Actual source code: da2.c

      2: #include <petsc/private/dmdaimpl.h>
      3: #include <petscdraw.h>

      5: static PetscErrorCode DMView_DA_2d(DM da,PetscViewer viewer)
      6: {
      7:   PetscMPIInt    rank;
      8:   PetscBool      iascii,isdraw,isglvis,isbinary;
      9:   DM_DA          *dd = (DM_DA*)da->data;
     10: #if defined(PETSC_HAVE_MATLAB_ENGINE)
     11:   PetscBool ismatlab;
     12: #endif

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

     16:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERASCII,&iascii);
     17:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERDRAW,&isdraw);
     18:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERGLVIS,&isglvis);
     19:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERBINARY,&isbinary);
     20: #if defined(PETSC_HAVE_MATLAB_ENGINE)
     21:   PetscObjectTypeCompare((PetscObject)viewer,PETSCVIEWERMATLAB,&ismatlab);
     22: #endif
     23:   if (iascii) {
     24:     PetscViewerFormat format;

     26:     PetscViewerGetFormat(viewer, &format);
     27:     if (format == PETSC_VIEWER_LOAD_BALANCE) {
     28:       PetscInt      i,nmax = 0,nmin = PETSC_MAX_INT,navg = 0,*nz,nzlocal;
     29:       DMDALocalInfo info;
     30:       PetscMPIInt   size;
     31:       MPI_Comm_size(PetscObjectComm((PetscObject)da),&size);
     32:       DMDAGetLocalInfo(da,&info);
     33:       nzlocal = info.xm*info.ym;
     34:       PetscMalloc1(size,&nz);
     35:       MPI_Allgather(&nzlocal,1,MPIU_INT,nz,1,MPIU_INT,PetscObjectComm((PetscObject)da));
     36:       for (i=0; i<(PetscInt)size; i++) {
     37:         nmax = PetscMax(nmax,nz[i]);
     38:         nmin = PetscMin(nmin,nz[i]);
     39:         navg += nz[i];
     40:       }
     41:       PetscFree(nz);
     42:       navg = navg/size;
     43:       PetscViewerASCIIPrintf(viewer,"  Load Balance - Grid Points: Min %D  avg %D  max %D\n",nmin,navg,nmax);
     44:       return 0;
     45:     }
     46:     if (format != PETSC_VIEWER_ASCII_VTK_DEPRECATED && format != PETSC_VIEWER_ASCII_VTK_CELL_DEPRECATED && format != PETSC_VIEWER_ASCII_GLVIS) {
     47:       DMDALocalInfo info;
     48:       DMDAGetLocalInfo(da,&info);
     49:       PetscViewerASCIIPushSynchronized(viewer);
     50:       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);
     51:       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);
     52:       PetscViewerFlush(viewer);
     53:       PetscViewerASCIIPopSynchronized(viewer);
     54:     } else if (format == PETSC_VIEWER_ASCII_GLVIS) {
     55:       DMView_DA_GLVis(da,viewer);
     56:     } else {
     57:       DMView_DA_VTK(da,viewer);
     58:     }
     59:   } else if (isdraw) {
     60:     PetscDraw      draw;
     61:     double         ymin = -1*dd->s-1,ymax = dd->N+dd->s;
     62:     double         xmin = -1*dd->s-1,xmax = dd->M+dd->s;
     63:     double         x,y;
     64:     PetscInt       base;
     65:     const PetscInt *idx;
     66:     char           node[10];
     67:     PetscBool      isnull;

     70:     PetscViewerDrawGetDraw(viewer,0,&draw);
     71:     PetscDrawIsNull(draw,&isnull);
     72:     if (isnull) return 0;

     74:     PetscDrawCheckResizedWindow(draw);
     75:     PetscDrawClear(draw);
     76:     PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);

     78:     PetscDrawCollectiveBegin(draw);
     79:     /* first processor draw all node lines */
     80:     if (rank == 0) {
     81:       ymin = 0.0; ymax = dd->N - 1;
     82:       for (xmin=0; xmin<dd->M; xmin++) {
     83:         PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);
     84:       }
     85:       xmin = 0.0; xmax = dd->M - 1;
     86:       for (ymin=0; ymin<dd->N; ymin++) {
     87:         PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);
     88:       }
     89:     }
     90:     PetscDrawCollectiveEnd(draw);
     91:     PetscDrawFlush(draw);
     92:     PetscDrawPause(draw);

     94:     PetscDrawCollectiveBegin(draw);
     95:     /* draw my box */
     96:     xmin = dd->xs/dd->w; xmax =(dd->xe-1)/dd->w; ymin = dd->ys; ymax = dd->ye - 1;
     97:     PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);
     98:     PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);
     99:     PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);
    100:     PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);
    101:     /* put in numbers */
    102:     base = (dd->base)/dd->w;
    103:     for (y=ymin; y<=ymax; y++) {
    104:       for (x=xmin; x<=xmax; x++) {
    105:         PetscSNPrintf(node,sizeof(node),"%d",(int)base++);
    106:         PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);
    107:       }
    108:     }
    109:     PetscDrawCollectiveEnd(draw);
    110:     PetscDrawFlush(draw);
    111:     PetscDrawPause(draw);

    113:     PetscDrawCollectiveBegin(draw);
    114:     /* overlay ghost numbers, useful for error checking */
    115:     ISLocalToGlobalMappingGetBlockIndices(da->ltogmap,&idx);
    116:     base = 0; xmin = dd->Xs; xmax = dd->Xe; ymin = dd->Ys; ymax = dd->Ye;
    117:     for (y=ymin; y<ymax; y++) {
    118:       for (x=xmin; x<xmax; x++) {
    119:         if ((base % dd->w) == 0) {
    120:           PetscSNPrintf(node,sizeof(node),"%d",(int)(idx[base/dd->w]));
    121:           PetscDrawString(draw,x/dd->w,y,PETSC_DRAW_BLUE,node);
    122:         }
    123:         base++;
    124:       }
    125:     }
    126:     ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap,&idx);
    127:     PetscDrawCollectiveEnd(draw);
    128:     PetscDrawFlush(draw);
    129:     PetscDrawPause(draw);
    130:     PetscDrawSave(draw);
    131:   } else if (isglvis) {
    132:     DMView_DA_GLVis(da,viewer);
    133:   } else if (isbinary) {
    134:     DMView_DA_Binary(da,viewer);
    135: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    136:   } else if (ismatlab) {
    137:     DMView_DA_Matlab(da,viewer);
    138: #endif
    139:   }
    140:   return 0;
    141: }

    143: #if defined(new)
    144: /*
    145:   DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix where local
    146:     function lives on a DMDA

    148:         y ~= (F(u + ha) - F(u))/h,
    149:   where F = nonlinear function, as set by SNESSetFunction()
    150:         u = current iterate
    151:         h = difference interval
    152: */
    153: PetscErrorCode DMDAGetDiagonal_MFFD(DM da,Vec U,Vec a)
    154: {
    155:   PetscScalar    h,*aa,*ww,v;
    156:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
    157:   PetscInt       gI,nI;
    158:   MatStencil     stencil;
    159:   DMDALocalInfo  info;

    161:   (*ctx->func)(0,U,a,ctx->funcctx);
    162:   (*ctx->funcisetbase)(U,ctx->funcctx);

    164:   VecGetArray(U,&ww);
    165:   VecGetArray(a,&aa);

    167:   nI = 0;
    168:   h  = ww[gI];
    169:   if (h == 0.0) h = 1.0;
    170:   if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
    171:   else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
    172:   h *= epsilon;

    174:   ww[gI] += h;
    175:   (*ctx->funci)(i,w,&v,ctx->funcctx);
    176:   aa[nI]  = (v - aa[nI])/h;
    177:   ww[gI] -= h;
    178:   nI++;

    180:   VecRestoreArray(U,&ww);
    181:   VecRestoreArray(a,&aa);
    182:   return 0;
    183: }
    184: #endif

    186: PetscErrorCode  DMSetUp_DA_2D(DM da)
    187: {
    188:   DM_DA            *dd = (DM_DA*)da->data;
    189:   const PetscInt   M            = dd->M;
    190:   const PetscInt   N            = dd->N;
    191:   PetscInt         m            = dd->m;
    192:   PetscInt         n            = dd->n;
    193:   const PetscInt   dof          = dd->w;
    194:   const PetscInt   s            = dd->s;
    195:   DMBoundaryType   bx           = dd->bx;
    196:   DMBoundaryType   by           = dd->by;
    197:   DMDAStencilType  stencil_type = dd->stencil_type;
    198:   PetscInt         *lx          = dd->lx;
    199:   PetscInt         *ly          = dd->ly;
    200:   MPI_Comm         comm;
    201:   PetscMPIInt      rank,size;
    202:   PetscInt         xs,xe,ys,ye,x,y,Xs,Xe,Ys,Ye,IXs,IXe,IYs,IYe;
    203:   PetscInt         up,down,left,right,i,n0,n1,n2,n3,n5,n6,n7,n8,*idx,nn;
    204:   PetscInt         xbase,*bases,*ldims,j,x_t,y_t,s_t,base,count;
    205:   PetscInt         s_x,s_y; /* s proportionalized to w */
    206:   PetscInt         sn0 = 0,sn2 = 0,sn6 = 0,sn8 = 0;
    207:   Vec              local,global;
    208:   VecScatter       gtol;
    209:   IS               to,from;

    212:   PetscObjectGetComm((PetscObject)da,&comm);
    213: #if !defined(PETSC_USE_64BIT_INDICES)
    215: #endif

    217:   MPI_Comm_size(comm,&size);
    218:   MPI_Comm_rank(comm,&rank);

    220:   dd->p = 1;
    221:   if (m != PETSC_DECIDE) {
    224:   }
    225:   if (n != PETSC_DECIDE) {
    228:   }

    230:   if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
    231:     if (n != PETSC_DECIDE) {
    232:       m = size/n;
    233:     } else if (m != PETSC_DECIDE) {
    234:       n = size/m;
    235:     } else {
    236:       /* try for squarish distribution */
    237:       m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N)));
    238:       if (!m) m = 1;
    239:       while (m > 0) {
    240:         n = size/m;
    241:         if (m*n == size) break;
    242:         m--;
    243:       }
    244:       if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
    245:     }

    252:   /*
    253:      Determine locally owned region
    254:      xs is the first local node number, x is the number of local nodes
    255:   */
    256:   if (!lx) {
    257:     PetscMalloc1(m, &dd->lx);
    258:     lx   = dd->lx;
    259:     for (i=0; i<m; i++) {
    260:       lx[i] = M/m + ((M % m) > i);
    261:     }
    262:   }
    263:   x  = lx[rank % m];
    264:   xs = 0;
    265:   for (i=0; i<(rank % m); i++) {
    266:     xs += lx[i];
    267:   }
    268:   if (PetscDefined(USE_DEBUG)) {
    269:     left = xs;
    270:     for (i=(rank % m); i<m; i++) {
    271:       left += lx[i];
    272:     }
    274:   }

    276:   /*
    277:      Determine locally owned region
    278:      ys is the first local node number, y is the number of local nodes
    279:   */
    280:   if (!ly) {
    281:     PetscMalloc1(n, &dd->ly);
    282:     ly   = dd->ly;
    283:     for (i=0; i<n; i++) {
    284:       ly[i] = N/n + ((N % n) > i);
    285:     }
    286:   }
    287:   y  = ly[rank/m];
    288:   ys = 0;
    289:   for (i=0; i<(rank/m); i++) {
    290:     ys += ly[i];
    291:   }
    292:   if (PetscDefined(USE_DEBUG)) {
    293:     left = ys;
    294:     for (i=(rank/m); i<n; i++) {
    295:       left += ly[i];
    296:     }
    298:   }

    300:   /*
    301:    check if the scatter requires more than one process neighbor or wraps around
    302:    the domain more than once
    303:   */
    306:   xe = xs + x;
    307:   ye = ys + y;

    309:   /* determine ghost region (Xs) and region scattered into (IXs)  */
    310:   if (xs-s > 0) {
    311:     Xs = xs - s; IXs = xs - s;
    312:   } else {
    313:     if (bx) {
    314:       Xs = xs - s;
    315:     } else {
    316:       Xs = 0;
    317:     }
    318:     IXs = 0;
    319:   }
    320:   if (xe+s <= M) {
    321:     Xe = xe + s; IXe = xe + s;
    322:   } else {
    323:     if (bx) {
    324:       Xs = xs - s; Xe = xe + s;
    325:     } else {
    326:       Xe = M;
    327:     }
    328:     IXe = M;
    329:   }

    331:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
    332:     IXs = xs - s;
    333:     IXe = xe + s;
    334:     Xs  = xs - s;
    335:     Xe  = xe + s;
    336:   }

    338:   if (ys-s > 0) {
    339:     Ys = ys - s; IYs = ys - s;
    340:   } else {
    341:     if (by) {
    342:       Ys = ys - s;
    343:     } else {
    344:       Ys = 0;
    345:     }
    346:     IYs = 0;
    347:   }
    348:   if (ye+s <= N) {
    349:     Ye = ye + s; IYe = ye + s;
    350:   } else {
    351:     if (by) {
    352:       Ye = ye + s;
    353:     } else {
    354:       Ye = N;
    355:     }
    356:     IYe = N;
    357:   }

    359:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
    360:     IYs = ys - s;
    361:     IYe = ye + s;
    362:     Ys  = ys - s;
    363:     Ye  = ye + s;
    364:   }

    366:   /* stencil length in each direction */
    367:   s_x = s;
    368:   s_y = s;

    370:   /* determine starting point of each processor */
    371:   nn       = x*y;
    372:   PetscMalloc2(size+1,&bases,size,&ldims);
    373:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
    374:   bases[0] = 0;
    375:   for (i=1; i<=size; i++) {
    376:     bases[i] = ldims[i-1];
    377:   }
    378:   for (i=1; i<=size; i++) {
    379:     bases[i] += bases[i-1];
    380:   }
    381:   base = bases[rank]*dof;

    383:   /* allocate the base parallel and sequential vectors */
    384:   dd->Nlocal = x*y*dof;
    385:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,NULL,&global);
    386:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
    387:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,NULL,&local);

    389:   /* generate global to local vector scatter and local to global mapping*/

    391:   /* global to local must include ghost points within the domain,
    392:      but not ghost points outside the domain that aren't periodic */
    393:   PetscMalloc1((IXe-IXs)*(IYe-IYs),&idx);
    394:   if (stencil_type == DMDA_STENCIL_BOX) {
    395:     left  = IXs - Xs; right = left + (IXe-IXs);
    396:     down  = IYs - Ys; up = down + (IYe-IYs);
    397:     count = 0;
    398:     for (i=down; i<up; i++) {
    399:       for (j=left; j<right; j++) {
    400:         idx[count++] = j + i*(Xe-Xs);
    401:       }
    402:     }
    403:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

    405:   } else {
    406:     /* must drop into cross shape region */
    407:     /*       ---------|
    408:             |  top    |
    409:          |---         ---| up
    410:          |   middle      |
    411:          |               |
    412:          ----         ---- down
    413:             | bottom  |
    414:             -----------
    415:          Xs xs        xe Xe */
    416:     left  = xs - Xs; right = left + x;
    417:     down  = ys - Ys; up = down + y;
    418:     count = 0;
    419:     /* bottom */
    420:     for (i=(IYs-Ys); i<down; i++) {
    421:       for (j=left; j<right; j++) {
    422:         idx[count++] = j + i*(Xe-Xs);
    423:       }
    424:     }
    425:     /* middle */
    426:     for (i=down; i<up; i++) {
    427:       for (j=(IXs-Xs); j<(IXe-Xs); j++) {
    428:         idx[count++] = j + i*(Xe-Xs);
    429:       }
    430:     }
    431:     /* top */
    432:     for (i=up; i<up+IYe-ye; i++) {
    433:       for (j=left; j<right; j++) {
    434:         idx[count++] = j + i*(Xe-Xs);
    435:       }
    436:     }
    437:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
    438:   }

    440:   /* determine who lies on each side of us stored in    n6 n7 n8
    441:                                                         n3    n5
    442:                                                         n0 n1 n2
    443:   */

    445:   /* Assume the Non-Periodic Case */
    446:   n1 = rank - m;
    447:   if (rank % m) {
    448:     n0 = n1 - 1;
    449:   } else {
    450:     n0 = -1;
    451:   }
    452:   if ((rank+1) % m) {
    453:     n2 = n1 + 1;
    454:     n5 = rank + 1;
    455:     n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
    456:   } else {
    457:     n2 = -1; n5 = -1; n8 = -1;
    458:   }
    459:   if (rank % m) {
    460:     n3 = rank - 1;
    461:     n6 = n3 + m; if (n6 >= m*n) n6 = -1;
    462:   } else {
    463:     n3 = -1; n6 = -1;
    464:   }
    465:   n7 = rank + m; if (n7 >= m*n) n7 = -1;

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

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

    483:     /* Handle Left and Right Sides */
    484:     if (n3 < 0) n3 = rank + (m-1);
    485:     if (n5 < 0) n5 = rank - (m-1);
    486:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    487:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    488:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    489:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    490:   } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
    491:     if (n1 < 0) n1 = rank + m * (n-1);
    492:     if (n7 < 0) n7 = rank - m * (n-1);
    493:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    494:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
    495:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    496:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
    497:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
    498:     if (n3 < 0) n3 = rank + (m-1);
    499:     if (n5 < 0) n5 = rank - (m-1);
    500:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    501:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    502:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    503:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    504:   }

    506:   PetscMalloc1(9,&dd->neighbors);

    508:   dd->neighbors[0] = n0;
    509:   dd->neighbors[1] = n1;
    510:   dd->neighbors[2] = n2;
    511:   dd->neighbors[3] = n3;
    512:   dd->neighbors[4] = rank;
    513:   dd->neighbors[5] = n5;
    514:   dd->neighbors[6] = n6;
    515:   dd->neighbors[7] = n7;
    516:   dd->neighbors[8] = n8;

    518:   if (stencil_type == DMDA_STENCIL_STAR) {
    519:     /* save corner processor numbers */
    520:     sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
    521:     n0  = n2 = n6 = n8 = -1;
    522:   }

    524:   PetscMalloc1((Xe-Xs)*(Ye-Ys),&idx);

    526:   nn = 0;
    527:   xbase = bases[rank];
    528:   for (i=1; i<=s_y; i++) {
    529:     if (n0 >= 0) { /* left below */
    530:       x_t = lx[n0 % m];
    531:       y_t = ly[(n0/m)];
    532:       s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    533:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    534:     }

    536:     if (n1 >= 0) { /* directly below */
    537:       x_t = x;
    538:       y_t = ly[(n1/m)];
    539:       s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    540:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    541:     } else if (by == DM_BOUNDARY_MIRROR) {
    542:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    543:     }

    545:     if (n2 >= 0) { /* right below */
    546:       x_t = lx[n2 % m];
    547:       y_t = ly[(n2/m)];
    548:       s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    549:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    550:     }
    551:   }

    553:   for (i=0; i<y; i++) {
    554:     if (n3 >= 0) { /* directly left */
    555:       x_t = lx[n3 % m];
    556:       /* y_t = y; */
    557:       s_t = bases[n3] + (i+1)*x_t - s_x;
    558:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    559:     } else if (bx == DM_BOUNDARY_MIRROR) {
    560:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    561:     }

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

    565:     if (n5 >= 0) { /* directly right */
    566:       x_t = lx[n5 % m];
    567:       /* y_t = y; */
    568:       s_t = bases[n5] + (i)*x_t;
    569:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    570:     } else if (bx == DM_BOUNDARY_MIRROR) {
    571:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    572:     }
    573:   }

    575:   for (i=1; i<=s_y; i++) {
    576:     if (n6 >= 0) { /* left above */
    577:       x_t = lx[n6 % m];
    578:       /* y_t = ly[(n6/m)]; */
    579:       s_t = bases[n6] + (i)*x_t - s_x;
    580:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    581:     }

    583:     if (n7 >= 0) { /* directly above */
    584:       x_t = x;
    585:       /* y_t = ly[(n7/m)]; */
    586:       s_t = bases[n7] + (i-1)*x_t;
    587:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    588:     } else if (by == DM_BOUNDARY_MIRROR) {
    589:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    590:     }

    592:     if (n8 >= 0) { /* right above */
    593:       x_t = lx[n8 % m];
    594:       /* y_t = ly[(n8/m)]; */
    595:       s_t = bases[n8] + (i-1)*x_t;
    596:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    597:     }
    598:   }

    600:   ISCreateBlock(comm,dof,nn,idx,PETSC_USE_POINTER,&from);
    601:   VecScatterCreate(global,from,local,to,&gtol);
    602:   PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);
    603:   ISDestroy(&to);
    604:   ISDestroy(&from);

    606:   if (stencil_type == DMDA_STENCIL_STAR) {
    607:     n0 = sn0; n2 = sn2; n6 = sn6; n8 = sn8;
    608:   }

    610:   if (((stencil_type == DMDA_STENCIL_STAR)  || (bx && bx != DM_BOUNDARY_PERIODIC) || (by && by != DM_BOUNDARY_PERIODIC))) {
    611:     /*
    612:         Recompute the local to global mappings, this time keeping the
    613:       information about the cross corner processor numbers and any ghosted
    614:       but not periodic indices.
    615:     */
    616:     nn    = 0;
    617:     xbase = bases[rank];
    618:     for (i=1; i<=s_y; i++) {
    619:       if (n0 >= 0) { /* left below */
    620:         x_t = lx[n0 % m];
    621:         y_t = ly[(n0/m)];
    622:         s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    623:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    624:       } else if (xs-Xs > 0 && ys-Ys > 0) {
    625:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    626:       }
    627:       if (n1 >= 0) { /* directly below */
    628:         x_t = x;
    629:         y_t = ly[(n1/m)];
    630:         s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    631:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    632:       } else if (ys-Ys > 0) {
    633:         if (by == DM_BOUNDARY_MIRROR) {
    634:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    635:         } else {
    636:           for (j=0; j<x; j++) idx[nn++] = -1;
    637:         }
    638:       }
    639:       if (n2 >= 0) { /* right below */
    640:         x_t = lx[n2 % m];
    641:         y_t = ly[(n2/m)];
    642:         s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    643:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    644:       } else if (Xe-xe> 0 && ys-Ys > 0) {
    645:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    646:       }
    647:     }

    649:     for (i=0; i<y; i++) {
    650:       if (n3 >= 0) { /* directly left */
    651:         x_t = lx[n3 % m];
    652:         /* y_t = y; */
    653:         s_t = bases[n3] + (i+1)*x_t - s_x;
    654:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    655:       } else if (xs-Xs > 0) {
    656:         if (bx == DM_BOUNDARY_MIRROR) {
    657:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    658:         } else {
    659:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    660:         }
    661:       }

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

    665:       if (n5 >= 0) { /* directly right */
    666:         x_t = lx[n5 % m];
    667:         /* y_t = y; */
    668:         s_t = bases[n5] + (i)*x_t;
    669:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    670:       } else if (Xe-xe > 0) {
    671:         if (bx == DM_BOUNDARY_MIRROR) {
    672:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    673:         } else {
    674:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    675:         }
    676:       }
    677:     }

    679:     for (i=1; i<=s_y; i++) {
    680:       if (n6 >= 0) { /* left above */
    681:         x_t = lx[n6 % m];
    682:         /* y_t = ly[(n6/m)]; */
    683:         s_t = bases[n6] + (i)*x_t - s_x;
    684:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    685:       } else if (xs-Xs > 0 && Ye-ye > 0) {
    686:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    687:       }
    688:       if (n7 >= 0) { /* directly above */
    689:         x_t = x;
    690:         /* y_t = ly[(n7/m)]; */
    691:         s_t = bases[n7] + (i-1)*x_t;
    692:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    693:       } else if (Ye-ye > 0) {
    694:         if (by == DM_BOUNDARY_MIRROR) {
    695:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    696:         } else {
    697:           for (j=0; j<x; j++) idx[nn++] = -1;
    698:         }
    699:       }
    700:       if (n8 >= 0) { /* right above */
    701:         x_t = lx[n8 % m];
    702:         /* y_t = ly[(n8/m)]; */
    703:         s_t = bases[n8] + (i-1)*x_t;
    704:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    705:       } else if (Xe-xe > 0 && Ye-ye > 0) {
    706:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    707:       }
    708:     }
    709:   }
    710:   /*
    711:      Set the local to global ordering in the global vector, this allows use
    712:      of VecSetValuesLocal().
    713:   */
    714:   ISLocalToGlobalMappingCreate(comm,dof,nn,idx,PETSC_OWN_POINTER,&da->ltogmap);
    715:   PetscLogObjectParent((PetscObject)da,(PetscObject)da->ltogmap);

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

    723:   VecDestroy(&local);
    724:   VecDestroy(&global);

    726:   dd->gtol      = gtol;
    727:   dd->base      = base;
    728:   da->ops->view = DMView_DA_2d;
    729:   dd->ltol      = NULL;
    730:   dd->ao        = NULL;
    731:   return 0;
    732: }

    734: /*@C
    735:    DMDACreate2d -  Creates an object that will manage the communication of  two-dimensional
    736:    regular array data that is distributed across some processors.

    738:    Collective

    740:    Input Parameters:
    741: +  comm - MPI communicator
    742: .  bx,by - type of ghost nodes the array have.
    743:          Use one of DM_BOUNDARY_NONE, DM_BOUNDARY_GHOSTED, DM_BOUNDARY_PERIODIC.
    744: .  stencil_type - stencil type.  Use either DMDA_STENCIL_BOX or DMDA_STENCIL_STAR.
    745: .  M,N - global dimension in each direction of the array
    746: .  m,n - corresponding number of processors in each dimension
    747:          (or PETSC_DECIDE to have calculated)
    748: .  dof - number of degrees of freedom per node
    749: .  s - stencil width
    750: -  lx, ly - arrays containing the number of nodes in each cell along
    751:            the x and y coordinates, or NULL. If non-null, these
    752:            must be of length as m and n, and the corresponding
    753:            m and n cannot be PETSC_DECIDE. The sum of the lx[] entries
    754:            must be M, and the sum of the ly[] entries must be N.

    756:    Output Parameter:
    757: .  da - the resulting distributed array object

    759:    Options Database Key:
    760: +  -dm_view - Calls DMView() at the conclusion of DMDACreate2d()
    761: .  -da_grid_x <nx> - number of grid points in x direction
    762: .  -da_grid_y <ny> - number of grid points in y direction
    763: .  -da_processors_x <nx> - number of processors in x direction
    764: .  -da_processors_y <ny> - number of processors in y direction
    765: .  -da_refine_x <rx> - refinement ratio in x direction
    766: .  -da_refine_y <ry> - refinement ratio in y direction
    767: -  -da_refine <n> - refine the DMDA n times before creating

    769:    Level: beginner

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

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

    780:    You must call DMSetUp() after this call before using this DM.

    782:    If you wish to use the options database to change values in the DMDA call DMSetFromOptions() after this call
    783:    but before DMSetUp().

    785: .seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate3d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
    786:           DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMLocalToLocalBegin(), DMLocalToLocalEnd(), DMDASetRefinementFactor(),
    787:           DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges(),
    788:           DMStagCreate2d()

    790: @*/

    792: PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
    793:                              PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
    794: {
    795:   DMDACreate(comm, da);
    796:   DMSetDimension(*da, 2);
    797:   DMDASetSizes(*da, M, N, 1);
    798:   DMDASetNumProcs(*da, m, n, PETSC_DECIDE);
    799:   DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);
    800:   DMDASetDof(*da, dof);
    801:   DMDASetStencilType(*da, stencil_type);
    802:   DMDASetStencilWidth(*da, s);
    803:   DMDASetOwnershipRanges(*da, lx, ly, NULL);
    804:   return 0;
    805: }