i<mat->rmap->n/mat->rmap->bs; i++) {
      ierr = MatDestroy(&bmat->diags[i]);CHKERRQ(ierr);
    }
  }
  if (bmat->a) {
    for (i=0; i<bmat->nz; i++) {
      ierr = MatDestroy(&bmat->a[i]);CHKERRQ(ierr);
    }
  }
  ierr = MatSeqXAIJFreeAIJ(mat,(PetscScalar**)&bmat->a,&bmat->j,&bmat->i);CHKERRQ(ierr);
  ierr = PetscFree(mat->data);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMult_BlockMat"
PetscErrorCode MatMult_BlockMat(Mat A,Vec x,Vec y)
{
  Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
  PetscErrorCode ierr;
  PetscScalar    *xx,*yy;
  PetscInt       *aj,i,*ii,jrow,m = A->rmap->n/A->rmap->bs,bs = A->rmap->bs,n,j;
  Mat            *aa;

  PetscFunctionBegin;
  /*
     Standard CSR multiply except each entry is a Mat
  */
  ierr = VecGetArray(x,&xx);CHKERRQ(ierr);

  ierr = VecSet(y,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
  aj   = bmat->j;
  aa   = bmat->a;
  ii   = bmat->i;
  for (i=0; i<m; i++) {
    jrow = ii[i];
    ierr = VecPlaceArray(bmat->left,yy + bs*i);CHKERRQ(ierr);
    n    = ii[i+1] - jrow;
    for (j=0; j<n; j++) {
      ierr = VecPlaceArray(bmat->right,xx + bs*aj[jrow]);CHKERRQ(ierr);
      ierr = MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);CHKERRQ(ierr);
      ierr = VecResetArray(bmat->right);CHKERRQ(ierr);
      jrow++;
    }
    ierr = VecResetArray(bmat->left);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr);
  ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMult_BlockMat_Symmetric"
PetscErrorCode MatMult_BlockMat_Symmetric(Mat A,Vec x,Vec y)
{
  Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
  PetscErrorCode ierr;
  PetscScalar    *xx,*yy;
  PetscInt       *aj,i,*ii,jrow,m = A->rmap->n/A->rmap->bs,bs = A->rmap->bs,n,j;
  Mat            *aa;

  PetscFunctionBegin;
  /*
     Standard CSR multiply except each entry is a Mat
  */
  ierr = VecGetArray(x,&xx);CHKERRQ(ierr);

  ierr = VecSet(y,0.0);CHKERRQ(ierr);
  ierr = VecGetArray(y,&yy);CHKERRQ(ierr);
  aj   = bmat->j;
  aa   = bmat->a;
  ii   = bmat->i;
  for (i=0; i<m; i++) {
    jrow = ii[i];
    n    = ii[i+1] - jrow;
    ierr = VecPlaceArray(bmat->left,yy + bs*i);CHKERRQ(ierr);
    ierr = VecPlaceArray(bmat->middle,xx + bs*i);CHKERRQ(ierr);
    /* if we ALWAYS required a diagonal entry then could remove this if test */
    if (aj[jrow] == i) {
      ierr = VecPlaceArray(bmat->right,xx + bs*aj[jrow]);CHKERRQ(ierr);
      ierr = MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);CHKERRQ(ierr);
      ierr = VecResetArray(bmat->right);CHKERRQ(ierr);
      jrow++;
      n--;
    }
    for (j=0; j<n; j++) {
      ierr = VecPlaceArray(bmat->right,xx + bs*aj[jrow]);CHKERRQ(ierr);            /* upper triangular part */
      ierr = MatMultAdd(aa[jrow],bmat->right,bmat->left,bmat->left);CHKERRQ(ierr);
      ierr = VecResetArray(bmat->right);CHKERRQ(ierr);

      ierr = VecPlaceArray(bmat->right,yy + bs*aj[jrow]);CHKERRQ(ierr);            /* lower triangular part */
      ierr = MatMultTransposeAdd(aa[jrow],bmat->middle,bmat->right,bmat->right);CHKERRQ(ierr);
      ierr = VecResetArray(bmat->right);CHKERRQ(ierr);
      jrow++;
    }
    ierr = VecResetArray(bmat->left);CHKERRQ(ierr);
    ierr = VecResetArray(bmat->middle);CHKERRQ(ierr);
  }
  ierr = VecRestoreArray(x,&xx);CHKERRQ(ierr);
  ierr = VecRestoreArray(y,&yy);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultAdd_BlockMat"
PetscErrorCode MatMultAdd_BlockMat(Mat A,Vec x,Vec y,Vec z)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTranspose_BlockMat"
PetscErrorCode MatMultTranspose_BlockMat(Mat A,Vec x,Vec y)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatMultTransposeAdd_BlockMat"
PetscErrorCode MatMultTransposeAdd_BlockMat(Mat A,Vec x,Vec y,Vec z)
{
  PetscFunctionBegin;
  PetscFunctionReturn(0);
}

/*
     Adds diagonal pointers to sparse matrix structure.
*/
#undef __FUNCT__
#define __FUNCT__ "MatMarkDiagonal_BlockMat"
PetscErrorCode MatMarkDiagonal_BlockMat(Mat A)
{
  Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
  PetscErrorCode ierr;
  PetscInt       i,j,mbs = A->rmap->n/A->rmap->bs;

  PetscFunctionBegin;
  if (!a->diag) {
    ierr = PetscMalloc(mbs*sizeof(PetscInt),&a->diag);CHKERRQ(ierr);
  }
  for (i=0; i<mbs; i++) {
    a->diag[i] = a->i[i+1];
    for (j=a->i[i]; j<a->i[i+1]; j++) {
      if (a->j[j] == i) {
        a->diag[i] = j;
        break;
      }
    }
  }
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatGetSubMatrix_BlockMat"
PetscErrorCode MatGetSubMatrix_BlockMat(Mat A,IS isrow,IS iscol,MatReuse scall,Mat *B)
{
  Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
  Mat_SeqAIJ     *c;
  PetscErrorCode ierr;
  PetscInt       i,k,first,step,lensi,nrows,ncols;
  PetscInt       *j_new,*i_new,*aj = a->j,*ailen = a->ilen;
  PetscScalar    *a_new;
  Mat            C,*aa = a->a;
  PetscBool      stride,equal;

  PetscFunctionBegin;
  ierr = ISEqual(isrow,iscol,&equal);CHKERRQ(ierr);
  if (!equal) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only for idential column and row indices");
  ierr = PetscObjectTypeCompare((PetscObject)iscol,ISSTRIDE,&stride);CHKERRQ(ierr);
  if (!stride) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Only for stride indices");
  ierr = ISStrideGetInfo(iscol,&first,&step);CHKERRQ(ierr);
  if (step != A->rmap->bs) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Can only select one entry from each block");

  ierr  = ISGetLocalSize(isrow,&nrows);CHKERRQ(ierr);
  ncols = nrows;

  /* create submatrix */
  if (scall == MAT_REUSE_MATRIX) {
    PetscInt n_cols,n_rows;
    C    = *B;
    ierr = MatGetSize(C,&n_rows,&n_cols);CHKERRQ(ierr);
    if (n_rows != nrows || n_cols != ncols) SETERRQ(PETSC_COMM_SELF,PETSC_ERR_ARG_SIZ,"Reused submatrix wrong size");
    ierr = MatZeroEntries(C);CHKERRQ(ierr);
  } else {
    ierr = MatCreate(PetscObjectComm((PetscObject)A),&C);CHKERRQ(ierr);
    ierr = MatSetSizes(C,nrows,ncols,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
    if (A->symmetric) {
      ierr = MatSetType(C,MATSEQSBAIJ);CHKERRQ(ierr);
    } else {
      ierr = MatSetType(C,MATSEQAIJ);CHKERRQ(ierr);
    }
    ierr = MatSeqAIJSetPreallocation(C,0,ailen);CHKERRQ(ierr);
    ierr = MatSeqSBAIJSetPreallocation(C,1,0,ailen);CHKERRQ(ierr);
  }
  c = (Mat_SeqAIJ*)C->data;

  /* loop over rows inserting into submatrix */
  a_new = c->a;
  j_new = c->j;
  i_new = c->i;

  for (i=0; i<nrows; i++) {
    lensi = ailen[i];
    for (k=0; k<lensi; k++) {
      *j_new++ = *aj++;
      ierr     = MatGetValue(*aa++,first,first,a_new++);CHKERRQ(ierr);
    }
    i_new[i+1] = i_new[i] + lensi;
    c->ilen[i] = lensi;
  }

  ierr = MatAssemblyBegin(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(C,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  *B   = C;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatAssemblyEnd_BlockMat"
PetscErrorCode MatAssemblyEnd_BlockMat(Mat A,MatAssemblyType mode)
{
  Mat_BlockMat   *a = (Mat_BlockMat*)A->data;
  PetscErrorCode ierr;
  PetscInt       fshift = 0,i,j,*ai = a->i,*aj = a->j,*imax = a->imax;
  PetscInt       m      = a->mbs,*ip,N,*ailen = a->ilen,rmax = 0;
  Mat            *aa    = a->a,*ap;

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

  if (m) rmax = ailen[0]; /* determine row with most nonzeros */
  for (i=1; i<m; i++) {
    /* move each row back by the amount of empty slots (fshift) before it*/
    fshift += imax[i-1] - ailen[i-1];
    rmax    = PetscMax(rmax,ailen[i]);
    if (fshift) {
      ip = aj + ai[i];
      ap = aa + ai[i];
      N  = ailen[i];
      for (j=0; j<N; j++) {
        ip[j-fshift] = ip[j];
        ap[j-fshift] = ap[j];
      }
    }
    ai[i] = ai[i-1] + ailen[i-1];
  }
  if (m) {
    fshift += imax[m-1] - ailen[m-1];
    ai[m]   = ai[m-1] + ailen[m-1];
  }
  /* reset ilen and imax for each row */
  for (i=0; i<m; i++) {
    ailen[i] = imax[i] = ai[i+1] - ai[i];
  }
  a->nz = ai[m];
  for (i=0; i<a->nz; i++) {
#if defined(PETSC_USE_DEBUG)
    if (!aa[i]) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Null matrix at location %D column %D nz %D",i,aj[i],a->nz);
#endif
    ierr = MatAssemblyBegin(aa[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(aa[i],MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  }
  ierr = PetscInfo4(A,"Matrix size: %D X %D; storage space: %D unneeded,%D used\n",m,A->cmap->n/A->cmap->bs,fshift,a->nz);CHKERRQ(ierr);
  ierr = PetscInfo1(A,"Number of mallocs during MatSetValues() is %D\n",a->reallocs);CHKERRQ(ierr);
  ierr = PetscInfo1(A,"Maximum nonzeros in any row is %D\n",rmax);CHKERRQ(ierr);

  A->info.mallocs    += a->reallocs;
  a->reallocs         = 0;
  A->info.nz_unneeded = (double)fshift;
  a->rmax             = rmax;

  A->same_nonzero = PETSC_TRUE;
  ierr            = MatMarkDiagonal_BlockMat(A);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatSetOption_BlockMat"
PetscErrorCode MatSetOption_BlockMat(Mat A,MatOption opt,PetscBool flg)
{
  PetscFunctionBegin;
  if (opt == MAT_SYMMETRIC && flg) {
    A->ops->sor  = MatSOR_BlockMat_Symmetric;
    A->ops->mult = MatMult_BlockMat_Symmetric;
  } else {
    PetscInfo1(A,"Unused matrix option %s\n",MatOptions[opt]);
  }
  PetscFunctionReturn(0);
}


static struct _MatOps MatOps_Values = {MatSetValues_BlockMat,
                                       0,
                                       0,
                                       MatMult_BlockMat,
                               /*  4*/ MatMultAdd_BlockMat,
                                       MatMultTranspose_BlockMat,
                                       MatMultTransposeAdd_BlockMat,
                                       0,
                                       0,
                                       0,
                               /* 10*/ 0,
                                       0,
                                       0,
                                       MatSOR_BlockMat,
                                       0,
                               /* 15*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 20*/ 0,
                                       MatAssemblyEnd_BlockMat,
                                       MatSetOption_BlockMat,
                                       0,
                               /* 24*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 29*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 34*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 39*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 44*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 49*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 54*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 59*/ MatGetSubMatrix_BlockMat,
                                       MatDestroy_BlockMat,
                                       MatView_BlockMat,
                                       0,
                                       0,
                               /* 64*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 69*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 74*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 79*/ 0,
                                       0,
                                       0,
                                       0,
                                       MatLoad_BlockMat,
                               /* 84*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 89*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 94*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /* 99*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*104*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*109*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*114*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*119*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*124*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*129*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*134*/ 0,
                                       0,
                                       0,
                                       0,
                                       0,
                               /*139*/ 0,
                                       0,
                                       0
};

#undef __FUNCT__
#define __FUNCT__ "MatBlockMatSetPreallocation"
/*@C
   MatBlockMatSetPreallocation - For good matrix assembly performance
   the user should preallocate the matrix storage by setting the parameter nz
   (or the array nnz).  By setting these parameters accurately, performance
   during matrix assembly can be increased by more than a factor of 50.

   Collective on MPI_Comm

   Input Parameters:
+  B - The matrix
.  bs - size of each block in matrix
.  nz - number of nonzeros per block row (same for all rows)
-  nnz - array containing the number of nonzeros in the various block rows
         (possibly different for each row) or NULL

   Notes:
     If nnz is given then nz is ignored

   Specify the preallocated storage with either nz or nnz (not both).
   Set nz=PETSC_DEFAULT and nnz=NULL for PETSc to control dynamic memory
   allocation.  For large problems you MUST preallocate memory or you
   will get TERRIBLE performance, see the users' manual chapter on matrices.

   Level: intermediate

.seealso: MatCreate(), MatCreateBlockMat(), MatSetValues()

@*/
PetscErrorCode  MatBlockMatSetPreallocation(Mat B,PetscInt bs,PetscInt nz,const PetscInt nnz[])
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = PetscTryMethod(B,"MatBlockMatSetPreallocation_C",(Mat,PetscInt,PetscInt,const PetscInt[]),(B,bs,nz,nnz));CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatBlockMatSetPreallocation_BlockMat"
PetscErrorCode  MatBlockMatSetPreallocation_BlockMat(Mat A,PetscInt bs,PetscInt nz,PetscInt *nnz)
{
  Mat_BlockMat   *bmat = (Mat_BlockMat*)A->data;
  PetscErrorCode ierr;
  PetscInt       i;

  PetscFunctionBegin;
  ierr = PetscLayoutSetBlockSize(A->rmap,bs);CHKERRQ(ierr);
  ierr = PetscLayoutSetBlockSize(A->cmap,bs);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(A->rmap);CHKERRQ(ierr);
  ierr = PetscLayoutSetUp(A->cmap);CHKERRQ(ierr);
  ierr = PetscLayoutGetBlockSize(A->rmap,&bs);CHKERRQ(ierr);

  if (nz == PETSC_DEFAULT || nz == PETSC_DECIDE) nz = 5;
  if (nz < 0) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nz cannot be less than 0: value %d",nz);
  if (nnz) {
    for (i=0; i<A->rmap->n/bs; i++) {
      if (nnz[i] < 0) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be less than 0: local row %d value %d",i,nnz[i]);
      if (nnz[i] > A->cmap->n/bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"nnz cannot be greater than row length: local row %d value %d rowlength %d",i,nnz[i],A->cmap->n/bs);
    }
  }
  bmat->mbs = A->rmap->n/bs;

  ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,bs,NULL,&bmat->right);CHKERRQ(ierr);
  ierr = VecCreateSeqWithArray(PETSC_COMM_SELF,1,bs,NULL,&bmat->middle);CHKERRQ(ierr);
  ierr = VecCreateSeq(PETSC_COMM_SELF,bs,&bmat->left);CHKERRQ(ierr);

  if (!bmat->imax) {
    ierr = PetscMalloc2(A->rmap->n,&bmat->imax,A->rmap->n,&bmat->ilen);CHKERRQ(ierr);
    ierr = PetscLogObjectMemory((PetscObject)A,2*A->rmap->n*sizeof(PetscInt));CHKERRQ(ierr);
  }
  if (nnz) {
    nz = 0;
    for (i=0; i<A->rmap->n/A->rmap->bs; i++) {
      bmat->imax[i] = nnz[i];
      nz           += nnz[i];
    }
  } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Currently requires block row by row preallocation");

  /* bmat->ilen will count nonzeros in each row so far. */
  for (i=0; i<bmat->mbs; i++) bmat->ilen[i] = 0;

  /* allocate the matrix space */
  ierr       = MatSeqXAIJFreeAIJ(A,(PetscScalar**)&bmat->a,&bmat->j,&bmat->i);CHKERRQ(ierr);
  ierr       = PetscMalloc3(nz,&bmat->a,nz,&bmat->j,A->rmap->n+1,&bmat->i);CHKERRQ(ierr);
  ierr       = PetscLogObjectMemory((PetscObject)A,(A->rmap->n+1)*sizeof(PetscInt)+nz*(sizeof(PetscScalar)+sizeof(PetscInt)));CHKERRQ(ierr);
  bmat->i[0] = 0;
  for (i=1; i<bmat->mbs+1; i++) {
    bmat->i[i] = bmat->i[i-1] + bmat->imax[i-1];
  }
  bmat->singlemalloc = PETSC_TRUE;
  bmat->free_a       = PETSC_TRUE;
  bmat->free_ij      = PETSC_TRUE;

  bmat->nz            = 0;
  bmat->maxnz         = nz;
  A->info.nz_unneeded = (double)bmat->maxnz;
  ierr                = MatSetOption(A,MAT_NEW_NONZERO_ALLOCATION_ERR,PETSC_TRUE);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

/*MC
   MATBLOCKMAT - A matrix that is defined by a set of Mat's that represents a sparse block matrix
                 consisting of (usually) sparse blocks.

  Level: advanced

.seealso: MatCreateBlockMat()

M*/

#undef __FUNCT__
#define __FUNCT__ "MatCreate_BlockMat"
PETSC_EXTERN PetscErrorCode MatCreate_BlockMat(Mat A)
{
  Mat_BlockMat   *b;
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr    = PetscNewLog(A,Mat_BlockMat,&b);CHKERRQ(ierr);
  A->data = (void*)b;
  ierr    = PetscMemcpy(A->ops,&MatOps_Values,sizeof(struct _MatOps));CHKERRQ(ierr);

  A->assembled    = PETSC_TRUE;
  A->preallocated = PETSC_FALSE;
  ierr            = PetscObjectChangeTypeName((PetscObject)A,MATBLOCKMAT);CHKERRQ(ierr);

  ierr = PetscObjectComposeFunction((PetscObject)A,"MatBlockMatSetPreallocation_C",MatBlockMatSetPreallocation_BlockMat);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatCreateBlockMat"
/*@C
   MatCreateBlockMat - Creates a new matrix based sparse Mat storage

  Collective on MPI_Comm

   Input Parameters:
+  comm - MPI communicator
.  m - number of rows
.  n  - number of columns
.  bs - size of each submatrix
.  nz  - expected maximum number of nonzero blocks in row (use PETSC_DEFAULT if not known)
-  nnz - expected number of nonzers per block row if known (use NULL otherwise)


   Output Parameter:
.  A - the matrix

   Level: intermediate

   PETSc requires that matrices and vectors being used for certain
   operations are partitioned accordingly.  For example, when
   creating a bmat matrix, A, that supports parallel matrix-vector
   products using MatMult(A,x,y) the user should set the number
   of local matrix rows to be the number of local elements of the
   corresponding result vector, y. Note that this is information is
   required for use of the matrix interface routines, even though
   the bmat matrix may not actually be physically partitioned.
   For example,

.keywords: matrix, bmat, create

.seealso: MATBLOCKMAT
@*/
PetscErrorCode  MatCreateBlockMat(MPI_Comm comm,PetscInt m,PetscInt n,PetscInt bs,PetscInt nz,PetscInt *nnz, Mat *A)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = MatCreate(comm,A);CHKERRQ(ierr);
  ierr = MatSetSizes(*A,m,n,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetType(*A,MATBLOCKMAT);CHKERRQ(ierr);
  ierr = MatBlockMatSetPreallocation(*A,bs,nz,nnz);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}