xref: /petsc/src/mat/impls/aij/mpi/fdmpiaij.c (revision 72c15787a93a19cd3df4570166440ecc4a2e18c2)

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

extern PetscErrorCode MatCreateColmap_MPIAIJ_Private(Mat);

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringApply_MPIAIJ"
PetscErrorCode  MatFDColoringApply_MPIAIJ(Mat J,MatFDColoring coloring,Vec x1,MatStructure *flag,void *sctx)
{
  PetscErrorCode (*f)(void*,Vec,Vec,void*) = (PetscErrorCode (*)(void*,Vec,Vec,void*))coloring->f;
  PetscErrorCode ierr;
  PetscInt       k,start,end,l,row,col,**vscaleforrow,nz;
  PetscScalar    dx,*y,*xx,*w3_array;
  PetscScalar    *vscale_array;
  PetscReal      epsilon = coloring->error_rel,umin = coloring->umin,unorm;
  Vec            w1      = coloring->w1,w2=coloring->w2,w3;
  void           *fctx   = coloring->fctx;
  PetscBool      flg     = PETSC_FALSE;
  PetscInt       ctype   = coloring->ctype,N,col_start=0,col_end=0;
  Mat_MPIAIJ     *aij = (Mat_MPIAIJ*)J->data;
  Mat            A=aij->A,B=aij->B;
  Mat_SeqAIJ     *cspA=(Mat_SeqAIJ*)A->data, *cspB=(Mat_SeqAIJ*)B->data;
  PetscMPIInt    rank;

  PetscFunctionBegin;
  //ierr = VecView(x1,PETSC_VIEWER_STDOUT_WORLD);
  //ierr = VecView(coloring->vscale,PETSC_VIEWER_STDOUT_WORLD);
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)J), &rank);CHKERRQ(ierr);
  ierr = MatSetUnfactored(J);CHKERRQ(ierr);
  ierr = PetscOptionsGetBool(NULL,"-mat_fd_coloring_dont_rezero",&flg,NULL);CHKERRQ(ierr);
  if (flg) {
    ierr = PetscInfo(coloring,"Not calling MatZeroEntries()\n");CHKERRQ(ierr);
  } else {
    PetscBool assembled;
    ierr = MatAssembled(J,&assembled);CHKERRQ(ierr);
    if (assembled) {
      ierr = MatZeroEntries(J);CHKERRQ(ierr);
    }
  }

  if (!coloring->vscale) { //ctype == IS_COLORING_GHOSTED ?
    printf("[%d] create a non-ghostedcoloring->vscale\n",rank);
    ierr = VecDuplicate(x1,&coloring->vscale);CHKERRQ(ierr);
    //SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_NULL,"Null Object: coloring->scale");
  }

  /* Set w1 = F(x1) */
  if (!coloring->fset) {
    ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = (*f)(sctx,x1,w1,fctx);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
  } else {
    coloring->fset = PETSC_FALSE;
  }

  if (!coloring->w3) {
    ierr = VecDuplicate(x1,&coloring->w3);CHKERRQ(ierr);
    ierr = PetscLogObjectParent((PetscObject)coloring,(PetscObject)coloring->w3);CHKERRQ(ierr);
  }
  w3 = coloring->w3;

  /* Compute vscale = dx - the local scale factors, including ghost points */
  ierr = VecGetOwnershipRange(w1,&start,&end);CHKERRQ(ierr); /* =J's row ownershipRange, used by ghosted x! */
  //printf("[%d] start end %d %d\n",rank,start,end);

  if (coloring->htype[0] == 'w') {
    /* tacky test; need to make systematic if we add other approaches to computing h*/
    ierr = VecNorm(x1,NORM_2,&unorm);CHKERRQ(ierr);
    dx = (1.0 + unorm)*epsilon;
    ierr = VecSet(coloring->vscale,dx);CHKERRQ(ierr);
  } else { // buggy!!!
    ierr = VecGetLocalSize(x1,&N);CHKERRQ(ierr);
    ierr = VecGetArray(x1,&xx);CHKERRQ(ierr);
    ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
    if (ctype == IS_COLORING_GHOSTED) {
      col_start = 0; col_end = N;
    } else if (ctype == IS_COLORING_GLOBAL) {
      xx           = xx - start;  //???
      vscale_array = vscale_array - start; //???
      col_start    = start; col_end = N + start;
    }
    for (col=col_start; col<col_end; col++) {
      /* Loop over each local column, vscale[col] = 1./(epsilon*dx[col]) */
      dx = xx[col];
      if (dx == (PetscScalar)0.0) dx = 1.0;
      if (PetscAbsScalar(dx) < umin && PetscRealPart(dx) >= 0.0)     dx = umin;
      else if (PetscRealPart(dx) < 0.0 && PetscAbsScalar(dx) < umin) dx = -umin;
      dx               *= epsilon;
      vscale_array[col] = (PetscScalar)dx;
    }
  }
  if (ctype == IS_COLORING_GLOBAL) vscale_array = vscale_array + start;
  ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  if (ctype == IS_COLORING_GLOBAL) {
    ierr = VecGhostUpdateBegin(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecGhostUpdateEnd(coloring->vscale,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
  }

  if (coloring->vscaleforrow) {
    vscaleforrow = coloring->vscaleforrow;
  } else SETERRQ(PetscObjectComm((PetscObject)J),PETSC_ERR_ARG_NULL,"Null Object: coloring->vscaleforrow");

  /* Loop over each color */
  nz = 0;
  ierr = VecGetArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  for (k=0; k<coloring->ncolors; k++) {
    coloring->currentcolor = k;

    /*
      Loop over each column associated with color
      adding the perturbation to the vector w3 = x1 + dx.
    */
    ierr = VecCopy(x1,w3);CHKERRQ(ierr);
    ierr = VecGetArray(w3,&w3_array);CHKERRQ(ierr);
    if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array - start;
    for (l=0; l<coloring->ncolumns[k]; l++) {
      col = coloring->columns[k][l]; /* local column (in global index!) of the matrix we are probing for */
      dx             = vscale_array[coloring->vscaleforrow[k][l]];
      w3_array[col] += dx;
      /*
      if (rank ==1) {
        printf("[%d] w3[%d] += vscale[%d] %g\n",rank,col,coloring->vscaleforrow[k][l],dx);
      }
       */
    }
    if (ctype == IS_COLORING_GLOBAL) w3_array = w3_array + start;
    ierr = VecRestoreArray(w3,&w3_array);CHKERRQ(ierr);

    /*
      Evaluate function at w3 = x1 + dx (here dx is a vector of perturbations)
                           w2 = F(x1 + dx) - F(x1)
    */
    ierr = PetscLogEventBegin(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = (*f)(sctx,w3,w2,fctx);CHKERRQ(ierr);
    ierr = PetscLogEventEnd(MAT_FDColoringFunction,0,0,0,0);CHKERRQ(ierr);
    ierr = VecAXPY(w2,-1.0,w1);CHKERRQ(ierr);

    /* Loop over rows of vector, putting results into Jacobian matrix */
    ierr = VecGetArray(w2,&y);CHKERRQ(ierr);
    for (l=0; l<coloring->nrows[k]; l++) {
      row                        = coloring->rows[k][l];   /* local row index */
      *(coloring->valaddr[nz++]) = y[row]/vscale_array[vscaleforrow[k][l]];
    }
    ierr = VecRestoreArray(w2,&y);CHKERRQ(ierr);
  } /* endof for each color */
  if (nz != cspA->nz + cspB->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"nz %d != mat->nz %d\n",nz,cspA->nz+cspB->nz);
  ierr = MatAssemblyBegin(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
  ierr = MatAssemblyEnd(J,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

  if (ctype == IS_COLORING_GLOBAL) xx = xx + start;
  ierr = VecRestoreArray(coloring->vscale,&vscale_array);CHKERRQ(ierr);
  ierr = VecRestoreArray(x1,&xx);CHKERRQ(ierr);

  coloring->currentcolor = -1;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "MatFDColoringCreate_MPIAIJ_new"
PetscErrorCode MatFDColoringCreate_MPIAIJ_new(Mat mat,ISColoring iscoloring,MatFDColoring c)
{
  Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode         ierr;
  PetscMPIInt            size,*ncolsonproc,*disp,nn;
  PetscInt               i,n,nrows,j,k,m,ncols,col;
  const PetscInt         *is,*A_ci,*A_cj,*B_ci,*B_cj,*row = NULL,*ltog=NULL;
  PetscInt               nis = iscoloring->n,nctot,*cols;
  PetscInt               *rowhit,cstart,cend,colb;
  PetscInt               *columnsforrow,l;
  IS                     *isa;
  ISLocalToGlobalMapping map = mat->cmap->mapping;
  PetscInt               ctype=c->ctype;
  Mat                    A=aij->A,B=aij->B;
  Mat_SeqAIJ             *cspA=(Mat_SeqAIJ*)A->data, *cspB=(Mat_SeqAIJ*)B->data;
  PetscScalar            *A_val=cspA->a,*B_val=cspB->a;
  PetscInt               spidx;
  PetscInt               *spidxA,*spidxB,nz;
  PetscScalar            **valaddrhit;

  PetscFunctionBegin;
  if (ctype == IS_COLORING_GHOSTED) {
    if(!map) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_INCOMP,"When using ghosted differencing matrix must have local to global mapping provided with MatSetLocalToGlobalMapping");
    ierr = ISLocalToGlobalMappingGetIndices(map,&ltog);CHKERRQ(ierr);
  }

  m         = mat->rmap->n;
  cstart    = mat->cmap->rstart;
  cend      = mat->cmap->rend;
  c->M      = mat->rmap->N;         /* set the global rows and columns and local rows */
  c->N      = mat->cmap->N;
  c->m      = m;
  c->rstart = mat->rmap->rstart;

  c->ncolors = nis;
  ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->columns);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->rows);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->columnsforrow);CHKERRQ(ierr);
  ierr       = PetscLogObjectMemory((PetscObject)c,5*nis*sizeof(PetscInt));CHKERRQ(ierr);

  /* Allow access to data structures of local part of matrix
   - creates aij->colmap which maps global column number to local number in part B */
  if (!aij->colmap) {
    ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
  }
  ierr = MatGetColumnIJ_SeqAIJ_Color(aij->A,0,PETSC_FALSE,PETSC_FALSE,&ncols,&A_ci,&A_cj,&spidxA,NULL);CHKERRQ(ierr);
  ierr = MatGetColumnIJ_SeqAIJ_Color(aij->B,0,PETSC_FALSE,PETSC_FALSE,&ncols,&B_ci,&B_cj,&spidxB,NULL);CHKERRQ(ierr);

  ierr = PetscMalloc2(m+1,PetscInt,&rowhit,m+1,PetscScalar*,&valaddrhit);CHKERRQ(ierr);
  ierr = PetscMalloc((m+1)*sizeof(PetscInt),&columnsforrow);CHKERRQ(ierr);
  nz = cspA->nz + cspB->nz; /* total nonzero entries of mat */
  ierr = PetscMalloc(nz*sizeof(PetscScalar*),&c->valaddr);CHKERRQ(ierr);

  nz = 0;
  ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);
  for (i=0; i<nis; i++) { /* for each local color */
    ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
    ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);

    c->ncolumns[i] = n; /* local number of columns of this color on this process */
    if (n) {
      ierr = PetscMalloc(n*sizeof(PetscInt),&c->columns[i]);CHKERRQ(ierr);
      ierr = PetscLogObjectMemory((PetscObject)c,n*sizeof(PetscInt));CHKERRQ(ierr);
      ierr = PetscMemcpy(c->columns[i],is,n*sizeof(PetscInt));CHKERRQ(ierr);
    } else {
      c->columns[i] = 0;
    }

    if (ctype == IS_COLORING_GLOBAL) {
      /* Determine nctot, the total (parallel) number of columns of this color */
      ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
      ierr = PetscMalloc2(size,PetscMPIInt,&ncolsonproc,size,PetscMPIInt,&disp);CHKERRQ(ierr);

      /* ncolsonproc[j]: local ncolumns on proc[j] of this color */
      ierr  = PetscMPIIntCast(n,&nn);CHKERRQ(ierr);
      ierr  = MPI_Allgather(&nn,1,MPI_INT,ncolsonproc,1,MPI_INT,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
      nctot = 0; for (j=0; j<size; j++) nctot += ncolsonproc[j];
      if (!nctot) {
        ierr = PetscInfo(mat,"Coloring of matrix has some unneeded colors with no corresponding rows\n");CHKERRQ(ierr);
      }

      disp[0] = 0;
      for (j=1; j<size; j++) {
        disp[j] = disp[j-1] + ncolsonproc[j-1];
      }

      /* Get cols, the complete list of columns for this color on each process */
      ierr = PetscMalloc((nctot+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
      ierr = MPI_Allgatherv((void*)is,n,MPIU_INT,cols,ncolsonproc,disp,MPIU_INT,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
      ierr = PetscFree2(ncolsonproc,disp);CHKERRQ(ierr);
    } else if (ctype == IS_COLORING_GHOSTED) {
      /* Determine local number of columns of this color on this process, including ghost points */
      nctot = n;
      ierr  = PetscMalloc((nctot+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
      ierr  = PetscMemcpy(cols,is,n*sizeof(PetscInt));CHKERRQ(ierr);
    } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not provided for this MatFDColoring type");

    /* Mark all rows affect by these columns */
    ierr = PetscMemzero(rowhit,m*sizeof(PetscInt));CHKERRQ(ierr);
    for (j=0; j<nctot; j++) { /* loop over columns*/
      if (ctype == IS_COLORING_GHOSTED) {
        col = ltog[cols[j]];
      } else {
        col = cols[j];
      }
      if (col >= cstart && col < cend) { /* column is in diagonal block of matrix A */
        row = A_cj + A_ci[col-cstart];
        nrows = A_ci[col-cstart+1] - A_ci[col-cstart];
        /* loop over columns of A marking them in rowhit */
        for (k=0; k<nrows; k++) {
          /* set valaddrhit for part A */
          spidx            = spidxA[A_ci[col-cstart] + k];
          valaddrhit[*row] = &A_val[spidx];
          rowhit[*row++]   = col + 1;
        }
      } else { /* column is in off-diagonal block of matrix B */
#if defined(PETSC_USE_CTABLE)
        ierr = PetscTableFind(aij->colmap,col+1,&colb);CHKERRQ(ierr);
        colb--;
#else
        colb = aij->colmap[col] - 1; /* local column index */
#endif
        if (colb == -1) {
          nrows = 0;
        } else {
          row   = B_cj + B_ci[colb];
          nrows = B_ci[colb+1] - B_ci[colb];
        }
        /* loop over columns of B marking them in rowhit */
        for (k=0; k<nrows; k++) {
          /* set valaddrhit for part B */
          spidx            = spidxB[B_ci[colb] + k];
          valaddrhit[*row] = &B_val[spidx];
          rowhit[*row++] = col + 1;
        }
      }
    }

    /* count the number of hits */
    nrows = 0;
    for (j=0; j<m; j++) {
      if (rowhit[j]) nrows++;
    }
    c->nrows[i] = nrows;
    ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->rows[i]);CHKERRQ(ierr);
    ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->columnsforrow[i]);CHKERRQ(ierr);
    ierr        = PetscLogObjectMemory((PetscObject)c,2*(nrows+1)*sizeof(PetscInt));CHKERRQ(ierr);
    nrows       = 0;
    for (j=0; j<m; j++) {
      if (rowhit[j]) {
        c->rows[i][nrows]          = j;              /* local row index */
        c->columnsforrow[i][nrows] = rowhit[j] - 1;  /* global column index */
        c->valaddr[nz++]           = valaddrhit[j];   /* address of mat value for this entry */
        nrows++;
      }
    }
    ierr = PetscFree(cols);CHKERRQ(ierr);
  }
  if (nz != cspA->nz + cspB->nz) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_WRONGSTATE,"nz %d != mat->nz %d\n",nz,cspA->nz+cspB->nz);

  /* Optimize by adding the vscale, and scaleforrow[][] fields;
     vscale contains the "diagonal" on processor scalings followed by the off processor */
  if (ctype == IS_COLORING_GLOBAL) {
    ierr = VecCreateGhost(PetscObjectComm((PetscObject)mat),m,PETSC_DETERMINE,B->cmap->n,aij->garray,&c->vscale);CHKERRQ(ierr);
    ierr = PetscMalloc(c->ncolors*sizeof(PetscInt*),&c->vscaleforrow);CHKERRQ(ierr);
    for (k=0; k<c->ncolors; k++) {
      ierr = PetscMalloc((c->nrows[k]+1)*sizeof(PetscInt),&c->vscaleforrow[k]);CHKERRQ(ierr);
      for (l=0; l<c->nrows[k]; l++) {
        col = c->columnsforrow[k][l];
        if (col >= cstart && col < cend) {
          /* column is in diagonal block of matrix */
          colb = col - cstart;
        } else {
          /* column  is in "off-processor" part */
#if defined(PETSC_USE_CTABLE)
          ierr = PetscTableFind(aij->colmap,col+1,&colb);CHKERRQ(ierr);
          colb--;
#else
          colb = aij->colmap[col] - 1;
#endif
          colb += cend - cstart;
        }
        c->vscaleforrow[k][l] = colb; /* local column index */
      }
    }
  } else if (ctype == IS_COLORING_GHOSTED) {
    /* Get gtol mapping */
    PetscInt N = mat->cmap->N,nlocal,*gtol;
    ierr = PetscMalloc((N+1)*sizeof(PetscInt),&gtol);CHKERRQ(ierr);
    for (i=0; i<N; i++) gtol[i] = -1;
    ierr = ISLocalToGlobalMappingGetSize(map,&nlocal);CHKERRQ(ierr);
    for (i=0; i<nlocal; i++) gtol[ltog[i]] = i;

    c->vscale = 0; /* will be created in MatFDColoringApply() */
    ierr      = PetscMalloc(c->ncolors*sizeof(PetscInt*),&c->vscaleforrow);CHKERRQ(ierr);
    for (k=0; k<c->ncolors; k++) {
      ierr = PetscMalloc((c->nrows[k]+1)*sizeof(PetscInt),&c->vscaleforrow[k]);CHKERRQ(ierr);
      for (l=0; l<c->nrows[k]; l++) {
        col                   = c->columnsforrow[k][l]; /* global column index */
        c->vscaleforrow[k][l] = gtol[col];              /* local column index */
      }
    }
    ierr = PetscFree(gtol);CHKERRQ(ierr);
  }
  ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);

  ierr = PetscFree2(rowhit,valaddrhit);CHKERRQ(ierr);
  ierr = PetscFree(columnsforrow);CHKERRQ(ierr);
  ierr = MatRestoreColumnIJ_SeqAIJ_Color(aij->A,0,PETSC_FALSE,PETSC_FALSE,&ncols,&A_ci,&A_cj,&spidxA,NULL);CHKERRQ(ierr);
  ierr = MatRestoreColumnIJ_SeqAIJ_Color(aij->B,0,PETSC_FALSE,PETSC_FALSE,&ncols,&B_ci,&B_cj,&spidxB,NULL);CHKERRQ(ierr);
  if (ctype == IS_COLORING_GHOSTED) {
    ierr = ISLocalToGlobalMappingRestoreIndices(map,&ltog);CHKERRQ(ierr);
  }

  mat->ops->fdcoloringapply = MatFDColoringApply_MPIAIJ;
  PetscFunctionReturn(0);
}

/*------------------------------------------------------*/
#undef __FUNCT__
#define __FUNCT__ "MatFDColoringCreate_MPIAIJ"
PetscErrorCode MatFDColoringCreate_MPIAIJ(Mat mat,ISColoring iscoloring,MatFDColoring c)
{
  Mat_MPIAIJ             *aij = (Mat_MPIAIJ*)mat->data;
  PetscErrorCode         ierr;
  PetscMPIInt            size,*ncolsonproc,*disp,nn;
  PetscInt               i,n,nrows,j,k,m,ncols,col;
  const PetscInt         *is,*A_ci,*A_cj,*B_ci,*B_cj,*rows = 0,*ltog;
  PetscInt               nis = iscoloring->n,nctot,*cols;
  PetscInt               *rowhit,M,cstart,cend,colb;
  PetscInt               *columnsforrow,l;
  IS                     *isa;
  PetscBool              done,flg;
  ISLocalToGlobalMapping map   = mat->cmap->mapping;
  PetscInt               ctype=c->ctype;
  PetscBool              new_impl=PETSC_FALSE;

  PetscFunctionBegin;
  ierr = PetscOptionsName("-new","using new impls","",&new_impl);CHKERRQ(ierr);
  if (new_impl){
    ierr =  MatFDColoringCreate_MPIAIJ_new(mat,iscoloring,c);CHKERRQ(ierr);
    PetscFunctionReturn(0);
  }
  if (ctype == IS_COLORING_GHOSTED && !map) SETERRQ(PetscObjectComm((PetscObject)mat),PETSC_ERR_ARG_INCOMP,"When using ghosted differencing matrix must have local to global mapping provided with MatSetLocalToGlobalMapping");

  if (map) {ierr = ISLocalToGlobalMappingGetIndices(map,&ltog);CHKERRQ(ierr);}
  else     ltog = NULL;
  ierr = ISColoringGetIS(iscoloring,PETSC_IGNORE,&isa);CHKERRQ(ierr);

  M         = mat->rmap->n;
  cstart    = mat->cmap->rstart;
  cend      = mat->cmap->rend;
  c->M      = mat->rmap->N;         /* set the global rows and columns and local rows */
  c->N      = mat->cmap->N;
  c->m      = mat->rmap->n;
  c->rstart = mat->rmap->rstart;

  c->ncolors = nis;
  ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->ncolumns);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->columns);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt),&c->nrows);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->rows);CHKERRQ(ierr);
  ierr       = PetscMalloc(nis*sizeof(PetscInt*),&c->columnsforrow);CHKERRQ(ierr);
  ierr       = PetscLogObjectMemory((PetscObject)c,5*nis*sizeof(PetscInt));CHKERRQ(ierr);

  /* Allow access to data structures of local part of matrix */
  if (!aij->colmap) {
    ierr = MatCreateColmap_MPIAIJ_Private(mat);CHKERRQ(ierr);
  }
  ierr = MatGetColumnIJ(aij->A,0,PETSC_FALSE,PETSC_FALSE,&ncols,&A_ci,&A_cj,&done);CHKERRQ(ierr);
  ierr = MatGetColumnIJ(aij->B,0,PETSC_FALSE,PETSC_FALSE,&ncols,&B_ci,&B_cj,&done);CHKERRQ(ierr);

  ierr = PetscMalloc((M+1)*sizeof(PetscInt),&rowhit);CHKERRQ(ierr);
  ierr = PetscMalloc((M+1)*sizeof(PetscInt),&columnsforrow);CHKERRQ(ierr);

  for (i=0; i<nis; i++) {
    ierr = ISGetLocalSize(isa[i],&n);CHKERRQ(ierr);
    ierr = ISGetIndices(isa[i],&is);CHKERRQ(ierr);

    c->ncolumns[i] = n; /* local number of columns of this color on this process */
    if (n) {
      ierr = PetscMalloc(n*sizeof(PetscInt),&c->columns[i]);CHKERRQ(ierr);
      ierr = PetscLogObjectMemory((PetscObject)c,n*sizeof(PetscInt));CHKERRQ(ierr);
      ierr = PetscMemcpy(c->columns[i],is,n*sizeof(PetscInt));CHKERRQ(ierr);
    } else {
      c->columns[i] = 0;
    }

    if (ctype == IS_COLORING_GLOBAL) {
      /* Determine the total (parallel) number of columns of this color */
      ierr = MPI_Comm_size(PetscObjectComm((PetscObject)mat),&size);CHKERRQ(ierr);
      ierr = PetscMalloc2(size,PetscMPIInt,&ncolsonproc,size,PetscMPIInt,&disp);CHKERRQ(ierr);

      ierr  = PetscMPIIntCast(n,&nn);CHKERRQ(ierr);
      ierr  = MPI_Allgather(&nn,1,MPI_INT,ncolsonproc,1,MPI_INT,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
      nctot = 0; for (j=0; j<size; j++) nctot += ncolsonproc[j];
      if (!nctot) {
        ierr = PetscInfo(mat,"Coloring of matrix has some unneeded colors with no corresponding rows\n");CHKERRQ(ierr);
      }

      disp[0] = 0;
      for (j=1; j<size; j++) {
        disp[j] = disp[j-1] + ncolsonproc[j-1];
      }

      /* Get complete list of columns for color on each processor */
      ierr = PetscMalloc((nctot+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
      ierr = MPI_Allgatherv((void*)is,n,MPIU_INT,cols,ncolsonproc,disp,MPIU_INT,PetscObjectComm((PetscObject)mat));CHKERRQ(ierr);
      ierr = PetscFree2(ncolsonproc,disp);CHKERRQ(ierr);
    } else if (ctype == IS_COLORING_GHOSTED) {
      /* Determine local number of columns of this color on this process, including ghost points */
      nctot = n;
      ierr  = PetscMalloc((nctot+1)*sizeof(PetscInt),&cols);CHKERRQ(ierr);
      ierr  = PetscMemcpy(cols,is,n*sizeof(PetscInt));CHKERRQ(ierr);
    } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_SUP,"Not provided for this MatFDColoring type");

    /*
       Mark all rows affect by these columns
    */
    /* Temporary option to allow for debugging/testing */
    flg  = PETSC_FALSE;
    ierr = PetscOptionsGetBool(NULL,"-matfdcoloring_slow",&flg,NULL);CHKERRQ(ierr);
    if (!flg) { /*-----------------------------------------------------------------------------*/
      /* crude, fast version */
      ierr = PetscMemzero(rowhit,M*sizeof(PetscInt));CHKERRQ(ierr);
      /* loop over columns*/
      for (j=0; j<nctot; j++) {
        if (ctype == IS_COLORING_GHOSTED) {
          col = ltog[cols[j]];
        } else {
          col = cols[j];
        }
        if (col >= cstart && col < cend) {
          /* column is in diagonal block of matrix */
          rows = A_cj + A_ci[col-cstart];
          m    = A_ci[col-cstart+1] - A_ci[col-cstart];
        } else {
#if defined(PETSC_USE_CTABLE)
          ierr = PetscTableFind(aij->colmap,col+1,&colb);CHKERRQ(ierr);
          colb--;
#else
          colb = aij->colmap[col] - 1;
#endif
          if (colb == -1) {
            m = 0;
          } else {
            rows = B_cj + B_ci[colb];
            m    = B_ci[colb+1] - B_ci[colb];
          }
        }
        /* loop over columns marking them in rowhit */
        for (k=0; k<m; k++) {
          rowhit[*rows++] = col + 1;
        }
      }

      /* count the number of hits */
      nrows = 0;
      for (j=0; j<M; j++) {
        if (rowhit[j]) nrows++;
      }
      c->nrows[i] = nrows;
      ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->rows[i]);CHKERRQ(ierr);
      ierr        = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->columnsforrow[i]);CHKERRQ(ierr);
      ierr        = PetscLogObjectMemory((PetscObject)c,2*(nrows+1)*sizeof(PetscInt));CHKERRQ(ierr);
      nrows       = 0;
      for (j=0; j<M; j++) {
        if (rowhit[j]) {
          c->rows[i][nrows]          = j;              /* local row index */
          c->columnsforrow[i][nrows] = rowhit[j] - 1;  /* global column index */
          nrows++;
        }
      }
    } else { /*-------------------------------------------------------------------------------*/
      /* slow version, using rowhit as a linked list */
      PetscInt currentcol,fm,mfm;
      rowhit[M] = M;
      nrows     = 0;
      /* loop over columns*/
      for (j=0; j<nctot; j++) {
        if (ctype == IS_COLORING_GHOSTED) {
          col = ltog[cols[j]];
        } else {
          col = cols[j];
        }
        if (col >= cstart && col < cend) {
          /* column is in diagonal block of matrix */
          rows = A_cj + A_ci[col-cstart];
          m    = A_ci[col-cstart+1] - A_ci[col-cstart];
        } else {
#if defined(PETSC_USE_CTABLE)
          ierr = PetscTableFind(aij->colmap,col+1,&colb);CHKERRQ(ierr);
          colb--;
#else
          colb = aij->colmap[col] - 1;
#endif
          if (colb == -1) {
            m = 0;
          } else {
            rows = B_cj + B_ci[colb];
            m    = B_ci[colb+1] - B_ci[colb];
          }
        }

        /* loop over columns marking them in rowhit */
        fm = M;    /* fm points to first entry in linked list */
        for (k=0; k<m; k++) {
          currentcol = *rows++;
          /* is it already in the list? */
          do {
            mfm = fm;
            fm  = rowhit[fm];
          } while (fm < currentcol);
          /* not in list so add it */
          if (fm != currentcol) {
            nrows++;
            columnsforrow[currentcol] = col;
            /* next three lines insert new entry into linked list */
            rowhit[mfm]        = currentcol;
            rowhit[currentcol] = fm;
            fm                 = currentcol;
            /* fm points to present position in list since we know the columns are sorted */
          } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"Invalid coloring of matrix detected");
        }
      }
      c->nrows[i] = nrows;

      ierr = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->rows[i]);CHKERRQ(ierr);
      ierr = PetscMalloc((nrows+1)*sizeof(PetscInt),&c->columnsforrow[i]);CHKERRQ(ierr);
      ierr = PetscLogObjectMemory((PetscObject)c,(nrows+1)*sizeof(PetscInt));CHKERRQ(ierr);
      /* now store the linked list of rows into c->rows[i] */
      nrows = 0;
      fm    = rowhit[M];
      do {
        c->rows[i][nrows]            = fm;
        c->columnsforrow[i][nrows++] = columnsforrow[fm];
        fm                           = rowhit[fm];
      } while (fm < M);
    } /* ---------------------------------------------------------------------------------------*/
    ierr = PetscFree(cols);CHKERRQ(ierr);
  }

  /* Optimize by adding the vscale, and scaleforrow[][] fields */
  /*
       vscale will contain the "diagonal" on processor scalings followed by the off processor
  */
  if (ctype == IS_COLORING_GLOBAL) {
    ierr = VecCreateGhost(PetscObjectComm((PetscObject)mat),aij->A->rmap->n,PETSC_DETERMINE,aij->B->cmap->n,aij->garray,&c->vscale);CHKERRQ(ierr);
    ierr = PetscMalloc(c->ncolors*sizeof(PetscInt*),&c->vscaleforrow);CHKERRQ(ierr);
    for (k=0; k<c->ncolors; k++) {
      ierr = PetscMalloc((c->nrows[k]+1)*sizeof(PetscInt),&c->vscaleforrow[k]);CHKERRQ(ierr);
      for (l=0; l<c->nrows[k]; l++) {
        col = c->columnsforrow[k][l];
        if (col >= cstart && col < cend) {
          /* column is in diagonal block of matrix */
          colb = col - cstart;
        } else {
          /* column  is in "off-processor" part */
#if defined(PETSC_USE_CTABLE)
          ierr = PetscTableFind(aij->colmap,col+1,&colb);CHKERRQ(ierr);
          colb--;
#else
          colb = aij->colmap[col] - 1;
#endif
          colb += cend - cstart;
        }
        c->vscaleforrow[k][l] = colb;
      }
    }
  } else if (ctype == IS_COLORING_GHOSTED) {
    /* Get gtol mapping */
    PetscInt N = mat->cmap->N,nlocal,*gtol;
    ierr = PetscMalloc((N+1)*sizeof(PetscInt),&gtol);CHKERRQ(ierr);
    for (i=0; i<N; i++) gtol[i] = -1;
    ierr = ISLocalToGlobalMappingGetSize(map,&nlocal);CHKERRQ(ierr);
    for (i=0; i<nlocal; i++) gtol[ltog[i]] = i;

    c->vscale = 0; /* will be created in MatFDColoringApply() */
    ierr      = PetscMalloc(c->ncolors*sizeof(PetscInt*),&c->vscaleforrow);CHKERRQ(ierr);
    for (k=0; k<c->ncolors; k++) {
      ierr = PetscMalloc((c->nrows[k]+1)*sizeof(PetscInt),&c->vscaleforrow[k]);CHKERRQ(ierr);
      for (l=0; l<c->nrows[k]; l++) {
        col = c->columnsforrow[k][l];      /* global column index */

        c->vscaleforrow[k][l] = gtol[col]; /* local column index */
      }
    }
    ierr = PetscFree(gtol);CHKERRQ(ierr);
  }
  ierr = ISColoringRestoreIS(iscoloring,&isa);CHKERRQ(ierr);

  ierr = PetscFree(rowhit);CHKERRQ(ierr);
  ierr = PetscFree(columnsforrow);CHKERRQ(ierr);
  ierr = MatRestoreColumnIJ(aij->A,0,PETSC_FALSE,PETSC_FALSE,&ncols,&A_ci,&A_cj,&done);CHKERRQ(ierr);
  ierr = MatRestoreColumnIJ(aij->B,0,PETSC_FALSE,PETSC_FALSE,&ncols,&B_ci,&B_cj,&done);CHKERRQ(ierr);
  if (map) {ierr = ISLocalToGlobalMappingRestoreIndices(map,&ltog);CHKERRQ(ierr);}
  PetscFunctionReturn(0);
}