xref: /petsc/src/dm/impls/da/da2.c (revision 45b6f7e9ecd564e8bb535880b270d4a8084ff211)

#include <petsc-private/dmdaimpl.h>    /*I   "petscdmda.h"   I*/
#include <petscdraw.h>

#undef __FUNCT__
#define __FUNCT__ "DMView_DA_2d"
PetscErrorCode DMView_DA_2d(DM da,PetscViewer viewer)
{
  PetscErrorCode ierr;
  PetscMPIInt    rank;
  PetscBool      iascii,isdraw,isbinary;
  DM_DA          *dd = (DM_DA*)da->data;
#if defined(PETSC_HAVE_MATLAB_ENGINE)
  PetscBool ismatlab;
#endif

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(PetscObjectComm((PetscObject)da),&rank);CHKERRQ(ierr);

  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);CHKERRQ(ierr);
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);CHKERRQ(ierr);
#if defined(PETSC_HAVE_MATLAB_ENGINE)
  ierr = PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERMATLAB,&ismatlab);CHKERRQ(ierr);
#endif
  if (iascii) {
    PetscViewerFormat format;

    ierr = PetscViewerGetFormat(viewer, &format);CHKERRQ(ierr);
    if (format != PETSC_VIEWER_ASCII_VTK && format != PETSC_VIEWER_ASCII_VTK_CELL) {
      DMDALocalInfo info;
      ierr = DMDAGetLocalInfo(da,&info);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer,"Processor [%d] M %D N %D m %D n %D w %D s %D\n",rank,dd->M,dd->N,dd->m,dd->n,dd->w,dd->s);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedPrintf(viewer,"X range of indices: %D %D, Y range of indices: %D %D\n",info.xs,info.xs+info.xm,info.ys,info.ys+info.ym);CHKERRQ(ierr);
      ierr = PetscViewerFlush(viewer);CHKERRQ(ierr);
      ierr = PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);CHKERRQ(ierr);
    } else {
      ierr = DMView_DA_VTK(da,viewer);CHKERRQ(ierr);
    }
  } else if (isdraw) {
    PetscDraw      draw;
    double         ymin = -1*dd->s-1,ymax = dd->N+dd->s;
    double         xmin = -1*dd->s-1,xmax = dd->M+dd->s;
    double         x,y;
    PetscInt       base;
    const PetscInt *idx;
    char           node[10];
    PetscBool      isnull;

    ierr = PetscViewerDrawGetDraw(viewer,0,&draw);CHKERRQ(ierr);
    ierr = PetscDrawIsNull(draw,&isnull);CHKERRQ(ierr); if (isnull) PetscFunctionReturn(0);
    if (!da->coordinates) {
      ierr = PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);CHKERRQ(ierr);
    }
    ierr = PetscDrawSynchronizedClear(draw);CHKERRQ(ierr);

    /* first processor draw all node lines */
    if (!rank) {
      ymin = 0.0; ymax = dd->N - 1;
      for (xmin=0; xmin<dd->M; xmin++) {
        ierr = PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);CHKERRQ(ierr);
      }
      xmin = 0.0; xmax = dd->M - 1;
      for (ymin=0; ymin<dd->N; ymin++) {
        ierr = PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);CHKERRQ(ierr);
      }
    }
    ierr = PetscDrawSynchronizedFlush(draw);CHKERRQ(ierr);
    ierr = PetscDrawPause(draw);CHKERRQ(ierr);

    /* draw my box */
    ymin = dd->ys; ymax = dd->ye - 1; xmin = dd->xs/dd->w;
    xmax =(dd->xe-1)/dd->w;
    ierr = PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);CHKERRQ(ierr);
    ierr = PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);CHKERRQ(ierr);
    ierr = PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);CHKERRQ(ierr);
    ierr = PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);CHKERRQ(ierr);

    /* put in numbers */
    base = (dd->base)/dd->w;
    for (y=ymin; y<=ymax; y++) {
      for (x=xmin; x<=xmax; x++) {
        sprintf(node,"%d",(int)base++);
        ierr = PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);CHKERRQ(ierr);
      }
    }

    ierr = PetscDrawSynchronizedFlush(draw);CHKERRQ(ierr);
    ierr = PetscDrawPause(draw);CHKERRQ(ierr);
    /* overlay ghost numbers, useful for error checking */
    /* put in numbers */

    base = 0;
    ierr = ISLocalToGlobalMappingGetBlockIndices(da->ltogmap,&idx);CHKERRQ(ierr);
    ymin = dd->Ys; ymax = dd->Ye; xmin = dd->Xs; xmax = dd->Xe;
    for (y=ymin; y<ymax; y++) {
      for (x=xmin; x<xmax; x++) {
        if ((base % dd->w) == 0) {
          sprintf(node,"%d",(int)(idx[base/dd->w]));
          ierr = PetscDrawString(draw,x/dd->w,y,PETSC_DRAW_BLUE,node);CHKERRQ(ierr);
        }
        base++;
      }
    }
    ierr = ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap,&idx);
    ierr = PetscDrawSynchronizedFlush(draw);CHKERRQ(ierr);
    ierr = PetscDrawPause(draw);CHKERRQ(ierr);
  } else if (isbinary) {
    ierr = DMView_DA_Binary(da,viewer);CHKERRQ(ierr);
#if defined(PETSC_HAVE_MATLAB_ENGINE)
  } else if (ismatlab) {
    ierr = DMView_DA_Matlab(da,viewer);CHKERRQ(ierr);
#endif
  }
  PetscFunctionReturn(0);
}

/*
      M is number of grid points
      m is number of processors

*/
#undef __FUNCT__
#define __FUNCT__ "DMDASplitComm2d"
PetscErrorCode  DMDASplitComm2d(MPI_Comm comm,PetscInt M,PetscInt N,PetscInt sw,MPI_Comm *outcomm)
{
  PetscErrorCode ierr;
  PetscInt       m,n = 0,x = 0,y = 0;
  PetscMPIInt    size,csize,rank;

  PetscFunctionBegin;
  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);

  csize = 4*size;
  do {
    if (csize % 4) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_INCOMP,"Cannot split communicator of size %d tried %d %D %D",size,csize,x,y);
    csize = csize/4;

    m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)csize)/((PetscReal)N)));
    if (!m) m = 1;
    while (m > 0) {
      n = csize/m;
      if (m*n == csize) break;
      m--;
    }
    if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}

    x = M/m + ((M % m) > ((csize-1) % m));
    y = (N + (csize-1)/m)/n;
  } while ((x < 4 || y < 4) && csize > 1);
  if (size != csize) {
    MPI_Group   entire_group,sub_group;
    PetscMPIInt i,*groupies;

    ierr = MPI_Comm_group(comm,&entire_group);CHKERRQ(ierr);
    ierr = PetscMalloc1(csize,&groupies);CHKERRQ(ierr);
    for (i=0; i<csize; i++) {
      groupies[i] = (rank/csize)*csize + i;
    }
    ierr = MPI_Group_incl(entire_group,csize,groupies,&sub_group);CHKERRQ(ierr);
    ierr = PetscFree(groupies);CHKERRQ(ierr);
    ierr = MPI_Comm_create(comm,sub_group,outcomm);CHKERRQ(ierr);
    ierr = MPI_Group_free(&entire_group);CHKERRQ(ierr);
    ierr = MPI_Group_free(&sub_group);CHKERRQ(ierr);
    ierr = PetscInfo1(0,"DMDASplitComm2d:Creating redundant coarse problems of size %d\n",csize);CHKERRQ(ierr);
  } else {
    *outcomm = comm;
  }
  PetscFunctionReturn(0);
}

#if defined(new)
#undef __FUNCT__
#define __FUNCT__ "DMDAGetDiagonal_MFFD"
/*
  DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix where local
    function lives on a DMDA

        y ~= (F(u + ha) - F(u))/h,
  where F = nonlinear function, as set by SNESSetFunction()
        u = current iterate
        h = difference interval
*/
PetscErrorCode DMDAGetDiagonal_MFFD(DM da,Vec U,Vec a)
{
  PetscScalar    h,*aa,*ww,v;
  PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
  PetscErrorCode ierr;
  PetscInt       gI,nI;
  MatStencil     stencil;
  DMDALocalInfo  info;

  PetscFunctionBegin;
  ierr = (*ctx->func)(0,U,a,ctx->funcctx);CHKERRQ(ierr);
  ierr = (*ctx->funcisetbase)(U,ctx->funcctx);CHKERRQ(ierr);

  ierr = VecGetArray(U,&ww);CHKERRQ(ierr);
  ierr = VecGetArray(a,&aa);CHKERRQ(ierr);

  nI = 0;
  h  = ww[gI];
  if (h == 0.0) h = 1.0;
  if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
  else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
  h *= epsilon;

  ww[gI] += h;
  ierr    = (*ctx->funci)(i,w,&v,ctx->funcctx);CHKERRQ(ierr);
  aa[nI]  = (v - aa[nI])/h;
  ww[gI] -= h;
  nI++;

  ierr = VecRestoreArray(U,&ww);CHKERRQ(ierr);
  ierr = VecRestoreArray(a,&aa);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}
#endif

#undef __FUNCT__
#define __FUNCT__ "DMSetUp_DA_2D"
PetscErrorCode  DMSetUp_DA_2D(DM da)
{
  DM_DA            *dd = (DM_DA*)da->data;
  const PetscInt   M            = dd->M;
  const PetscInt   N            = dd->N;
  PetscInt         m            = dd->m;
  PetscInt         n            = dd->n;
  const PetscInt   dof          = dd->w;
  const PetscInt   s            = dd->s;
  DMBoundaryType   bx           = dd->bx;
  DMBoundaryType   by           = dd->by;
  DMDAStencilType  stencil_type = dd->stencil_type;
  PetscInt         *lx          = dd->lx;
  PetscInt         *ly          = dd->ly;
  MPI_Comm         comm;
  PetscMPIInt      rank,size;
  PetscInt         xs,xe,ys,ye,x,y,Xs,Xe,Ys,Ye,start,end,IXs,IXe,IYs,IYe;
  PetscInt         up,down,left,right,i,n0,n1,n2,n3,n5,n6,n7,n8,*idx,nn;
  PetscInt         xbase,*bases,*ldims,j,x_t,y_t,s_t,base,count;
  PetscInt         s_x,s_y; /* s proportionalized to w */
  PetscInt         sn0 = 0,sn2 = 0,sn6 = 0,sn8 = 0;
  Vec              local,global;
  VecScatter       ltog,gtol;
  IS               to,from;
  PetscErrorCode   ierr;

  PetscFunctionBegin;
  if (stencil_type == DMDA_STENCIL_BOX && (bx == DM_BOUNDARY_MIRROR || by == DM_BOUNDARY_MIRROR)) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Mirror boundary and box stencil");
  ierr = PetscObjectGetComm((PetscObject)da,&comm);CHKERRQ(ierr);
#if !defined(PETSC_USE_64BIT_INDICES)
  if (((Petsc64bitInt) M)*((Petsc64bitInt) N)*((Petsc64bitInt) dof) > (Petsc64bitInt) PETSC_MPI_INT_MAX) SETERRQ3(comm,PETSC_ERR_INT_OVERFLOW,"Mesh of %D by %D by %D (dof) is too large for 32 bit indices",M,N,dof);
#endif

  if (dof < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Must have 1 or more degrees of freedom per node: %D",dof);
  if (s < 0) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Stencil width cannot be negative: %D",s);

  ierr = MPI_Comm_size(comm,&size);CHKERRQ(ierr);
  ierr = MPI_Comm_rank(comm,&rank);CHKERRQ(ierr);

  if (m != PETSC_DECIDE) {
    if (m < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
    else if (m > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
  }
  if (n != PETSC_DECIDE) {
    if (n < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
    else if (n > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
  }

  if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
    if (n != PETSC_DECIDE) {
      m = size/n;
    } else if (m != PETSC_DECIDE) {
      n = size/m;
    } else {
      /* try for squarish distribution */
      m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N)));
      if (!m) m = 1;
      while (m > 0) {
        n = size/m;
        if (m*n == size) break;
        m--;
      }
      if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
    }
    if (m*n != size) SETERRQ(comm,PETSC_ERR_PLIB,"Unable to create partition, check the size of the communicator and input m and n ");
  } else if (m*n != size) SETERRQ(comm,PETSC_ERR_ARG_OUTOFRANGE,"Given Bad partition");

  if (M < m) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Partition in x direction is too fine! %D %D",M,m);
  if (N < n) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Partition in y direction is too fine! %D %D",N,n);

  /*
     Determine locally owned region
     xs is the first local node number, x is the number of local nodes
  */
  if (!lx) {
    ierr = PetscMalloc1(m, &dd->lx);CHKERRQ(ierr);
    lx   = dd->lx;
    for (i=0; i<m; i++) {
      lx[i] = M/m + ((M % m) > i);
    }
  }
  x  = lx[rank % m];
  xs = 0;
  for (i=0; i<(rank % m); i++) {
    xs += lx[i];
  }
#if defined(PETSC_USE_DEBUG)
  left = xs;
  for (i=(rank % m); i<m; i++) {
    left += lx[i];
  }
  if (left != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of lx across processors not equal to M: %D %D",left,M);
#endif

  /*
     Determine locally owned region
     ys is the first local node number, y is the number of local nodes
  */
  if (!ly) {
    ierr = PetscMalloc1(n, &dd->ly);CHKERRQ(ierr);
    ly   = dd->ly;
    for (i=0; i<n; i++) {
      ly[i] = N/n + ((N % n) > i);
    }
  }
  y  = ly[rank/m];
  ys = 0;
  for (i=0; i<(rank/m); i++) {
    ys += ly[i];
  }
#if defined(PETSC_USE_DEBUG)
  left = ys;
  for (i=(rank/m); i<n; i++) {
    left += ly[i];
  }
  if (left != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of ly across processors not equal to N: %D %D",left,N);
#endif

  /*
   check if the scatter requires more than one process neighbor or wraps around
   the domain more than once
  */
  if ((x < s) && ((m > 1) || (bx == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local x-width of domain x %D is smaller than stencil width s %D",x,s);
  if ((y < s) && ((n > 1) || (by == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local y-width of domain y %D is smaller than stencil width s %D",y,s);
  xe = xs + x;
  ye = ys + y;

  /* determine ghost region (Xs) and region scattered into (IXs)  */
  if (xs-s > 0) {
    Xs = xs - s; IXs = xs - s;
  } else {
    if (bx) {
      Xs = xs - s;
    } else {
      Xs = 0;
    }
    IXs = 0;
  }
  if (xe+s <= M) {
    Xe = xe + s; IXe = xe + s;
  } else {
    if (bx) {
      Xs = xs - s; Xe = xe + s;
    } else {
      Xe = M;
    }
    IXe = M;
  }

  if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
    IXs = xs - s;
    IXe = xe + s;
    Xs  = xs - s;
    Xe  = xe + s;
  }

  if (ys-s > 0) {
    Ys = ys - s; IYs = ys - s;
  } else {
    if (by) {
      Ys = ys - s;
    } else {
      Ys = 0;
    }
    IYs = 0;
  }
  if (ye+s <= N) {
    Ye = ye + s; IYe = ye + s;
  } else {
    if (by) {
      Ye = ye + s;
    } else {
      Ye = N;
    }
    IYe = N;
  }

  if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
    IYs = ys - s;
    IYe = ye + s;
    Ys  = ys - s;
    Ye  = ye + s;
  }

  /* stencil length in each direction */
  s_x = s;
  s_y = s;

  /* determine starting point of each processor */
  nn       = x*y;
  ierr     = PetscMalloc2(size+1,&bases,size,&ldims);CHKERRQ(ierr);
  ierr     = MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);CHKERRQ(ierr);
  bases[0] = 0;
  for (i=1; i<=size; i++) {
    bases[i] = ldims[i-1];
  }
  for (i=1; i<=size; i++) {
    bases[i] += bases[i-1];
  }
  base = bases[rank]*dof;

  /* allocate the base parallel and sequential vectors */
  dd->Nlocal = x*y*dof;
  ierr       = VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,0,&global);CHKERRQ(ierr);
  dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
  ierr       = VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,0,&local);CHKERRQ(ierr);

  /* generate appropriate vector scatters */
  /* local to global inserts non-ghost point region into global */
  ierr = VecGetOwnershipRange(global,&start,&end);CHKERRQ(ierr);
  ierr = ISCreateStride(comm,x*y*dof,start,1,&to);CHKERRQ(ierr);

  ierr  = PetscMalloc1(x*y,&idx);CHKERRQ(ierr);
  left  = xs - Xs; right = left + x;
  down  = ys - Ys; up = down + y;
  count = 0;
  for (i=down; i<up; i++) {
    for (j=left; j<right; j++) {
      idx[count++] = i*(Xe-Xs) + j;
    }
  }

  ierr = ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&from);CHKERRQ(ierr);
  ierr = VecScatterCreate(local,from,global,to,&ltog);CHKERRQ(ierr);
  ierr = PetscLogObjectParent((PetscObject)da,(PetscObject)ltog);CHKERRQ(ierr);
  ierr = ISDestroy(&from);CHKERRQ(ierr);
  ierr = ISDestroy(&to);CHKERRQ(ierr);

  /* global to local must include ghost points within the domain,
     but not ghost points outside the domain that aren't periodic */
  if (stencil_type == DMDA_STENCIL_BOX) {
    count = (IXe-IXs)*(IYe-IYs);
    ierr  = PetscMalloc1(count,&idx);CHKERRQ(ierr);

    left  = IXs - Xs; right = left + (IXe-IXs);
    down  = IYs - Ys; up = down + (IYe-IYs);
    count = 0;
    for (i=down; i<up; i++) {
      for (j=left; j<right; j++) {
        idx[count++] = j + i*(Xe-Xs);
      }
    }
    ierr = ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);CHKERRQ(ierr);

  } else {
    /* must drop into cross shape region */
    /*       ---------|
            |  top    |
         |---         ---| up
         |   middle      |
         |               |
         ----         ---- down
            | bottom  |
            -----------
         Xs xs        xe Xe */
    count = (ys-IYs)*x + y*(IXe-IXs) + (IYe-ye)*x;
    ierr  = PetscMalloc1(count,&idx);CHKERRQ(ierr);

    left  = xs - Xs; right = left + x;
    down  = ys - Ys; up = down + y;
    count = 0;
    /* bottom */
    for (i=(IYs-Ys); i<down; i++) {
      for (j=left; j<right; j++) {
        idx[count++] = j + i*(Xe-Xs);
      }
    }
    /* middle */
    for (i=down; i<up; i++) {
      for (j=(IXs-Xs); j<(IXe-Xs); j++) {
        idx[count++] = j + i*(Xe-Xs);
      }
    }
    /* top */
    for (i=up; i<up+IYe-ye; i++) {
      for (j=left; j<right; j++) {
        idx[count++] = j + i*(Xe-Xs);
      }
    }
    ierr = ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);CHKERRQ(ierr);
  }


  /* determine who lies on each side of us stored in    n6 n7 n8
                                                        n3    n5
                                                        n0 n1 n2
  */

  /* Assume the Non-Periodic Case */
  n1 = rank - m;
  if (rank % m) {
    n0 = n1 - 1;
  } else {
    n0 = -1;
  }
  if ((rank+1) % m) {
    n2 = n1 + 1;
    n5 = rank + 1;
    n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
  } else {
    n2 = -1; n5 = -1; n8 = -1;
  }
  if (rank % m) {
    n3 = rank - 1;
    n6 = n3 + m; if (n6 >= m*n) n6 = -1;
  } else {
    n3 = -1; n6 = -1;
  }
  n7 = rank + m; if (n7 >= m*n) n7 = -1;

  if (bx == DM_BOUNDARY_PERIODIC && by == DM_BOUNDARY_PERIODIC) {
    /* Modify for Periodic Cases */
    /* Handle all four corners */
    if ((n6 < 0) && (n7 < 0) && (n3 < 0)) n6 = m-1;
    if ((n8 < 0) && (n7 < 0) && (n5 < 0)) n8 = 0;
    if ((n2 < 0) && (n5 < 0) && (n1 < 0)) n2 = size-m;
    if ((n0 < 0) && (n3 < 0) && (n1 < 0)) n0 = size-1;

    /* Handle Top and Bottom Sides */
    if (n1 < 0) n1 = rank + m * (n-1);
    if (n7 < 0) n7 = rank - m * (n-1);
    if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
    if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;

    /* Handle Left and Right Sides */
    if (n3 < 0) n3 = rank + (m-1);
    if (n5 < 0) n5 = rank - (m-1);
    if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
  } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
    if (n1 < 0) n1 = rank + m * (n-1);
    if (n7 < 0) n7 = rank - m * (n-1);
    if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
    if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
  } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
    if (n3 < 0) n3 = rank + (m-1);
    if (n5 < 0) n5 = rank - (m-1);
    if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
  }

  ierr = PetscMalloc1(9,&dd->neighbors);CHKERRQ(ierr);

  dd->neighbors[0] = n0;
  dd->neighbors[1] = n1;
  dd->neighbors[2] = n2;
  dd->neighbors[3] = n3;
  dd->neighbors[4] = rank;
  dd->neighbors[5] = n5;
  dd->neighbors[6] = n6;
  dd->neighbors[7] = n7;
  dd->neighbors[8] = n8;

  if (stencil_type == DMDA_STENCIL_STAR) {
    /* save corner processor numbers */
    sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
    n0  = n2 = n6 = n8 = -1;
  }

  ierr = PetscMalloc1((Xe-Xs)*(Ye-Ys),&idx);CHKERRQ(ierr);
  ierr = PetscLogObjectMemory((PetscObject)da,(Xe-Xs)*(Ye-Ys)*sizeof(PetscInt));CHKERRQ(ierr);

  nn = 0;
  xbase = bases[rank];
  for (i=1; i<=s_y; i++) {
    if (n0 >= 0) { /* left below */
      x_t = lx[n0 % m];
      y_t = ly[(n0/m)];
      s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    }

    if (n1 >= 0) { /* directly below */
      x_t = x;
      y_t = ly[(n1/m)];
      s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
      for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    } else if (by == DM_BOUNDARY_MIRROR) {
      for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    }

    if (n2 >= 0) { /* right below */
      x_t = lx[n2 % m];
      y_t = ly[(n2/m)];
      s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    }
  }

  for (i=0; i<y; i++) {
    if (n3 >= 0) { /* directly left */
      x_t = lx[n3 % m];
      /* y_t = y; */
      s_t = bases[n3] + (i+1)*x_t - s_x;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    } else if (bx == DM_BOUNDARY_MIRROR) {
      for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    }

    for (j=0; j<x; j++) idx[nn++] = xbase++; /* interior */

    if (n5 >= 0) { /* directly right */
      x_t = lx[n5 % m];
      /* y_t = y; */
      s_t = bases[n5] + (i)*x_t;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    } else if (bx == DM_BOUNDARY_MIRROR) {
      for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    }
  }

  for (i=1; i<=s_y; i++) {
    if (n6 >= 0) { /* left above */
      x_t = lx[n6 % m];
      /* y_t = ly[(n6/m)]; */
      s_t = bases[n6] + (i)*x_t - s_x;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    }

    if (n7 >= 0) { /* directly above */
      x_t = x;
      /* y_t = ly[(n7/m)]; */
      s_t = bases[n7] + (i-1)*x_t;
      for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    } else if (by == DM_BOUNDARY_MIRROR) {
      for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    }

    if (n8 >= 0) { /* right above */
      x_t = lx[n8 % m];
      /* y_t = ly[(n8/m)]; */
      s_t = bases[n8] + (i-1)*x_t;
      for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    }
  }

  ierr = ISCreateBlock(comm,dof,nn,idx,PETSC_COPY_VALUES,&from);CHKERRQ(ierr);
  ierr = VecScatterCreate(global,from,local,to,&gtol);CHKERRQ(ierr);
  ierr = PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);CHKERRQ(ierr);
  ierr = ISDestroy(&to);CHKERRQ(ierr);
  ierr = ISDestroy(&from);CHKERRQ(ierr);

  if (stencil_type == DMDA_STENCIL_STAR) {
    n0 = sn0; n2 = sn2; n6 = sn6; n8 = sn8;
  }

  if (((stencil_type == DMDA_STENCIL_STAR)  ||
       (bx && bx != DM_BOUNDARY_PERIODIC) ||
       (by && by != DM_BOUNDARY_PERIODIC))) {
    /*
        Recompute the local to global mappings, this time keeping the
      information about the cross corner processor numbers and any ghosted
      but not periodic indices.
    */
    nn    = 0;
    xbase = bases[rank];
    for (i=1; i<=s_y; i++) {
      if (n0 >= 0) { /* left below */
        x_t = lx[n0 % m];
        y_t = ly[(n0/m)];
        s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (xs-Xs > 0 && ys-Ys > 0) {
        for (j=0; j<s_x; j++) idx[nn++] = -1;
      }
      if (n1 >= 0) { /* directly below */
        x_t = x;
        y_t = ly[(n1/m)];
        s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
        for (j=0; j<x_t; j++) idx[nn++] = s_t++;
      } else if (ys-Ys > 0) {
        if (by == DM_BOUNDARY_MIRROR) {
          for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
        } else {
          for (j=0; j<x; j++) idx[nn++] = -1;
        }
      }
      if (n2 >= 0) { /* right below */
        x_t = lx[n2 % m];
        y_t = ly[(n2/m)];
        s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (Xe-xe> 0 && ys-Ys > 0) {
        for (j=0; j<s_x; j++) idx[nn++] = -1;
      }
    }

    for (i=0; i<y; i++) {
      if (n3 >= 0) { /* directly left */
        x_t = lx[n3 % m];
        /* y_t = y; */
        s_t = bases[n3] + (i+1)*x_t - s_x;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (xs-Xs > 0) {
        if (bx == DM_BOUNDARY_MIRROR) {
          for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
        } else {
          for (j=0; j<s_x; j++) idx[nn++] = -1;
        }
      }

      for (j=0; j<x; j++) idx[nn++] = xbase++; /* interior */

      if (n5 >= 0) { /* directly right */
        x_t = lx[n5 % m];
        /* y_t = y; */
        s_t = bases[n5] + (i)*x_t;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (Xe-xe > 0) {
        if (bx == DM_BOUNDARY_MIRROR) {
          for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
        } else {
          for (j=0; j<s_x; j++) idx[nn++] = -1;
        }
      }
    }

    for (i=1; i<=s_y; i++) {
      if (n6 >= 0) { /* left above */
        x_t = lx[n6 % m];
        /* y_t = ly[(n6/m)]; */
        s_t = bases[n6] + (i)*x_t - s_x;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (xs-Xs > 0 && Ye-ye > 0) {
        for (j=0; j<s_x; j++) idx[nn++] = -1;
      }
      if (n7 >= 0) { /* directly above */
        x_t = x;
        /* y_t = ly[(n7/m)]; */
        s_t = bases[n7] + (i-1)*x_t;
        for (j=0; j<x_t; j++) idx[nn++] = s_t++;
      } else if (Ye-ye > 0) {
        if (by == DM_BOUNDARY_MIRROR) {
          for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
        } else {
          for (j=0; j<x; j++) idx[nn++] = -1;
        }
      }
      if (n8 >= 0) { /* right above */
        x_t = lx[n8 % m];
        /* y_t = ly[(n8/m)]; */
        s_t = bases[n8] + (i-1)*x_t;
        for (j=0; j<s_x; j++) idx[nn++] = s_t++;
      } else if (Xe-xe > 0 && Ye-ye > 0) {
        for (j=0; j<s_x; j++) idx[nn++] = -1;
      }
    }
  }
  /*
     Set the local to global ordering in the global vector, this allows use
     of VecSetValuesLocal().
  */
  ierr = ISLocalToGlobalMappingCreate(comm,dof,nn,idx,PETSC_OWN_POINTER,&da->ltogmap);CHKERRQ(ierr);
  ierr = PetscLogObjectParent((PetscObject)da,(PetscObject)da->ltogmap);CHKERRQ(ierr);

  ierr  = PetscFree2(bases,ldims);CHKERRQ(ierr);
  dd->m = m;  dd->n  = n;
  /* note petsc expects xs/xe/Xs/Xe to be multiplied by #dofs in many places */
  dd->xs = xs*dof; dd->xe = xe*dof; dd->ys = ys; dd->ye = ye; dd->zs = 0; dd->ze = 1;
  dd->Xs = Xs*dof; dd->Xe = Xe*dof; dd->Ys = Ys; dd->Ye = Ye; dd->Zs = 0; dd->Ze = 1;

  ierr = VecDestroy(&local);CHKERRQ(ierr);
  ierr = VecDestroy(&global);CHKERRQ(ierr);

  dd->gtol      = gtol;
  dd->ltog      = ltog;
  dd->base      = base;
  da->ops->view = DMView_DA_2d;
  dd->ltol      = NULL;
  dd->ao        = NULL;
  PetscFunctionReturn(0);
}

#undef __FUNCT__
#define __FUNCT__ "DMDACreate2d"
/*@C
   DMDACreate2d -  Creates an object that will manage the communication of  two-dimensional
   regular array data that is distributed across some processors.

   Collective on MPI_Comm

   Input Parameters:
+  comm - MPI communicator
.  bx,by - type of ghost nodes the array have.
         Use one of DM_BOUNDARY_NONE, DM_BOUNDARY_GHOSTED, DM_BOUNDARY_PERIODIC.
.  stencil_type - stencil type.  Use either DMDA_STENCIL_BOX or DMDA_STENCIL_STAR.
.  M,N - global dimension in each direction of the array (use -M and or -N to indicate that it may be set to a different value
            from the command line with -da_grid_x <M> -da_grid_y <N>)
.  m,n - corresponding number of processors in each dimension
         (or PETSC_DECIDE to have calculated)
.  dof - number of degrees of freedom per node
.  s - stencil width
-  lx, ly - arrays containing the number of nodes in each cell along
           the x and y coordinates, or NULL. If non-null, these
           must be of length as m and n, and the corresponding
           m and n cannot be PETSC_DECIDE. The sum of the lx[] entries
           must be M, and the sum of the ly[] entries must be N.

   Output Parameter:
.  da - the resulting distributed array object

   Options Database Key:
+  -dm_view - Calls DMView() at the conclusion of DMDACreate2d()
.  -da_grid_x <nx> - number of grid points in x direction, if M < 0
.  -da_grid_y <ny> - number of grid points in y direction, if N < 0
.  -da_processors_x <nx> - number of processors in x direction
.  -da_processors_y <ny> - number of processors in y direction
.  -da_refine_x <rx> - refinement ratio in x direction
.  -da_refine_y <ry> - refinement ratio in y direction
-  -da_refine <n> - refine the DMDA n times before creating, if M or N < 0


   Level: beginner

   Notes:
   The stencil type DMDA_STENCIL_STAR with width 1 corresponds to the
   standard 5-pt stencil, while DMDA_STENCIL_BOX with width 1 denotes
   the standard 9-pt stencil.

   The array data itself is NOT stored in the DMDA, it is stored in Vec objects;
   The appropriate vector objects can be obtained with calls to DMCreateGlobalVector()
   and DMCreateLocalVector() and calls to VecDuplicate() if more are needed.

.keywords: distributed array, create, two-dimensional

.seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate3d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
          DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMLocalToLocalBegin(), DMLocalToLocalEnd(), DMDASetRefinementFactor(),
          DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges()

@*/

PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
                          PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
{
  PetscErrorCode ierr;

  PetscFunctionBegin;
  ierr = DMDACreate(comm, da);CHKERRQ(ierr);
  ierr = DMDASetDim(*da, 2);CHKERRQ(ierr);
  ierr = DMDASetSizes(*da, M, N, 1);CHKERRQ(ierr);
  ierr = DMDASetNumProcs(*da, m, n, PETSC_DECIDE);CHKERRQ(ierr);
  ierr = DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);CHKERRQ(ierr);
  ierr = DMDASetDof(*da, dof);CHKERRQ(ierr);
  ierr = DMDASetStencilType(*da, stencil_type);CHKERRQ(ierr);
  ierr = DMDASetStencilWidth(*da, s);CHKERRQ(ierr);
  ierr = DMDASetOwnershipRanges(*da, lx, ly, NULL);CHKERRQ(ierr);
  /* This violates the behavior for other classes, but right now users expect negative dimensions to be handled this way */
  ierr = DMSetFromOptions(*da);CHKERRQ(ierr);
  ierr = DMSetUp(*da);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}