Date: 2013-07-02T14:44:52+00:00

Actual source code: da3.c
petsc-3.4.2 2013-07-02

      2: /*
      3:    Code for manipulating distributed regular 3d arrays in parallel.
      4:    File created by Peter Mell  7/14/95
      5:  */

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

      9: #include <petscdraw.h>
     12: PetscErrorCode DMView_DA_3d(DM da,PetscViewer viewer)
     13: {
     15:   PetscMPIInt    rank;
     16:   PetscBool      iascii,isdraw,isbinary;
     17:   DM_DA          *dd = (DM_DA*)da->data;
     18: #if defined(PETSC_HAVE_MATLAB_ENGINE)
     19:   PetscBool ismatlab;
     20: #endif

     23:   MPI_Comm_rank(PetscObjectComm((PetscObject)da),&rank);

     25:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
     26:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
     27:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);
     28: #if defined(PETSC_HAVE_MATLAB_ENGINE)
     29:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERMATLAB,&ismatlab);
     30: #endif
     31:   if (iascii) {
     32:     PetscViewerFormat format;

     34:     PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
     35:     PetscViewerGetFormat(viewer, &format);
     36:     if (format != PETSC_VIEWER_ASCII_VTK && format != PETSC_VIEWER_ASCII_VTK_CELL) {
     37:       DMDALocalInfo info;
     38:       DMDAGetLocalInfo(da,&info);
     39:       PetscViewerASCIISynchronizedPrintf(viewer,"Processor [%d] M %D N %D P %D m %D n %D p %D w %D s %D\n",rank,dd->M,dd->N,dd->P,dd->m,dd->n,dd->p,dd->w,dd->s);
     40:       PetscViewerASCIISynchronizedPrintf(viewer,"X range of indices: %D %D, Y range of indices: %D %D, Z range of indices: %D %D\n",
     41:                                                 info.xs,info.xs+info.xm,info.ys,info.ys+info.ym,info.zs,info.zs+info.zm);
     42: #if !defined(PETSC_USE_COMPLEX)
     43:       if (da->coordinates) {
     44:         PetscInt        last;
     45:         const PetscReal *coors;
     46:         VecGetArrayRead(da->coordinates,&coors);
     47:         VecGetLocalSize(da->coordinates,&last);
     48:         last = last - 3;
     49:         PetscViewerASCIISynchronizedPrintf(viewer,"Lower left corner %G %G %G : Upper right %G %G %G\n",coors[0],coors[1],coors[2],coors[last],coors[last+1],coors[last+2]);
     50:         VecRestoreArrayRead(da->coordinates,&coors);
     51:       }
     52: #endif
     53:       PetscViewerFlush(viewer);
     54:       PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);
     55:     } else {
     56:       DMView_DA_VTK(da,viewer);
     57:     }
     58:   } else if (isdraw) {
     59:     PetscDraw draw;
     60:     PetscReal ymin = -1.0,ymax = (PetscReal)dd->N;
     61:     PetscReal xmin = -1.0,xmax = (PetscReal)((dd->M+2)*dd->P),x,y,ycoord,xcoord;
     62:     PetscInt  k,plane,base,*idx;
     63:     char      node[10];
     64:     PetscBool isnull;

     66:     PetscViewerDrawGetDraw(viewer,0,&draw);
     67:     PetscDrawIsNull(draw,&isnull); if (isnull) return(0);
     68:     PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);
     69:     PetscDrawSynchronizedClear(draw);

     71:     /* first processor draw all node lines */
     72:     if (!rank) {
     73:       for (k=0; k<dd->P; k++) {
     74:         ymin = 0.0; ymax = (PetscReal)(dd->N - 1);
     75:         for (xmin=(PetscReal)(k*(dd->M+1)); xmin<(PetscReal)(dd->M+(k*(dd->M+1))); xmin++) {
     76:           PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);
     77:         }

     79:         xmin = (PetscReal)(k*(dd->M+1)); xmax = xmin + (PetscReal)(dd->M - 1);
     80:         for (ymin=0; ymin<(PetscReal)dd->N; ymin++) {
     81:           PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);
     82:         }
     83:       }
     84:     }
     85:     PetscDrawSynchronizedFlush(draw);
     86:     PetscDrawPause(draw);

     88:     for (k=0; k<dd->P; k++) {  /*Go through and draw for each plane*/
     89:       if ((k >= dd->zs) && (k < dd->ze)) {
     90:         /* draw my box */
     91:         ymin = dd->ys;
     92:         ymax = dd->ye - 1;
     93:         xmin = dd->xs/dd->w    + (dd->M+1)*k;
     94:         xmax =(dd->xe-1)/dd->w + (dd->M+1)*k;

     96:         PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);
     97:         PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);
     98:         PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);
     99:         PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);

    101:         xmin = dd->xs/dd->w;
    102:         xmax =(dd->xe-1)/dd->w;

    104:         /* put in numbers*/
    105:         base = (dd->base+(dd->xe-dd->xs)*(dd->ye-dd->ys)*(k-dd->zs))/dd->w;

    107:         /* Identify which processor owns the box */
    108:         sprintf(node,"%d",rank);
    109:         PetscDrawString(draw,xmin+(dd->M+1)*k+.2,ymin+.3,PETSC_DRAW_RED,node);

    111:         for (y=ymin; y<=ymax; y++) {
    112:           for (x=xmin+(dd->M+1)*k; x<=xmax+(dd->M+1)*k; x++) {
    113:             sprintf(node,"%d",(int)base++);
    114:             PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);
    115:           }
    116:         }

    118:       }
    119:     }
    120:     PetscDrawSynchronizedFlush(draw);
    121:     PetscDrawPause(draw);

    123:     for (k=0-dd->s; k<dd->P+dd->s; k++) {
    124:       /* Go through and draw for each plane */
    125:       if ((k >= dd->Zs) && (k < dd->Ze)) {

    127:         /* overlay ghost numbers, useful for error checking */
    128:         base = (dd->Xe-dd->Xs)*(dd->Ye-dd->Ys)*(k-dd->Zs); idx = dd->idx;
    129:         plane=k;
    130:         /* Keep z wrap around points on the dradrawg */
    131:         if (k<0) plane=dd->P+k;
    132:         if (k>=dd->P) plane=k-dd->P;
    133:         ymin = dd->Ys; ymax = dd->Ye;
    134:         xmin = (dd->M+1)*plane*dd->w;
    135:         xmax = (dd->M+1)*plane*dd->w+dd->M*dd->w;
    136:         for (y=ymin; y<ymax; y++) {
    137:           for (x=xmin+dd->Xs; x<xmin+dd->Xe; x+=dd->w) {
    138:             sprintf(node,"%d",(int)(idx[base]/dd->w));
    139:             ycoord = y;
    140:             /*Keep y wrap around points on drawing */
    141:             if (y<0) ycoord = dd->N+y;

    143:             if (y>=dd->N) ycoord = y-dd->N;
    144:             xcoord = x;   /* Keep x wrap points on drawing */

    146:             if (x<xmin) xcoord = xmax - (xmin-x);
    147:             if (x>=xmax) xcoord = xmin + (x-xmax);
    148:             PetscDrawString(draw,xcoord/dd->w,ycoord,PETSC_DRAW_BLUE,node);
    149:             base+=dd->w;
    150:           }
    151:         }
    152:       }
    153:     }
    154:     PetscDrawSynchronizedFlush(draw);
    155:     PetscDrawPause(draw);
    156:   } else if (isbinary) {
    157:     DMView_DA_Binary(da,viewer);
    158: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    159:   } else if (ismatlab) {
    160:     DMView_DA_Matlab(da,viewer);
    161: #endif
    162:   }
    163:   return(0);
    164: }

    168: PetscErrorCode  DMSetUp_DA_3D(DM da)
    169: {
    170:   DM_DA            *dd          = (DM_DA*)da->data;
    171:   const PetscInt   M            = dd->M;
    172:   const PetscInt   N            = dd->N;
    173:   const PetscInt   P            = dd->P;
    174:   PetscInt         m            = dd->m;
    175:   PetscInt         n            = dd->n;
    176:   PetscInt         p            = dd->p;
    177:   const PetscInt   dof          = dd->w;
    178:   const PetscInt   s            = dd->s;
    179:   DMDABoundaryType bx           = dd->bx;
    180:   DMDABoundaryType by           = dd->by;
    181:   DMDABoundaryType bz           = dd->bz;
    182:   DMDAStencilType  stencil_type = dd->stencil_type;
    183:   PetscInt         *lx          = dd->lx;
    184:   PetscInt         *ly          = dd->ly;
    185:   PetscInt         *lz          = dd->lz;
    186:   MPI_Comm         comm;
    187:   PetscMPIInt      rank,size;
    188:   PetscInt         xs = 0,xe,ys = 0,ye,zs = 0,ze,x = 0,y = 0,z = 0;
    189:   PetscInt         Xs,Xe,Ys,Ye,Zs,Ze,IXs,IXe,IYs,IYe,IZs,IZe,start,end,pm;
    190:   PetscInt         left,right,up,down,bottom,top,i,j,k,*idx,*idx_cpy,nn;
    191:   const PetscInt   *idx_full;
    192:   PetscInt         n0,n1,n2,n3,n4,n5,n6,n7,n8,n9,n10,n11,n12,n14;
    193:   PetscInt         n15,n16,n17,n18,n19,n20,n21,n22,n23,n24,n25,n26;
    194:   PetscInt         *bases,*ldims,base,x_t,y_t,z_t,s_t,count,s_x,s_y,s_z;
    195:   PetscInt         sn0  = 0,sn1 = 0,sn2 = 0,sn3 = 0,sn5 = 0,sn6 = 0,sn7 = 0;
    196:   PetscInt         sn8  = 0,sn9 = 0,sn11 = 0,sn15 = 0,sn24 = 0,sn25 = 0,sn26 = 0;
    197:   PetscInt         sn17 = 0,sn18 = 0,sn19 = 0,sn20 = 0,sn21 = 0,sn23 = 0;
    198:   Vec              local,global;
    199:   VecScatter       ltog,gtol;
    200:   IS               to,from,ltogis;
    201:   PetscBool        twod;
    202:   PetscErrorCode   ierr;

    206:   if (stencil_type == DMDA_STENCIL_BOX && (bx == DMDA_BOUNDARY_MIRROR || by == DMDA_BOUNDARY_MIRROR || bz == DMDA_BOUNDARY_MIRROR)) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Mirror boundary and box stencil");
    207:   PetscObjectGetComm((PetscObject) da, &comm);
    208: #if !defined(PETSC_USE_64BIT_INDICES)
    209:   if (((Petsc64bitInt) M)*((Petsc64bitInt) N)*((Petsc64bitInt) P)*((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);
    210: #endif

    212:   MPI_Comm_size(comm,&size);
    213:   MPI_Comm_rank(comm,&rank);

    215:   if (m != PETSC_DECIDE) {
    216:     if (m < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
    217:     else if (m > size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
    218:   }
    219:   if (n != PETSC_DECIDE) {
    220:     if (n < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
    221:     else if (n > size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
    222:   }
    223:   if (p != PETSC_DECIDE) {
    224:     if (p < 1) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Z direction: %D",p);
    225:     else if (p > size) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Z direction: %D %d",p,size);
    226:   }
    227:   if ((m > 0) && (n > 0) && (p > 0) && (m*n*p != size)) SETERRQ4(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"m %D * n %D * p %D != size %d",m,n,p,size);

    229:   /* Partition the array among the processors */
    230:   if (m == PETSC_DECIDE && n != PETSC_DECIDE && p != PETSC_DECIDE) {
    231:     m = size/(n*p);
    232:   } else if (m != PETSC_DECIDE && n == PETSC_DECIDE && p != PETSC_DECIDE) {
    233:     n = size/(m*p);
    234:   } else if (m != PETSC_DECIDE && n != PETSC_DECIDE && p == PETSC_DECIDE) {
    235:     p = size/(m*n);
    236:   } else if (m == PETSC_DECIDE && n == PETSC_DECIDE && p != PETSC_DECIDE) {
    237:     /* try for squarish distribution */
    238:     m = (int)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N*p)));
    239:     if (!m) m = 1;
    240:     while (m > 0) {
    241:       n = size/(m*p);
    242:       if (m*n*p == size) break;
    243:       m--;
    244:     }
    245:     if (!m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"bad p value: p = %D",p);
    246:     if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
    247:   } else if (m == PETSC_DECIDE && n != PETSC_DECIDE && p == PETSC_DECIDE) {
    248:     /* try for squarish distribution */
    249:     m = (int)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)P*n)));
    250:     if (!m) m = 1;
    251:     while (m > 0) {
    252:       p = size/(m*n);
    253:       if (m*n*p == size) break;
    254:       m--;
    255:     }
    256:     if (!m) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"bad n value: n = %D",n);
    257:     if (M > P && m < p) {PetscInt _m = m; m = p; p = _m;}
    258:   } else if (m != PETSC_DECIDE && n == PETSC_DECIDE && p == PETSC_DECIDE) {
    259:     /* try for squarish distribution */
    260:     n = (int)(0.5 + PetscSqrtReal(((PetscReal)N)*((PetscReal)size)/((PetscReal)P*m)));
    261:     if (!n) n = 1;
    262:     while (n > 0) {
    263:       p = size/(m*n);
    264:       if (m*n*p == size) break;
    265:       n--;
    266:     }
    267:     if (!n) SETERRQ1(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"bad m value: m = %D",n);
    268:     if (N > P && n < p) {PetscInt _n = n; n = p; p = _n;}
    269:   } else if (m == PETSC_DECIDE && n == PETSC_DECIDE && p == PETSC_DECIDE) {
    270:     /* try for squarish distribution */
    271:     n = (PetscInt)(0.5 + PetscPowReal(((PetscReal)N*N)*((PetscReal)size)/((PetscReal)P*M),(PetscReal)(1./3.)));
    272:     if (!n) n = 1;
    273:     while (n > 0) {
    274:       pm = size/n;
    275:       if (n*pm == size) break;
    276:       n--;
    277:     }
    278:     if (!n) n = 1;
    279:     m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)P*n)));
    280:     if (!m) m = 1;
    281:     while (m > 0) {
    282:       p = size/(m*n);
    283:       if (m*n*p == size) break;
    284:       m--;
    285:     }
    286:     if (M > P && m < p) {PetscInt _m = m; m = p; p = _m;}
    287:   } else if (m*n*p != size) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_ARG_OUTOFRANGE,"Given Bad partition");

    289:   if (m*n*p != size) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_PLIB,"Could not find good partition");
    290:   if (M < m) SETERRQ2(PetscObjectComm((PetscObject)da),PETSC_ERR_ARG_OUTOFRANGE,"Partition in x direction is too fine! %D %D",M,m);
    291:   if (N < n) SETERRQ2(PetscObjectComm((PetscObject)da),PETSC_ERR_ARG_OUTOFRANGE,"Partition in y direction is too fine! %D %D",N,n);
    292:   if (P < p) SETERRQ2(PetscObjectComm((PetscObject)da),PETSC_ERR_ARG_OUTOFRANGE,"Partition in z direction is too fine! %D %D",P,p);

    294:   /*
    295:      Determine locally owned region
    296:      [x, y, or z]s is the first local node number, [x, y, z] is the number of local nodes
    297:   */

    299:   if (!lx) {
    300:     PetscMalloc(m*sizeof(PetscInt), &dd->lx);
    301:     lx   = dd->lx;
    302:     for (i=0; i<m; i++) lx[i] = M/m + ((M % m) > (i % m));
    303:   }
    304:   x  = lx[rank % m];
    305:   xs = 0;
    306:   for (i=0; i<(rank%m); i++) xs += lx[i];
    307:   if ((x < s) && ((m > 1) || (bx == DMDA_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);

    309:   if (!ly) {
    310:     PetscMalloc(n*sizeof(PetscInt), &dd->ly);
    311:     ly   = dd->ly;
    312:     for (i=0; i<n; i++) ly[i] = N/n + ((N % n) > (i % n));
    313:   }
    314:   y = ly[(rank % (m*n))/m];
    315:   if ((y < s) && ((n > 1) || (by == DMDA_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);

    317:   ys = 0;
    318:   for (i=0; i<(rank % (m*n))/m; i++) ys += ly[i];

    320:   if (!lz) {
    321:     PetscMalloc(p*sizeof(PetscInt), &dd->lz);
    322:     lz = dd->lz;
    323:     for (i=0; i<p; i++) lz[i] = P/p + ((P % p) > (i % p));
    324:   }
    325:   z = lz[rank/(m*n)];

    327:   /* note this is different than x- and y-, as we will handle as an important special
    328:    case when p=P=1 and DMDA_BOUNDARY_PERIODIC and s > z.  This is to deal with 2D problems
    329:    in a 3D code.  Additional code for this case is noted with "2d case" comments */
    330:   twod = PETSC_FALSE;
    331:   if (P == 1) twod = PETSC_TRUE;
    332:   else if ((z < s) && ((p > 1) || (bz == DMDA_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local z-width of domain z %D is smaller than stencil width s %D",z,s);
    333:   zs = 0;
    334:   for (i=0; i<(rank/(m*n)); i++) zs += lz[i];
    335:   ye = ys + y;
    336:   xe = xs + x;
    337:   ze = zs + z;

    339:   /* determine ghost region (Xs) and region scattered into (IXs)  */
    340:   if (xs-s > 0) {
    341:     Xs = xs - s; IXs = xs - s;
    342:   } else {
    343:     if (bx) Xs = xs - s;
    344:     else Xs = 0;
    345:     IXs = 0;
    346:   }
    347:   if (xe+s <= M) {
    348:     Xe = xe + s; IXe = xe + s;
    349:   } else {
    350:     if (bx) {
    351:       Xs = xs - s; Xe = xe + s;
    352:     } else Xe = M;
    353:     IXe = M;
    354:   }

    356:   if (bx == DMDA_BOUNDARY_PERIODIC || bx == DMDA_BOUNDARY_MIRROR) {
    357:     IXs = xs - s;
    358:     IXe = xe + s;
    359:     Xs  = xs - s;
    360:     Xe  = xe + s;
    361:   }

    363:   if (ys-s > 0) {
    364:     Ys = ys - s; IYs = ys - s;
    365:   } else {
    366:     if (by) Ys = ys - s;
    367:     else Ys = 0;
    368:     IYs = 0;
    369:   }
    370:   if (ye+s <= N) {
    371:     Ye = ye + s; IYe = ye + s;
    372:   } else {
    373:     if (by) Ye = ye + s;
    374:     else Ye = N;
    375:     IYe = N;
    376:   }

    378:   if (by == DMDA_BOUNDARY_PERIODIC || by == DMDA_BOUNDARY_MIRROR) {
    379:     IYs = ys - s;
    380:     IYe = ye + s;
    381:     Ys  = ys - s;
    382:     Ye  = ye + s;
    383:   }

    385:   if (zs-s > 0) {
    386:     Zs = zs - s; IZs = zs - s;
    387:   } else {
    388:     if (bz) Zs = zs - s;
    389:     else Zs = 0;
    390:     IZs = 0;
    391:   }
    392:   if (ze+s <= P) {
    393:     Ze = ze + s; IZe = ze + s;
    394:   } else {
    395:     if (bz) Ze = ze + s;
    396:     else Ze = P;
    397:     IZe = P;
    398:   }

    400:   if (bz == DMDA_BOUNDARY_PERIODIC || bz == DMDA_BOUNDARY_MIRROR) {
    401:     IZs = zs - s;
    402:     IZe = ze + s;
    403:     Zs  = zs - s;
    404:     Ze  = ze + s;
    405:   }

    407:   /* Resize all X parameters to reflect w */
    408:   s_x = s;
    409:   s_y = s;
    410:   s_z = s;

    412:   /* determine starting point of each processor */
    413:   nn       = x*y*z;
    414:   PetscMalloc2(size+1,PetscInt,&bases,size,PetscInt,&ldims);
    415:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
    416:   bases[0] = 0;
    417:   for (i=1; i<=size; i++) bases[i] = ldims[i-1];
    418:   for (i=1; i<=size; i++) bases[i] += bases[i-1];
    419:   base = bases[rank]*dof;

    421:   /* allocate the base parallel and sequential vectors */
    422:   dd->Nlocal = x*y*z*dof;
    423:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,0,&global);
    424:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*(Ze-Zs)*dof;
    425:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,0,&local);

    427:   /* generate appropriate vector scatters */
    428:   /* local to global inserts non-ghost point region into global */
    429:   VecGetOwnershipRange(global,&start,&end);
    430:   ISCreateStride(comm,x*y*z*dof,start,1,&to);

    432:   PetscMalloc(x*y*z*sizeof(PetscInt),&idx);
    433:   left   = xs - Xs; right = left + x;
    434:   bottom = ys - Ys; top = bottom + y;
    435:   down   = zs - Zs; up  = down + z;
    436:   count  = 0;
    437:   for (i=down; i<up; i++) {
    438:     for (j=bottom; j<top; j++) {
    439:       for (k=left; k<right; k++) {
    440:         idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    441:       }
    442:     }
    443:   }

    445:   ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&from);
    446:   VecScatterCreate(local,from,global,to,&ltog);
    447:   PetscLogObjectParent(da,ltog);
    448:   ISDestroy(&from);
    449:   ISDestroy(&to);

    451:   /* global to local must include ghost points within the domain,
    452:      but not ghost points outside the domain that aren't periodic */
    453:   if (stencil_type == DMDA_STENCIL_BOX) {
    454:     count = (IXe-IXs)*(IYe-IYs)*(IZe-IZs);
    455:     PetscMalloc(count*sizeof(PetscInt),&idx);

    457:     left   = IXs - Xs; right = left + (IXe-IXs);
    458:     bottom = IYs - Ys; top = bottom + (IYe-IYs);
    459:     down   = IZs - Zs; up  = down + (IZe-IZs);
    460:     count  = 0;
    461:     for (i=down; i<up; i++) {
    462:       for (j=bottom; j<top; j++) {
    463:         for (k=left; k<right; k++) {
    464:           idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    465:         }
    466:       }
    467:     }
    468:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

    470:   } else {
    471:     /* This is way ugly! We need to list the funny cross type region */
    472:     count = ((ys-IYs) + (IYe-ye))*x*z + ((xs-IXs) + (IXe-xe))*y*z + ((zs-IZs) + (IZe-ze))*x*y + x*y*z;
    473:     PetscMalloc(count*sizeof(PetscInt),&idx);

    475:     left   = xs - Xs; right = left + x;
    476:     bottom = ys - Ys; top = bottom + y;
    477:     down   = zs - Zs;   up  = down + z;
    478:     count  = 0;
    479:     /* the bottom chunck */
    480:     for (i=(IZs-Zs); i<down; i++) {
    481:       for (j=bottom; j<top; j++) {
    482:         for (k=left; k<right; k++) idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    483:       }
    484:     }
    485:     /* the middle piece */
    486:     for (i=down; i<up; i++) {
    487:       /* front */
    488:       for (j=(IYs-Ys); j<bottom; j++) {
    489:         for (k=left; k<right; k++) idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    490:       }
    491:       /* middle */
    492:       for (j=bottom; j<top; j++) {
    493:         for (k=IXs-Xs; k<IXe-Xs; k++) idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    494:       }
    495:       /* back */
    496:       for (j=top; j<top+IYe-ye; j++) {
    497:         for (k=left; k<right; k++) idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    498:       }
    499:     }
    500:     /* the top piece */
    501:     for (i=up; i<up+IZe-ze; i++) {
    502:       for (j=bottom; j<top; j++) {
    503:         for (k=left; k<right; k++) idx[count++] = (i*(Ye-Ys) + j)*(Xe-Xs) + k;
    504:       }
    505:     }
    506:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
    507:   }

    509:   /* determine who lies on each side of use stored in    n24 n25 n26
    510:                                                          n21 n22 n23
    511:                                                          n18 n19 n20

    513:                                                          n15 n16 n17
    514:                                                          n12     n14
    515:                                                          n9  n10 n11

    517:                                                          n6  n7  n8
    518:                                                          n3  n4  n5
    519:                                                          n0  n1  n2
    520:   */

    522:   /* Solve for X,Y, and Z Periodic Case First, Then Modify Solution */
    523:   /* Assume Nodes are Internal to the Cube */
    524:   n0 = rank - m*n - m - 1;
    525:   n1 = rank - m*n - m;
    526:   n2 = rank - m*n - m + 1;
    527:   n3 = rank - m*n -1;
    528:   n4 = rank - m*n;
    529:   n5 = rank - m*n + 1;
    530:   n6 = rank - m*n + m - 1;
    531:   n7 = rank - m*n + m;
    532:   n8 = rank - m*n + m + 1;

    534:   n9  = rank - m - 1;
    535:   n10 = rank - m;
    536:   n11 = rank - m + 1;
    537:   n12 = rank - 1;
    538:   n14 = rank + 1;
    539:   n15 = rank + m - 1;
    540:   n16 = rank + m;
    541:   n17 = rank + m + 1;

    543:   n18 = rank + m*n - m - 1;
    544:   n19 = rank + m*n - m;
    545:   n20 = rank + m*n - m + 1;
    546:   n21 = rank + m*n - 1;
    547:   n22 = rank + m*n;
    548:   n23 = rank + m*n + 1;
    549:   n24 = rank + m*n + m - 1;
    550:   n25 = rank + m*n + m;
    551:   n26 = rank + m*n + m + 1;

    553:   /* Assume Pieces are on Faces of Cube */

    555:   if (xs == 0) { /* First assume not corner or edge */
    556:     n0  = rank       -1 - (m*n);
    557:     n3  = rank + m   -1 - (m*n);
    558:     n6  = rank + 2*m -1 - (m*n);
    559:     n9  = rank       -1;
    560:     n12 = rank + m   -1;
    561:     n15 = rank + 2*m -1;
    562:     n18 = rank       -1 + (m*n);
    563:     n21 = rank + m   -1 + (m*n);
    564:     n24 = rank + 2*m -1 + (m*n);
    565:   }

    567:   if (xe == M) { /* First assume not corner or edge */
    568:     n2  = rank -2*m +1 - (m*n);
    569:     n5  = rank - m  +1 - (m*n);
    570:     n8  = rank      +1 - (m*n);
    571:     n11 = rank -2*m +1;
    572:     n14 = rank - m  +1;
    573:     n17 = rank      +1;
    574:     n20 = rank -2*m +1 + (m*n);
    575:     n23 = rank - m  +1 + (m*n);
    576:     n26 = rank      +1 + (m*n);
    577:   }

    579:   if (ys==0) { /* First assume not corner or edge */
    580:     n0  = rank + m * (n-1) -1 - (m*n);
    581:     n1  = rank + m * (n-1)    - (m*n);
    582:     n2  = rank + m * (n-1) +1 - (m*n);
    583:     n9  = rank + m * (n-1) -1;
    584:     n10 = rank + m * (n-1);
    585:     n11 = rank + m * (n-1) +1;
    586:     n18 = rank + m * (n-1) -1 + (m*n);
    587:     n19 = rank + m * (n-1)    + (m*n);
    588:     n20 = rank + m * (n-1) +1 + (m*n);
    589:   }

    591:   if (ye == N) { /* First assume not corner or edge */
    592:     n6  = rank - m * (n-1) -1 - (m*n);
    593:     n7  = rank - m * (n-1)    - (m*n);
    594:     n8  = rank - m * (n-1) +1 - (m*n);
    595:     n15 = rank - m * (n-1) -1;
    596:     n16 = rank - m * (n-1);
    597:     n17 = rank - m * (n-1) +1;
    598:     n24 = rank - m * (n-1) -1 + (m*n);
    599:     n25 = rank - m * (n-1)    + (m*n);
    600:     n26 = rank - m * (n-1) +1 + (m*n);
    601:   }

    603:   if (zs == 0) { /* First assume not corner or edge */
    604:     n0 = size - (m*n) + rank - m - 1;
    605:     n1 = size - (m*n) + rank - m;
    606:     n2 = size - (m*n) + rank - m + 1;
    607:     n3 = size - (m*n) + rank - 1;
    608:     n4 = size - (m*n) + rank;
    609:     n5 = size - (m*n) + rank + 1;
    610:     n6 = size - (m*n) + rank + m - 1;
    611:     n7 = size - (m*n) + rank + m;
    612:     n8 = size - (m*n) + rank + m + 1;
    613:   }

    615:   if (ze == P) { /* First assume not corner or edge */
    616:     n18 = (m*n) - (size-rank) - m - 1;
    617:     n19 = (m*n) - (size-rank) - m;
    618:     n20 = (m*n) - (size-rank) - m + 1;
    619:     n21 = (m*n) - (size-rank) - 1;
    620:     n22 = (m*n) - (size-rank);
    621:     n23 = (m*n) - (size-rank) + 1;
    622:     n24 = (m*n) - (size-rank) + m - 1;
    623:     n25 = (m*n) - (size-rank) + m;
    624:     n26 = (m*n) - (size-rank) + m + 1;
    625:   }

    627:   if ((xs==0) && (zs==0)) { /* Assume an edge, not corner */
    628:     n0 = size - m*n + rank + m-1 - m;
    629:     n3 = size - m*n + rank + m-1;
    630:     n6 = size - m*n + rank + m-1 + m;
    631:   }

    633:   if ((xs==0) && (ze==P)) { /* Assume an edge, not corner */
    634:     n18 = m*n - (size - rank) + m-1 - m;
    635:     n21 = m*n - (size - rank) + m-1;
    636:     n24 = m*n - (size - rank) + m-1 + m;
    637:   }

    639:   if ((xs==0) && (ys==0)) { /* Assume an edge, not corner */
    640:     n0  = rank + m*n -1 - m*n;
    641:     n9  = rank + m*n -1;
    642:     n18 = rank + m*n -1 + m*n;
    643:   }

    645:   if ((xs==0) && (ye==N)) { /* Assume an edge, not corner */
    646:     n6  = rank - m*(n-1) + m-1 - m*n;
    647:     n15 = rank - m*(n-1) + m-1;
    648:     n24 = rank - m*(n-1) + m-1 + m*n;
    649:   }

    651:   if ((xe==M) && (zs==0)) { /* Assume an edge, not corner */
    652:     n2 = size - (m*n-rank) - (m-1) - m;
    653:     n5 = size - (m*n-rank) - (m-1);
    654:     n8 = size - (m*n-rank) - (m-1) + m;
    655:   }

    657:   if ((xe==M) && (ze==P)) { /* Assume an edge, not corner */
    658:     n20 = m*n - (size - rank) - (m-1) - m;
    659:     n23 = m*n - (size - rank) - (m-1);
    660:     n26 = m*n - (size - rank) - (m-1) + m;
    661:   }

    663:   if ((xe==M) && (ys==0)) { /* Assume an edge, not corner */
    664:     n2  = rank + m*(n-1) - (m-1) - m*n;
    665:     n11 = rank + m*(n-1) - (m-1);
    666:     n20 = rank + m*(n-1) - (m-1) + m*n;
    667:   }

    669:   if ((xe==M) && (ye==N)) { /* Assume an edge, not corner */
    670:     n8  = rank - m*n +1 - m*n;
    671:     n17 = rank - m*n +1;
    672:     n26 = rank - m*n +1 + m*n;
    673:   }

    675:   if ((ys==0) && (zs==0)) { /* Assume an edge, not corner */
    676:     n0 = size - m + rank -1;
    677:     n1 = size - m + rank;
    678:     n2 = size - m + rank +1;
    679:   }

    681:   if ((ys==0) && (ze==P)) { /* Assume an edge, not corner */
    682:     n18 = m*n - (size - rank) + m*(n-1) -1;
    683:     n19 = m*n - (size - rank) + m*(n-1);
    684:     n20 = m*n - (size - rank) + m*(n-1) +1;
    685:   }

    687:   if ((ye==N) && (zs==0)) { /* Assume an edge, not corner */
    688:     n6 = size - (m*n-rank) - m * (n-1) -1;
    689:     n7 = size - (m*n-rank) - m * (n-1);
    690:     n8 = size - (m*n-rank) - m * (n-1) +1;
    691:   }

    693:   if ((ye==N) && (ze==P)) { /* Assume an edge, not corner */
    694:     n24 = rank - (size-m) -1;
    695:     n25 = rank - (size-m);
    696:     n26 = rank - (size-m) +1;
    697:   }

    699:   /* Check for Corners */
    700:   if ((xs==0) && (ys==0) && (zs==0)) n0  = size -1;
    701:   if ((xs==0) && (ys==0) && (ze==P)) n18 = m*n-1;
    702:   if ((xs==0) && (ye==N) && (zs==0)) n6  = (size-1)-m*(n-1);
    703:   if ((xs==0) && (ye==N) && (ze==P)) n24 = m-1;
    704:   if ((xe==M) && (ys==0) && (zs==0)) n2  = size-m;
    705:   if ((xe==M) && (ys==0) && (ze==P)) n20 = m*n-m;
    706:   if ((xe==M) && (ye==N) && (zs==0)) n8  = size-m*n;
    707:   if ((xe==M) && (ye==N) && (ze==P)) n26 = 0;

    709:   /* Check for when not X,Y, and Z Periodic */

    711:   /* If not X periodic */
    712:   if (bx != DMDA_BOUNDARY_PERIODIC) {
    713:     if (xs==0) n0 = n3 = n6 = n9  = n12 = n15 = n18 = n21 = n24 = -2;
    714:     if (xe==M) n2 = n5 = n8 = n11 = n14 = n17 = n20 = n23 = n26 = -2;
    715:   }

    717:   /* If not Y periodic */
    718:   if (by != DMDA_BOUNDARY_PERIODIC) {
    719:     if (ys==0) n0 = n1 = n2 = n9  = n10 = n11 = n18 = n19 = n20 = -2;
    720:     if (ye==N) n6 = n7 = n8 = n15 = n16 = n17 = n24 = n25 = n26 = -2;
    721:   }

    723:   /* If not Z periodic */
    724:   if (bz != DMDA_BOUNDARY_PERIODIC) {
    725:     if (zs==0) n0  = n1  = n2  = n3  = n4  = n5  = n6  = n7  = n8  = -2;
    726:     if (ze==P) n18 = n19 = n20 = n21 = n22 = n23 = n24 = n25 = n26 = -2;
    727:   }

    729:   PetscMalloc(27*sizeof(PetscInt),&dd->neighbors);

    731:   dd->neighbors[0]  = n0;
    732:   dd->neighbors[1]  = n1;
    733:   dd->neighbors[2]  = n2;
    734:   dd->neighbors[3]  = n3;
    735:   dd->neighbors[4]  = n4;
    736:   dd->neighbors[5]  = n5;
    737:   dd->neighbors[6]  = n6;
    738:   dd->neighbors[7]  = n7;
    739:   dd->neighbors[8]  = n8;
    740:   dd->neighbors[9]  = n9;
    741:   dd->neighbors[10] = n10;
    742:   dd->neighbors[11] = n11;
    743:   dd->neighbors[12] = n12;
    744:   dd->neighbors[13] = rank;
    745:   dd->neighbors[14] = n14;
    746:   dd->neighbors[15] = n15;
    747:   dd->neighbors[16] = n16;
    748:   dd->neighbors[17] = n17;
    749:   dd->neighbors[18] = n18;
    750:   dd->neighbors[19] = n19;
    751:   dd->neighbors[20] = n20;
    752:   dd->neighbors[21] = n21;
    753:   dd->neighbors[22] = n22;
    754:   dd->neighbors[23] = n23;
    755:   dd->neighbors[24] = n24;
    756:   dd->neighbors[25] = n25;
    757:   dd->neighbors[26] = n26;

    759:   /* If star stencil then delete the corner neighbors */
    760:   if (stencil_type == DMDA_STENCIL_STAR) {
    761:     /* save information about corner neighbors */
    762:     sn0 = n0; sn1 = n1; sn2 = n2; sn3 = n3; sn5 = n5; sn6 = n6; sn7 = n7;
    763:     sn8 = n8; sn9 = n9; sn11 = n11; sn15 = n15; sn17 = n17; sn18 = n18;
    764:     sn19 = n19; sn20 = n20; sn21 = n21; sn23 = n23; sn24 = n24; sn25 = n25;
    765:     sn26 = n26;
    766:     n0 = n1 = n2 = n3 = n5 = n6 = n7 = n8 = n9 = n11 = n15 = n17 = n18 = n19 = n20 = n21 = n23 = n24 = n25 = n26 = -1;
    767:   }

    769:   PetscMalloc((Xe-Xs)*(Ye-Ys)*(Ze-Zs)*sizeof(PetscInt),&idx);
    770:   PetscLogObjectMemory(da,(Xe-Xs)*(Ye-Ys)*(Ze-Zs)*sizeof(PetscInt));

    772:   nn = 0;
    773:   /* Bottom Level */
    774:   for (k=0; k<s_z; k++) {
    775:     for (i=1; i<=s_y; i++) {
    776:       if (n0 >= 0) { /* left below */
    777:         x_t = lx[n0 % m];
    778:         y_t = ly[(n0 % (m*n))/m];
    779:         z_t = lz[n0 / (m*n)];
    780:         s_t = bases[n0] + x_t*y_t*z_t - (s_y-i)*x_t - s_x - (s_z-k-1)*x_t*y_t;
    781:         if (twod && (s_t < 0)) s_t = bases[n0] + x_t*y_t*z_t - (s_y-i)*x_t - s_x; /* 2D case */
    782:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    783:       }
    784:       if (n1 >= 0) { /* directly below */
    785:         x_t = x;
    786:         y_t = ly[(n1 % (m*n))/m];
    787:         z_t = lz[n1 / (m*n)];
    788:         s_t = bases[n1] + x_t*y_t*z_t - (s_y+1-i)*x_t - (s_z-k-1)*x_t*y_t;
    789:         if (twod && (s_t < 0)) s_t = bases[n1] + x_t*y_t*z_t - (s_y+1-i)*x_t; /* 2D case */
    790:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    791:       }
    792:       if (n2 >= 0) { /* right below */
    793:         x_t = lx[n2 % m];
    794:         y_t = ly[(n2 % (m*n))/m];
    795:         z_t = lz[n2 / (m*n)];
    796:         s_t = bases[n2] + x_t*y_t*z_t - (s_y+1-i)*x_t - (s_z-k-1)*x_t*y_t;
    797:         if (twod && (s_t < 0)) s_t = bases[n2] + x_t*y_t*z_t - (s_y+1-i)*x_t; /* 2D case */
    798:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    799:       }
    800:     }

    802:     for (i=0; i<y; i++) {
    803:       if (n3 >= 0) { /* directly left */
    804:         x_t = lx[n3 % m];
    805:         y_t = y;
    806:         z_t = lz[n3 / (m*n)];
    807:         s_t = bases[n3] + (i+1)*x_t - s_x + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    808:         if (twod && (s_t < 0)) s_t = bases[n3] + (i+1)*x_t - s_x + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    809:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    810:       }

    812:       if (n4 >= 0) { /* middle */
    813:         x_t = x;
    814:         y_t = y;
    815:         z_t = lz[n4 / (m*n)];
    816:         s_t = bases[n4] + i*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    817:         if (twod && (s_t < 0)) s_t = bases[n4] + i*x_t + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    818:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    819:       } else if (bz == DMDA_BOUNDARY_MIRROR) {
    820:         for (j=0; j<x; j++) idx[nn++] = 0;
    821:       }

    823:       if (n5 >= 0) { /* directly right */
    824:         x_t = lx[n5 % m];
    825:         y_t = y;
    826:         z_t = lz[n5 / (m*n)];
    827:         s_t = bases[n5] + i*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    828:         if (twod && (s_t < 0)) s_t = bases[n5] + i*x_t + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    829:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    830:       }
    831:     }

    833:     for (i=1; i<=s_y; i++) {
    834:       if (n6 >= 0) { /* left above */
    835:         x_t = lx[n6 % m];
    836:         y_t = ly[(n6 % (m*n))/m];
    837:         z_t = lz[n6 / (m*n)];
    838:         s_t = bases[n6] + i*x_t - s_x + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    839:         if (twod && (s_t < 0)) s_t = bases[n6] + i*x_t - s_x + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    840:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    841:       }
    842:       if (n7 >= 0) { /* directly above */
    843:         x_t = x;
    844:         y_t = ly[(n7 % (m*n))/m];
    845:         z_t = lz[n7 / (m*n)];
    846:         s_t = bases[n7] + (i-1)*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    847:         if (twod && (s_t < 0)) s_t = bases[n7] + (i-1)*x_t + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    848:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    849:       }
    850:       if (n8 >= 0) { /* right above */
    851:         x_t = lx[n8 % m];
    852:         y_t = ly[(n8 % (m*n))/m];
    853:         z_t = lz[n8 / (m*n)];
    854:         s_t = bases[n8] + (i-1)*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    855:         if (twod && (s_t < 0)) s_t = bases[n8] + (i-1)*x_t + x_t*y_t*z_t - x_t*y_t; /* 2D case */
    856:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    857:       }
    858:     }
    859:   }

    861:   /* Middle Level */
    862:   for (k=0; k<z; k++) {
    863:     for (i=1; i<=s_y; i++) {
    864:       if (n9 >= 0) { /* left below */
    865:         x_t = lx[n9 % m];
    866:         y_t = ly[(n9 % (m*n))/m];
    867:         /* z_t = z; */
    868:         s_t = bases[n9] - (s_y-i)*x_t -s_x + (k+1)*x_t*y_t;
    869:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    870:       }
    871:       if (n10 >= 0) { /* directly below */
    872:         x_t = x;
    873:         y_t = ly[(n10 % (m*n))/m];
    874:         /* z_t = z; */
    875:         s_t = bases[n10] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    876:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    877:       }  else if (by == DMDA_BOUNDARY_MIRROR) {
    878:         for (j=0; j<x; j++) idx[nn++] = 0;
    879:       }
    880:       if (n11 >= 0) { /* right below */
    881:         x_t = lx[n11 % m];
    882:         y_t = ly[(n11 % (m*n))/m];
    883:         /* z_t = z; */
    884:         s_t = bases[n11] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    885:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    886:       }
    887:     }

    889:     for (i=0; i<y; i++) {
    890:       if (n12 >= 0) { /* directly left */
    891:         x_t = lx[n12 % m];
    892:         y_t = y;
    893:         /* z_t = z; */
    894:         s_t = bases[n12] + (i+1)*x_t - s_x + k*x_t*y_t;
    895:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    896:       }  else if (bx == DMDA_BOUNDARY_MIRROR) {
    897:         for (j=0; j<s_x; j++) idx[nn++] = 0;
    898:       }

    900:       /* Interior */
    901:       s_t = bases[rank] + i*x + k*x*y;
    902:       for (j=0; j<x; j++) idx[nn++] = s_t++;

    904:       if (n14 >= 0) { /* directly right */
    905:         x_t = lx[n14 % m];
    906:         y_t = y;
    907:         /* z_t = z; */
    908:         s_t = bases[n14] + i*x_t + k*x_t*y_t;
    909:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    910:       } else if (bx == DMDA_BOUNDARY_MIRROR) {
    911:         for (j=0; j<s_x; j++) idx[nn++] = 0;
    912:       }
    913:     }

    915:     for (i=1; i<=s_y; i++) {
    916:       if (n15 >= 0) { /* left above */
    917:         x_t = lx[n15 % m];
    918:         y_t = ly[(n15 % (m*n))/m];
    919:         /* z_t = z; */
    920:         s_t = bases[n15] + i*x_t - s_x + k*x_t*y_t;
    921:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    922:       }
    923:       if (n16 >= 0) { /* directly above */
    924:         x_t = x;
    925:         y_t = ly[(n16 % (m*n))/m];
    926:         /* z_t = z; */
    927:         s_t = bases[n16] + (i-1)*x_t + k*x_t*y_t;
    928:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    929:       } else if (by == DMDA_BOUNDARY_MIRROR) {
    930:         for (j=0; j<x; j++) idx[nn++] = 0;
    931:       }
    932:       if (n17 >= 0) { /* right above */
    933:         x_t = lx[n17 % m];
    934:         y_t = ly[(n17 % (m*n))/m];
    935:         /* z_t = z; */
    936:         s_t = bases[n17] + (i-1)*x_t + k*x_t*y_t;
    937:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    938:       }
    939:     }
    940:   }

    942:   /* Upper Level */
    943:   for (k=0; k<s_z; k++) {
    944:     for (i=1; i<=s_y; i++) {
    945:       if (n18 >= 0) { /* left below */
    946:         x_t = lx[n18 % m];
    947:         y_t = ly[(n18 % (m*n))/m];
    948:         /* z_t = lz[n18 / (m*n)]; */
    949:         s_t = bases[n18] - (s_y-i)*x_t -s_x + (k+1)*x_t*y_t;
    950:         if (twod && (s_t >= M*N*P)) s_t = bases[n18] - (s_y-i)*x_t -s_x + x_t*y_t; /* 2d case */
    951:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    952:       }
    953:       if (n19 >= 0) { /* directly below */
    954:         x_t = x;
    955:         y_t = ly[(n19 % (m*n))/m];
    956:         /* z_t = lz[n19 / (m*n)]; */
    957:         s_t = bases[n19] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    958:         if (twod && (s_t >= M*N*P)) s_t = bases[n19] - (s_y+1-i)*x_t + x_t*y_t; /* 2d case */
    959:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    960:       }
    961:       if (n20 >= 0) { /* right below */
    962:         x_t = lx[n20 % m];
    963:         y_t = ly[(n20 % (m*n))/m];
    964:         /* z_t = lz[n20 / (m*n)]; */
    965:         s_t = bases[n20] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    966:         if (twod && (s_t >= M*N*P)) s_t = bases[n20] - (s_y+1-i)*x_t + x_t*y_t; /* 2d case */
    967:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    968:       }
    969:     }

    971:     for (i=0; i<y; i++) {
    972:       if (n21 >= 0) { /* directly left */
    973:         x_t = lx[n21 % m];
    974:         y_t = y;
    975:         /* z_t = lz[n21 / (m*n)]; */
    976:         s_t = bases[n21] + (i+1)*x_t - s_x + k*x_t*y_t;
    977:         if (twod && (s_t >= M*N*P)) s_t = bases[n21] + (i+1)*x_t - s_x;  /* 2d case */
    978:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    979:       }

    981:       if (n22 >= 0) { /* middle */
    982:         x_t = x;
    983:         y_t = y;
    984:         /* z_t = lz[n22 / (m*n)]; */
    985:         s_t = bases[n22] + i*x_t + k*x_t*y_t;
    986:         if (twod && (s_t >= M*N*P)) s_t = bases[n22] + i*x_t; /* 2d case */
    987:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    988:       } else if (bz == DMDA_BOUNDARY_MIRROR) {
    989:         for (j=0; j<x; j++) idx[nn++] = 0;
    990:       }

    992:       if (n23 >= 0) { /* directly right */
    993:         x_t = lx[n23 % m];
    994:         y_t = y;
    995:         /* z_t = lz[n23 / (m*n)]; */
    996:         s_t = bases[n23] + i*x_t + k*x_t*y_t;
    997:         if (twod && (s_t >= M*N*P)) s_t = bases[n23] + i*x_t; /* 2d case */
    998:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    999:       }
    1000:     }

    1002:     for (i=1; i<=s_y; i++) {
    1003:       if (n24 >= 0) { /* left above */
    1004:         x_t = lx[n24 % m];
    1005:         y_t = ly[(n24 % (m*n))/m];
    1006:         /* z_t = lz[n24 / (m*n)]; */
    1007:         s_t = bases[n24] + i*x_t - s_x + k*x_t*y_t;
    1008:         if (twod && (s_t >= M*N*P)) s_t = bases[n24] + i*x_t - s_x; /* 2d case */
    1009:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1010:       }
    1011:       if (n25 >= 0) { /* directly above */
    1012:         x_t = x;
    1013:         y_t = ly[(n25 % (m*n))/m];
    1014:         /* z_t = lz[n25 / (m*n)]; */
    1015:         s_t = bases[n25] + (i-1)*x_t + k*x_t*y_t;
    1016:         if (twod && (s_t >= M*N*P)) s_t = bases[n25] + (i-1)*x_t; /* 2d case */
    1017:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1018:       }
    1019:       if (n26 >= 0) { /* right above */
    1020:         x_t = lx[n26 % m];
    1021:         y_t = ly[(n26 % (m*n))/m];
    1022:         /* z_t = lz[n26 / (m*n)]; */
    1023:         s_t = bases[n26] + (i-1)*x_t + k*x_t*y_t;
    1024:         if (twod && (s_t >= M*N*P)) s_t = bases[n26] + (i-1)*x_t; /* 2d case */
    1025:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1026:       }
    1027:     }
    1028:   }

    1030:   ISCreateBlock(comm,dof,nn,idx,PETSC_COPY_VALUES,&from);
    1031:   VecScatterCreate(global,from,local,to,&gtol);
    1032:   PetscLogObjectParent(da,gtol);
    1033:   ISDestroy(&to);
    1034:   ISDestroy(&from);

    1036:   if (stencil_type == DMDA_STENCIL_STAR) {
    1037:     n0  = sn0;  n1  = sn1;  n2  = sn2;  n3  = sn3;  n5  = sn5;  n6  = sn6; n7 = sn7;
    1038:     n8  = sn8;  n9  = sn9;  n11 = sn11; n15 = sn15; n17 = sn17; n18 = sn18;
    1039:     n19 = sn19; n20 = sn20; n21 = sn21; n23 = sn23; n24 = sn24; n25 = sn25;
    1040:     n26 = sn26;
    1041:   }

    1043:   if (((stencil_type == DMDA_STENCIL_STAR) ||
    1044:       (bx != DMDA_BOUNDARY_PERIODIC && bx) ||
    1045:       (by != DMDA_BOUNDARY_PERIODIC && by) ||
    1046:        (bz != DMDA_BOUNDARY_PERIODIC && bz))) {
    1047:     /*
    1048:         Recompute the local to global mappings, this time keeping the
    1049:       information about the cross corner processor numbers.
    1050:     */
    1051:     nn = 0;
    1052:     /* Bottom Level */
    1053:     for (k=0; k<s_z; k++) {
    1054:       for (i=1; i<=s_y; i++) {
    1055:         if (n0 >= 0) { /* left below */
    1056:           x_t = lx[n0 % m];
    1057:           y_t = ly[(n0 % (m*n))/m];
    1058:           z_t = lz[n0 / (m*n)];
    1059:           s_t = bases[n0] + x_t*y_t*z_t - (s_y-i)*x_t - s_x - (s_z-k-1)*x_t*y_t;
    1060:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1061:         } else if (Xs-xs < 0 && Ys-ys < 0 && Zs-zs < 0) {
    1062:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1063:         }
    1064:         if (n1 >= 0) { /* directly below */
    1065:           x_t = x;
    1066:           y_t = ly[(n1 % (m*n))/m];
    1067:           z_t = lz[n1 / (m*n)];
    1068:           s_t = bases[n1] + x_t*y_t*z_t - (s_y+1-i)*x_t - (s_z-k-1)*x_t*y_t;
    1069:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1070:         } else if (Ys-ys < 0 && Zs-zs < 0) {
    1071:           for (j=0; j<x; j++) idx[nn++] = -1;
    1072:         }
    1073:         if (n2 >= 0) { /* right below */
    1074:           x_t = lx[n2 % m];
    1075:           y_t = ly[(n2 % (m*n))/m];
    1076:           z_t = lz[n2 / (m*n)];
    1077:           s_t = bases[n2] + x_t*y_t*z_t - (s_y+1-i)*x_t - (s_z-k-1)*x_t*y_t;
    1078:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1079:         } else if (xe-Xe < 0 && Ys-ys < 0 && Zs-zs < 0) {
    1080:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1081:         }
    1082:       }

    1084:       for (i=0; i<y; i++) {
    1085:         if (n3 >= 0) { /* directly left */
    1086:           x_t = lx[n3 % m];
    1087:           y_t = y;
    1088:           z_t = lz[n3 / (m*n)];
    1089:           s_t = bases[n3] + (i+1)*x_t - s_x + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1090:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1091:         } else if (Xs-xs < 0 && Zs-zs < 0) {
    1092:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1093:         }

    1095:         if (n4 >= 0) { /* middle */
    1096:           x_t = x;
    1097:           y_t = y;
    1098:           z_t = lz[n4 / (m*n)];
    1099:           s_t = bases[n4] + i*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1100:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1101:         } else if (Zs-zs < 0) {
    1102:           if (bz == DMDA_BOUNDARY_MIRROR) {
    1103:             for (j=0; j<x; j++) idx[nn++] = 0;
    1104:           } else {
    1105:             for (j=0; j<x; j++) idx[nn++] = -1;
    1106:           }
    1107:         }

    1109:         if (n5 >= 0) { /* directly right */
    1110:           x_t = lx[n5 % m];
    1111:           y_t = y;
    1112:           z_t = lz[n5 / (m*n)];
    1113:           s_t = bases[n5] + i*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1114:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1115:         } else if (xe-Xe < 0 && Zs-zs < 0) {
    1116:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1117:         }
    1118:       }

    1120:       for (i=1; i<=s_y; i++) {
    1121:         if (n6 >= 0) { /* left above */
    1122:           x_t = lx[n6 % m];
    1123:           y_t = ly[(n6 % (m*n))/m];
    1124:           z_t = lz[n6 / (m*n)];
    1125:           s_t = bases[n6] + i*x_t - s_x + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1126:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1127:         } else if (Xs-xs < 0 && ye-Ye < 0 && Zs-zs < 0) {
    1128:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1129:         }
    1130:         if (n7 >= 0) { /* directly above */
    1131:           x_t = x;
    1132:           y_t = ly[(n7 % (m*n))/m];
    1133:           z_t = lz[n7 / (m*n)];
    1134:           s_t = bases[n7] + (i-1)*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1135:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1136:         } else if (ye-Ye < 0 && Zs-zs < 0) {
    1137:           for (j=0; j<x; j++) idx[nn++] = -1;
    1138:         }
    1139:         if (n8 >= 0) { /* right above */
    1140:           x_t = lx[n8 % m];
    1141:           y_t = ly[(n8 % (m*n))/m];
    1142:           z_t = lz[n8 / (m*n)];
    1143:           s_t = bases[n8] + (i-1)*x_t + x_t*y_t*z_t - (s_z-k)*x_t*y_t;
    1144:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1145:         } else if (xe-Xe < 0 && ye-Ye < 0 && Zs-zs < 0) {
    1146:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1147:         }
    1148:       }
    1149:     }

    1151:     /* Middle Level */
    1152:     for (k=0; k<z; k++) {
    1153:       for (i=1; i<=s_y; i++) {
    1154:         if (n9 >= 0) { /* left below */
    1155:           x_t = lx[n9 % m];
    1156:           y_t = ly[(n9 % (m*n))/m];
    1157:           /* z_t = z; */
    1158:           s_t = bases[n9] - (s_y-i)*x_t -s_x + (k+1)*x_t*y_t;
    1159:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1160:         } else if (Xs-xs < 0 && Ys-ys < 0) {
    1161:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1162:         }
    1163:         if (n10 >= 0) { /* directly below */
    1164:           x_t = x;
    1165:           y_t = ly[(n10 % (m*n))/m];
    1166:           /* z_t = z; */
    1167:           s_t = bases[n10] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    1168:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1169:         } else if (Ys-ys < 0) {
    1170:           if (by == DMDA_BOUNDARY_MIRROR) {
    1171:             for (j=0; j<x; j++) idx[nn++] = -1;
    1172:           } else {
    1173:             for (j=0; j<x; j++) idx[nn++] = -1;
    1174:           }
    1175:         }
    1176:         if (n11 >= 0) { /* right below */
    1177:           x_t = lx[n11 % m];
    1178:           y_t = ly[(n11 % (m*n))/m];
    1179:           /* z_t = z; */
    1180:           s_t = bases[n11] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    1181:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1182:         } else if (xe-Xe < 0 && Ys-ys < 0) {
    1183:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1184:         }
    1185:       }

    1187:       for (i=0; i<y; i++) {
    1188:         if (n12 >= 0) { /* directly left */
    1189:           x_t = lx[n12 % m];
    1190:           y_t = y;
    1191:           /* z_t = z; */
    1192:           s_t = bases[n12] + (i+1)*x_t - s_x + k*x_t*y_t;
    1193:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1194:         } else if (Xs-xs < 0) {
    1195:           if (bx == DMDA_BOUNDARY_MIRROR) {
    1196:             for (j=0; j<s_x; j++) idx[nn++] = 0;
    1197:           } else {
    1198:             for (j=0; j<s_x; j++) idx[nn++] = -1;
    1199:           }
    1200:         }

    1202:         /* Interior */
    1203:         s_t = bases[rank] + i*x + k*x*y;
    1204:         for (j=0; j<x; j++) idx[nn++] = s_t++;

    1206:         if (n14 >= 0) { /* directly right */
    1207:           x_t = lx[n14 % m];
    1208:           y_t = y;
    1209:           /* z_t = z; */
    1210:           s_t = bases[n14] + i*x_t + k*x_t*y_t;
    1211:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1212:         } else if (xe-Xe < 0) {
    1213:           if (bx == DMDA_BOUNDARY_MIRROR) {
    1214:             for (j=0; j<s_x; j++) idx[nn++] = 0;
    1215:           } else {
    1216:             for (j=0; j<s_x; j++) idx[nn++] = -1;
    1217:           }
    1218:         }
    1219:       }

    1221:       for (i=1; i<=s_y; i++) {
    1222:         if (n15 >= 0) { /* left above */
    1223:           x_t = lx[n15 % m];
    1224:           y_t = ly[(n15 % (m*n))/m];
    1225:           /* z_t = z; */
    1226:           s_t = bases[n15] + i*x_t - s_x + k*x_t*y_t;
    1227:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1228:         } else if (Xs-xs < 0 && ye-Ye < 0) {
    1229:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1230:         }
    1231:         if (n16 >= 0) { /* directly above */
    1232:           x_t = x;
    1233:           y_t = ly[(n16 % (m*n))/m];
    1234:           /* z_t = z; */
    1235:           s_t = bases[n16] + (i-1)*x_t + k*x_t*y_t;
    1236:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1237:         } else if (ye-Ye < 0) {
    1238:           if (by == DMDA_BOUNDARY_MIRROR) {
    1239:             for (j=0; j<x; j++) idx[nn++] = 0;
    1240:           } else {
    1241:             for (j=0; j<x; j++) idx[nn++] = -1;
    1242:           }
    1243:         }
    1244:         if (n17 >= 0) { /* right above */
    1245:           x_t = lx[n17 % m];
    1246:           y_t = ly[(n17 % (m*n))/m];
    1247:           /* z_t = z; */
    1248:           s_t = bases[n17] + (i-1)*x_t + k*x_t*y_t;
    1249:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1250:         } else if (xe-Xe < 0 && ye-Ye < 0) {
    1251:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1252:         }
    1253:       }
    1254:     }

    1256:     /* Upper Level */
    1257:     for (k=0; k<s_z; k++) {
    1258:       for (i=1; i<=s_y; i++) {
    1259:         if (n18 >= 0) { /* left below */
    1260:           x_t = lx[n18 % m];
    1261:           y_t = ly[(n18 % (m*n))/m];
    1262:           /* z_t = lz[n18 / (m*n)]; */
    1263:           s_t = bases[n18] - (s_y-i)*x_t -s_x + (k+1)*x_t*y_t;
    1264:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1265:         } else if (Xs-xs < 0 && Ys-ys < 0 && ze-Ze < 0) {
    1266:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1267:         }
    1268:         if (n19 >= 0) { /* directly below */
    1269:           x_t = x;
    1270:           y_t = ly[(n19 % (m*n))/m];
    1271:           /* z_t = lz[n19 / (m*n)]; */
    1272:           s_t = bases[n19] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    1273:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1274:         } else if (Ys-ys < 0 && ze-Ze < 0) {
    1275:           for (j=0; j<x; j++) idx[nn++] = -1;
    1276:         }
    1277:         if (n20 >= 0) { /* right below */
    1278:           x_t = lx[n20 % m];
    1279:           y_t = ly[(n20 % (m*n))/m];
    1280:           /* z_t = lz[n20 / (m*n)]; */
    1281:           s_t = bases[n20] - (s_y+1-i)*x_t + (k+1)*x_t*y_t;
    1282:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1283:         } else if (xe-Xe < 0 && Ys-ys < 0 && ze-Ze < 0) {
    1284:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1285:         }
    1286:       }

    1288:       for (i=0; i<y; i++) {
    1289:         if (n21 >= 0) { /* directly left */
    1290:           x_t = lx[n21 % m];
    1291:           y_t = y;
    1292:           /* z_t = lz[n21 / (m*n)]; */
    1293:           s_t = bases[n21] + (i+1)*x_t - s_x + k*x_t*y_t;
    1294:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1295:         } else if (Xs-xs < 0 && ze-Ze < 0) {
    1296:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1297:         }

    1299:         if (n22 >= 0) { /* middle */
    1300:           x_t = x;
    1301:           y_t = y;
    1302:           /* z_t = lz[n22 / (m*n)]; */
    1303:           s_t = bases[n22] + i*x_t + k*x_t*y_t;
    1304:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1305:         } else if (ze-Ze < 0) {
    1306:           if (bz == DMDA_BOUNDARY_MIRROR) {
    1307:             for (j=0; j<x; j++) idx[nn++] = 0;
    1308:           } else {
    1309:             for (j=0; j<x; j++) idx[nn++] = -1;
    1310:           }
    1311:         }

    1313:         if (n23 >= 0) { /* directly right */
    1314:           x_t = lx[n23 % m];
    1315:           y_t = y;
    1316:           /* z_t = lz[n23 / (m*n)]; */
    1317:           s_t = bases[n23] + i*x_t + k*x_t*y_t;
    1318:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1319:         } else if (xe-Xe < 0 && ze-Ze < 0) {
    1320:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1321:         }
    1322:       }

    1324:       for (i=1; i<=s_y; i++) {
    1325:         if (n24 >= 0) { /* left above */
    1326:           x_t = lx[n24 % m];
    1327:           y_t = ly[(n24 % (m*n))/m];
    1328:           /* z_t = lz[n24 / (m*n)]; */
    1329:           s_t = bases[n24] + i*x_t - s_x + k*x_t*y_t;
    1330:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1331:         } else if (Xs-xs < 0 && ye-Ye < 0 && ze-Ze < 0) {
    1332:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1333:         }
    1334:         if (n25 >= 0) { /* directly above */
    1335:           x_t = x;
    1336:           y_t = ly[(n25 % (m*n))/m];
    1337:           /* z_t = lz[n25 / (m*n)]; */
    1338:           s_t = bases[n25] + (i-1)*x_t + k*x_t*y_t;
    1339:           for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    1340:         } else if (ye-Ye < 0 && ze-Ze < 0) {
    1341:           for (j=0; j<x; j++) idx[nn++] = -1;
    1342:         }
    1343:         if (n26 >= 0) { /* right above */
    1344:           x_t = lx[n26 % m];
    1345:           y_t = ly[(n26 % (m*n))/m];
    1346:           /* z_t = lz[n26 / (m*n)]; */
    1347:           s_t = bases[n26] + (i-1)*x_t + k*x_t*y_t;
    1348:           for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    1349:         } else if (xe-Xe < 0 && ye-Ye < 0 && ze-Ze < 0) {
    1350:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    1351:         }
    1352:       }
    1353:     }
    1354:   }
    1355:   /*
    1356:      Set the local to global ordering in the global vector, this allows use
    1357:      of VecSetValuesLocal().
    1358:   */
    1359:   ISCreateBlock(comm,dof,nn,idx,PETSC_OWN_POINTER,&ltogis);
    1360:   PetscMalloc(nn*dof*sizeof(PetscInt),&idx_cpy);
    1361:   PetscLogObjectMemory(da,nn*dof*sizeof(PetscInt));
    1362:   ISGetIndices(ltogis, &idx_full);
    1363:   PetscMemcpy(idx_cpy,idx_full,nn*dof*sizeof(PetscInt));
    1364:   ISRestoreIndices(ltogis, &idx_full);
    1365:   ISLocalToGlobalMappingCreateIS(ltogis,&da->ltogmap);
    1366:   PetscLogObjectParent(da,da->ltogmap);
    1367:   ISDestroy(&ltogis);
    1368:   ISLocalToGlobalMappingBlock(da->ltogmap,dd->w,&da->ltogmapb);
    1369:   PetscLogObjectParent(da,da->ltogmap);

    1371:   PetscFree2(bases,ldims);
    1372:   dd->m = m;  dd->n  = n;  dd->p  = p;
    1373:   /* note petsc expects xs/xe/Xs/Xe to be multiplied by #dofs in many places */
    1374:   dd->xs = xs*dof; dd->xe = xe*dof; dd->ys = ys; dd->ye = ye; dd->zs = zs; dd->ze = ze;
    1375:   dd->Xs = Xs*dof; dd->Xe = Xe*dof; dd->Ys = Ys; dd->Ye = Ye; dd->Zs = Zs; dd->Ze = Ze;

    1377:   VecDestroy(&local);
    1378:   VecDestroy(&global);

    1380:   dd->gtol      = gtol;
    1381:   dd->ltog      = ltog;
    1382:   dd->idx       = idx_cpy;
    1383:   dd->Nl        = nn*dof;
    1384:   dd->base      = base;
    1385:   da->ops->view = DMView_DA_3d;
    1386:   dd->ltol      = NULL;
    1387:   dd->ao        = NULL;
    1388:   return(0);
    1389: }

    1394: /*@C
    1395:    DMDACreate3d - Creates an object that will manage the communication of three-dimensional
    1396:    regular array data that is distributed across some processors.

    1398:    Collective on MPI_Comm

    1400:    Input Parameters:
    1401: +  comm - MPI communicator
    1402: .  bx,by,bz - type of ghost nodes the array have.
    1403:          Use one of DMDA_BOUNDARY_NONE, DMDA_BOUNDARY_GHOSTED, DMDA_BOUNDARY_PERIODIC.
    1404: .  stencil_type - Type of stencil (DMDA_STENCIL_STAR or DMDA_STENCIL_BOX)
    1405: .  M,N,P - global dimension in each direction of the array (use -M, -N, and or -P to indicate that it may be set to a different value
    1406:             from the command line with -da_grid_x <M> -da_grid_y <N> -da_grid_z <P>)
    1407: .  m,n,p - corresponding number of processors in each dimension
    1408:            (or PETSC_DECIDE to have calculated)
    1409: .  dof - number of degrees of freedom per node
    1410: .  s - stencil width
    1411: -  lx, ly, lz - arrays containing the number of nodes in each cell along
    1412:           the x, y, and z coordinates, or NULL. If non-null, these
    1413:           must be of length as m,n,p and the corresponding
    1414:           m,n, or p cannot be PETSC_DECIDE. Sum of the lx[] entries must be M, sum of
    1415:           the ly[] must N, sum of the lz[] must be P

    1417:    Output Parameter:
    1418: .  da - the resulting distributed array object

    1420:    Options Database Key:
    1421: +  -dm_view - Calls DMView() at the conclusion of DMDACreate3d()
    1422: .  -da_grid_x <nx> - number of grid points in x direction, if M < 0
    1423: .  -da_grid_y <ny> - number of grid points in y direction, if N < 0
    1424: .  -da_grid_z <nz> - number of grid points in z direction, if P < 0
    1425: .  -da_processors_x <MX> - number of processors in x direction
    1426: .  -da_processors_y <MY> - number of processors in y direction
    1427: .  -da_processors_z <MZ> - number of processors in z direction
    1428: .  -da_refine_x <rx> - refinement ratio in x direction
    1429: .  -da_refine_y <ry> - refinement ratio in y direction
    1430: .  -da_refine_z <rz>- refinement ratio in z directio
    1431: -  -da_refine <n> - refine the DMDA n times before creating it, , if M, N, or P < 0

    1433:    Level: beginner

    1435:    Notes:
    1436:    The stencil type DMDA_STENCIL_STAR with width 1 corresponds to the
    1437:    standard 7-pt stencil, while DMDA_STENCIL_BOX with width 1 denotes
    1438:    the standard 27-pt stencil.

    1440:    The array data itself is NOT stored in the DMDA, it is stored in Vec objects;
    1441:    The appropriate vector objects can be obtained with calls to DMCreateGlobalVector()
    1442:    and DMCreateLocalVector() and calls to VecDuplicate() if more are needed.

    1444: .keywords: distributed array, create, three-dimensional

    1446: .seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate2d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
    1447:           DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMDALocalToLocalBegin(), DMDALocalToLocalEnd(), DMDASetRefinementFactor(),
    1448:           DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges()

    1450: @*/
    1451: PetscErrorCode  DMDACreate3d(MPI_Comm comm,DMDABoundaryType bx,DMDABoundaryType by,DMDABoundaryType bz,DMDAStencilType stencil_type,PetscInt M,
    1452:                PetscInt N,PetscInt P,PetscInt m,PetscInt n,PetscInt p,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],const PetscInt lz[],DM *da)
    1453: {

    1457:   DMDACreate(comm, da);
    1458:   DMDASetDim(*da, 3);
    1459:   DMDASetSizes(*da, M, N, P);
    1460:   DMDASetNumProcs(*da, m, n, p);
    1461:   DMDASetBoundaryType(*da, bx, by, bz);
    1462:   DMDASetDof(*da, dof);
    1463:   DMDASetStencilType(*da, stencil_type);
    1464:   DMDASetStencilWidth(*da, s);
    1465:   DMDASetOwnershipRanges(*da, lx, ly, lz);
    1466:   /* This violates the behavior for other classes, but right now users expect negative dimensions to be handled this way */
    1467:   DMSetFromOptions(*da);
    1468:   DMSetUp(*da);
    1469:   DMViewFromOptions(*da,NULL,"-dm_view");
    1470:   return(0);
    1471: }