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: {
      8:   PetscMPIInt    rank;
      9:   PetscBool      iascii,isdraw,isglvis,isbinary;
     10:   DM_DA          *dd = (DM_DA*)da->data;
     11: #if defined(PETSC_HAVE_MATLAB_ENGINE)
     12:   PetscBool ismatlab;
     13: #endif

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

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

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

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

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

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

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

    114:     PetscDrawCollectiveBegin(draw);
    115:     /* overlay ghost numbers, useful for error checking */
    116:     ISLocalToGlobalMappingGetBlockIndices(da->ltogmap,&idx);
    117:     base = 0; xmin = dd->Xs; xmax = dd->Xe; ymin = dd->Ys; ymax = dd->Ye;
    118:     for (y=ymin; y<ymax; y++) {
    119:       for (x=xmin; x<xmax; x++) {
    120:         if ((base % dd->w) == 0) {
    121:           PetscSNPrintf(node,sizeof(node),"%d",(int)(idx[base/dd->w]));
    122:           PetscDrawString(draw,x/dd->w,y,PETSC_DRAW_BLUE,node);
    123:         }
    124:         base++;
    125:       }
    126:     }
    127:     ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap,&idx);
    128:     PetscDrawCollectiveEnd(draw);
    129:     PetscDrawFlush(draw);
    130:     PetscDrawPause(draw);
    131:     PetscDrawSave(draw);
    132:   } else if (isglvis) {
    133:     DMView_DA_GLVis(da,viewer);
    134:   } else if (isbinary) {
    135:     DMView_DA_Binary(da,viewer);
    136: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    137:   } else if (ismatlab) {
    138:     DMView_DA_Matlab(da,viewer);
    139: #endif
    140:   }
    141:   return(0);
    142: }

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

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

    165:   (*ctx->func)(0,U,a,ctx->funcctx);
    166:   (*ctx->funcisetbase)(U,ctx->funcctx);

    168:   VecGetArray(U,&ww);
    169:   VecGetArray(a,&aa);

    171:   nI = 0;
    172:   h  = ww[gI];
    173:   if (h == 0.0) h = 1.0;
    174:   if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
    175:   else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
    176:   h *= epsilon;

    178:   ww[gI] += h;
    179:   (*ctx->funci)(i,w,&v,ctx->funcctx);
    180:   aa[nI]  = (v - aa[nI])/h;
    181:   ww[gI] -= h;
    182:   nI++;

    184:   VecRestoreArray(U,&ww);
    185:   VecRestoreArray(a,&aa);
    186:   return(0);
    187: }
    188: #endif

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

    217:   if (stencil_type == DMDA_STENCIL_BOX && (bx == DM_BOUNDARY_MIRROR || by == DM_BOUNDARY_MIRROR)) SETERRQ(PetscObjectComm((PetscObject)da),PETSC_ERR_SUP,"Mirror boundary and box stencil");
    218:   PetscObjectGetComm((PetscObject)da,&comm);
    219: #if !defined(PETSC_USE_64BIT_INDICES)
    220:   if (((PetscInt64) M)*((PetscInt64) N)*((PetscInt64) dof) > (PetscInt64) 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);
    221: #endif

    223:   MPI_Comm_size(comm,&size);
    224:   MPI_Comm_rank(comm,&rank);

    226:   dd->p = 1;
    227:   if (m != PETSC_DECIDE) {
    228:     if (m < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
    229:     else if (m > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
    230:   }
    231:   if (n != PETSC_DECIDE) {
    232:     if (n < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
    233:     else if (n > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
    234:   }

    236:   if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
    237:     if (n != PETSC_DECIDE) {
    238:       m = size/n;
    239:     } else if (m != PETSC_DECIDE) {
    240:       n = size/m;
    241:     } else {
    242:       /* try for squarish distribution */
    243:       m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N)));
    244:       if (!m) m = 1;
    245:       while (m > 0) {
    246:         n = size/m;
    247:         if (m*n == size) break;
    248:         m--;
    249:       }
    250:       if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
    251:     }
    252:     if (m*n != size) SETERRQ(comm,PETSC_ERR_PLIB,"Unable to create partition, check the size of the communicator and input m and n ");
    253:   } else if (m*n != size) SETERRQ(comm,PETSC_ERR_ARG_OUTOFRANGE,"Given Bad partition");

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

    258:   /*
    259:      Determine locally owned region
    260:      xs is the first local node number, x is the number of local nodes
    261:   */
    262:   if (!lx) {
    263:     PetscMalloc1(m, &dd->lx);
    264:     lx   = dd->lx;
    265:     for (i=0; i<m; i++) {
    266:       lx[i] = M/m + ((M % m) > i);
    267:     }
    268:   }
    269:   x  = lx[rank % m];
    270:   xs = 0;
    271:   for (i=0; i<(rank % m); i++) {
    272:     xs += lx[i];
    273:   }
    274:   if (PetscDefined(USE_DEBUG)) {
    275:     left = xs;
    276:     for (i=(rank % m); i<m; i++) {
    277:       left += lx[i];
    278:     }
    279:     if (left != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of lx across processors not equal to M: %D %D",left,M);
    280:   }

    282:   /*
    283:      Determine locally owned region
    284:      ys is the first local node number, y is the number of local nodes
    285:   */
    286:   if (!ly) {
    287:     PetscMalloc1(n, &dd->ly);
    288:     ly   = dd->ly;
    289:     for (i=0; i<n; i++) {
    290:       ly[i] = N/n + ((N % n) > i);
    291:     }
    292:   }
    293:   y  = ly[rank/m];
    294:   ys = 0;
    295:   for (i=0; i<(rank/m); i++) {
    296:     ys += ly[i];
    297:   }
    298:   if (PetscDefined(USE_DEBUG)) {
    299:     left = ys;
    300:     for (i=(rank/m); i<n; i++) {
    301:       left += ly[i];
    302:     }
    303:     if (left != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of ly across processors not equal to N: %D %D",left,N);
    304:   }

    306:   /*
    307:    check if the scatter requires more than one process neighbor or wraps around
    308:    the domain more than once
    309:   */
    310:   if ((x < s) && ((m > 1) || (bx == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local x-width of domain x %D is smaller than stencil width s %D",x,s);
    311:   if ((y < s) && ((n > 1) || (by == DM_BOUNDARY_PERIODIC))) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Local y-width of domain y %D is smaller than stencil width s %D",y,s);
    312:   xe = xs + x;
    313:   ye = ys + y;

    315:   /* determine ghost region (Xs) and region scattered into (IXs)  */
    316:   if (xs-s > 0) {
    317:     Xs = xs - s; IXs = xs - s;
    318:   } else {
    319:     if (bx) {
    320:       Xs = xs - s;
    321:     } else {
    322:       Xs = 0;
    323:     }
    324:     IXs = 0;
    325:   }
    326:   if (xe+s <= M) {
    327:     Xe = xe + s; IXe = xe + s;
    328:   } else {
    329:     if (bx) {
    330:       Xs = xs - s; Xe = xe + s;
    331:     } else {
    332:       Xe = M;
    333:     }
    334:     IXe = M;
    335:   }

    337:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
    338:     IXs = xs - s;
    339:     IXe = xe + s;
    340:     Xs  = xs - s;
    341:     Xe  = xe + s;
    342:   }

    344:   if (ys-s > 0) {
    345:     Ys = ys - s; IYs = ys - s;
    346:   } else {
    347:     if (by) {
    348:       Ys = ys - s;
    349:     } else {
    350:       Ys = 0;
    351:     }
    352:     IYs = 0;
    353:   }
    354:   if (ye+s <= N) {
    355:     Ye = ye + s; IYe = ye + s;
    356:   } else {
    357:     if (by) {
    358:       Ye = ye + s;
    359:     } else {
    360:       Ye = N;
    361:     }
    362:     IYe = N;
    363:   }

    365:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
    366:     IYs = ys - s;
    367:     IYe = ye + s;
    368:     Ys  = ys - s;
    369:     Ye  = ye + s;
    370:   }

    372:   /* stencil length in each direction */
    373:   s_x = s;
    374:   s_y = s;

    376:   /* determine starting point of each processor */
    377:   nn       = x*y;
    378:   PetscMalloc2(size+1,&bases,size,&ldims);
    379:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
    380:   bases[0] = 0;
    381:   for (i=1; i<=size; i++) {
    382:     bases[i] = ldims[i-1];
    383:   }
    384:   for (i=1; i<=size; i++) {
    385:     bases[i] += bases[i-1];
    386:   }
    387:   base = bases[rank]*dof;

    389:   /* allocate the base parallel and sequential vectors */
    390:   dd->Nlocal = x*y*dof;
    391:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,NULL,&global);
    392:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
    393:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,NULL,&local);

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

    397:   /* global to local must include ghost points within the domain,
    398:      but not ghost points outside the domain that aren't periodic */
    399:   PetscMalloc1((IXe-IXs)*(IYe-IYs),&idx);
    400:   if (stencil_type == DMDA_STENCIL_BOX) {
    401:     left  = IXs - Xs; right = left + (IXe-IXs);
    402:     down  = IYs - Ys; up = down + (IYe-IYs);
    403:     count = 0;
    404:     for (i=down; i<up; i++) {
    405:       for (j=left; j<right; j++) {
    406:         idx[count++] = j + i*(Xe-Xs);
    407:       }
    408:     }
    409:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

    411:   } else {
    412:     /* must drop into cross shape region */
    413:     /*       ---------|
    414:             |  top    |
    415:          |---         ---| up
    416:          |   middle      |
    417:          |               |
    418:          ----         ---- down
    419:             | bottom  |
    420:             -----------
    421:          Xs xs        xe Xe */
    422:     left  = xs - Xs; right = left + x;
    423:     down  = ys - Ys; up = down + y;
    424:     count = 0;
    425:     /* bottom */
    426:     for (i=(IYs-Ys); i<down; i++) {
    427:       for (j=left; j<right; j++) {
    428:         idx[count++] = j + i*(Xe-Xs);
    429:       }
    430:     }
    431:     /* middle */
    432:     for (i=down; i<up; i++) {
    433:       for (j=(IXs-Xs); j<(IXe-Xs); j++) {
    434:         idx[count++] = j + i*(Xe-Xs);
    435:       }
    436:     }
    437:     /* top */
    438:     for (i=up; i<up+IYe-ye; i++) {
    439:       for (j=left; j<right; j++) {
    440:         idx[count++] = j + i*(Xe-Xs);
    441:       }
    442:     }
    443:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
    444:   }

    447:   /* determine who lies on each side of us stored in    n6 n7 n8
    448:                                                         n3    n5
    449:                                                         n0 n1 n2
    450:   */

    452:   /* Assume the Non-Periodic Case */
    453:   n1 = rank - m;
    454:   if (rank % m) {
    455:     n0 = n1 - 1;
    456:   } else {
    457:     n0 = -1;
    458:   }
    459:   if ((rank+1) % m) {
    460:     n2 = n1 + 1;
    461:     n5 = rank + 1;
    462:     n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
    463:   } else {
    464:     n2 = -1; n5 = -1; n8 = -1;
    465:   }
    466:   if (rank % m) {
    467:     n3 = rank - 1;
    468:     n6 = n3 + m; if (n6 >= m*n) n6 = -1;
    469:   } else {
    470:     n3 = -1; n6 = -1;
    471:   }
    472:   n7 = rank + m; if (n7 >= m*n) n7 = -1;

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

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

    490:     /* Handle Left and Right Sides */
    491:     if (n3 < 0) n3 = rank + (m-1);
    492:     if (n5 < 0) n5 = rank - (m-1);
    493:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    494:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    495:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    496:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    497:   } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
    498:     if (n1 < 0) n1 = rank + m * (n-1);
    499:     if (n7 < 0) n7 = rank - m * (n-1);
    500:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    501:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
    502:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    503:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
    504:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
    505:     if (n3 < 0) n3 = rank + (m-1);
    506:     if (n5 < 0) n5 = rank - (m-1);
    507:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    508:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    509:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    510:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    511:   }

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

    515:   dd->neighbors[0] = n0;
    516:   dd->neighbors[1] = n1;
    517:   dd->neighbors[2] = n2;
    518:   dd->neighbors[3] = n3;
    519:   dd->neighbors[4] = rank;
    520:   dd->neighbors[5] = n5;
    521:   dd->neighbors[6] = n6;
    522:   dd->neighbors[7] = n7;
    523:   dd->neighbors[8] = n8;

    525:   if (stencil_type == DMDA_STENCIL_STAR) {
    526:     /* save corner processor numbers */
    527:     sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
    528:     n0  = n2 = n6 = n8 = -1;
    529:   }

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

    533:   nn = 0;
    534:   xbase = bases[rank];
    535:   for (i=1; i<=s_y; i++) {
    536:     if (n0 >= 0) { /* left below */
    537:       x_t = lx[n0 % m];
    538:       y_t = ly[(n0/m)];
    539:       s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    540:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    541:     }

    543:     if (n1 >= 0) { /* directly below */
    544:       x_t = x;
    545:       y_t = ly[(n1/m)];
    546:       s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    547:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    548:     } else if (by == DM_BOUNDARY_MIRROR) {
    549:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    550:     }

    552:     if (n2 >= 0) { /* right below */
    553:       x_t = lx[n2 % m];
    554:       y_t = ly[(n2/m)];
    555:       s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    556:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    557:     }
    558:   }

    560:   for (i=0; i<y; i++) {
    561:     if (n3 >= 0) { /* directly left */
    562:       x_t = lx[n3 % m];
    563:       /* y_t = y; */
    564:       s_t = bases[n3] + (i+1)*x_t - s_x;
    565:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    566:     } else if (bx == DM_BOUNDARY_MIRROR) {
    567:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    568:     }

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

    572:     if (n5 >= 0) { /* directly right */
    573:       x_t = lx[n5 % m];
    574:       /* y_t = y; */
    575:       s_t = bases[n5] + (i)*x_t;
    576:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    577:     } else if (bx == DM_BOUNDARY_MIRROR) {
    578:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    579:     }
    580:   }

    582:   for (i=1; i<=s_y; i++) {
    583:     if (n6 >= 0) { /* left above */
    584:       x_t = lx[n6 % m];
    585:       /* y_t = ly[(n6/m)]; */
    586:       s_t = bases[n6] + (i)*x_t - s_x;
    587:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    588:     }

    590:     if (n7 >= 0) { /* directly above */
    591:       x_t = x;
    592:       /* y_t = ly[(n7/m)]; */
    593:       s_t = bases[n7] + (i-1)*x_t;
    594:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    595:     } else if (by == DM_BOUNDARY_MIRROR) {
    596:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    597:     }

    599:     if (n8 >= 0) { /* right above */
    600:       x_t = lx[n8 % m];
    601:       /* y_t = ly[(n8/m)]; */
    602:       s_t = bases[n8] + (i-1)*x_t;
    603:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    604:     }
    605:   }

    607:   ISCreateBlock(comm,dof,nn,idx,PETSC_USE_POINTER,&from);
    608:   VecScatterCreate(global,from,local,to,&gtol);
    609:   PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);
    610:   ISDestroy(&to);
    611:   ISDestroy(&from);

    613:   if (stencil_type == DMDA_STENCIL_STAR) {
    614:     n0 = sn0; n2 = sn2; n6 = sn6; n8 = sn8;
    615:   }

    617:   if (((stencil_type == DMDA_STENCIL_STAR)  || (bx && bx != DM_BOUNDARY_PERIODIC) || (by && by != DM_BOUNDARY_PERIODIC))) {
    618:     /*
    619:         Recompute the local to global mappings, this time keeping the
    620:       information about the cross corner processor numbers and any ghosted
    621:       but not periodic indices.
    622:     */
    623:     nn    = 0;
    624:     xbase = bases[rank];
    625:     for (i=1; i<=s_y; i++) {
    626:       if (n0 >= 0) { /* left below */
    627:         x_t = lx[n0 % m];
    628:         y_t = ly[(n0/m)];
    629:         s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    630:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    631:       } else if (xs-Xs > 0 && ys-Ys > 0) {
    632:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    633:       }
    634:       if (n1 >= 0) { /* directly below */
    635:         x_t = x;
    636:         y_t = ly[(n1/m)];
    637:         s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    638:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    639:       } else if (ys-Ys > 0) {
    640:         if (by == DM_BOUNDARY_MIRROR) {
    641:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    642:         } else {
    643:           for (j=0; j<x; j++) idx[nn++] = -1;
    644:         }
    645:       }
    646:       if (n2 >= 0) { /* right below */
    647:         x_t = lx[n2 % m];
    648:         y_t = ly[(n2/m)];
    649:         s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    650:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    651:       } else if (Xe-xe> 0 && ys-Ys > 0) {
    652:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    653:       }
    654:     }

    656:     for (i=0; i<y; i++) {
    657:       if (n3 >= 0) { /* directly left */
    658:         x_t = lx[n3 % m];
    659:         /* y_t = y; */
    660:         s_t = bases[n3] + (i+1)*x_t - s_x;
    661:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    662:       } else if (xs-Xs > 0) {
    663:         if (bx == DM_BOUNDARY_MIRROR) {
    664:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    665:         } else {
    666:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    667:         }
    668:       }

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

    672:       if (n5 >= 0) { /* directly right */
    673:         x_t = lx[n5 % m];
    674:         /* y_t = y; */
    675:         s_t = bases[n5] + (i)*x_t;
    676:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    677:       } else if (Xe-xe > 0) {
    678:         if (bx == DM_BOUNDARY_MIRROR) {
    679:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    680:         } else {
    681:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    682:         }
    683:       }
    684:     }

    686:     for (i=1; i<=s_y; i++) {
    687:       if (n6 >= 0) { /* left above */
    688:         x_t = lx[n6 % m];
    689:         /* y_t = ly[(n6/m)]; */
    690:         s_t = bases[n6] + (i)*x_t - s_x;
    691:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    692:       } else if (xs-Xs > 0 && Ye-ye > 0) {
    693:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    694:       }
    695:       if (n7 >= 0) { /* directly above */
    696:         x_t = x;
    697:         /* y_t = ly[(n7/m)]; */
    698:         s_t = bases[n7] + (i-1)*x_t;
    699:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    700:       } else if (Ye-ye > 0) {
    701:         if (by == DM_BOUNDARY_MIRROR) {
    702:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    703:         } else {
    704:           for (j=0; j<x; j++) idx[nn++] = -1;
    705:         }
    706:       }
    707:       if (n8 >= 0) { /* right above */
    708:         x_t = lx[n8 % m];
    709:         /* y_t = ly[(n8/m)]; */
    710:         s_t = bases[n8] + (i-1)*x_t;
    711:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    712:       } else if (Xe-xe > 0 && Ye-ye > 0) {
    713:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    714:       }
    715:     }
    716:   }
    717:   /*
    718:      Set the local to global ordering in the global vector, this allows use
    719:      of VecSetValuesLocal().
    720:   */
    721:   ISLocalToGlobalMappingCreate(comm,dof,nn,idx,PETSC_OWN_POINTER,&da->ltogmap);
    722:   PetscLogObjectParent((PetscObject)da,(PetscObject)da->ltogmap);

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

    730:   VecDestroy(&local);
    731:   VecDestroy(&global);

    733:   dd->gtol      = gtol;
    734:   dd->base      = base;
    735:   da->ops->view = DMView_DA_2d;
    736:   dd->ltol      = NULL;
    737:   dd->ao        = NULL;
    738:   return(0);
    739: }

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

    745:    Collective

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

    763:    Output Parameter:
    764: .  da - the resulting distributed array object

    766:    Options Database Key:
    767: +  -dm_view - Calls DMView() at the conclusion of DMDACreate2d()
    768: .  -da_grid_x <nx> - number of grid points in x direction
    769: .  -da_grid_y <ny> - number of grid points in y direction
    770: .  -da_processors_x <nx> - number of processors in x direction
    771: .  -da_processors_y <ny> - number of processors in y direction
    772: .  -da_refine_x <rx> - refinement ratio in x direction
    773: .  -da_refine_y <ry> - refinement ratio in y direction
    774: -  -da_refine <n> - refine the DMDA n times before creating

    777:    Level: beginner

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

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

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

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

    793: .seealso: DMDestroy(), DMView(), DMDACreate1d(), DMDACreate3d(), DMGlobalToLocalBegin(), DMDAGetRefinementFactor(),
    794:           DMGlobalToLocalEnd(), DMLocalToGlobalBegin(), DMLocalToLocalBegin(), DMLocalToLocalEnd(), DMDASetRefinementFactor(),
    795:           DMDAGetInfo(), DMCreateGlobalVector(), DMCreateLocalVector(), DMDACreateNaturalVector(), DMLoad(), DMDAGetOwnershipRanges(),
    796:           DMStagCreate2d()

    798: @*/

    800: PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
    801:                              PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
    802: {

    806:   DMDACreate(comm, da);
    807:   DMSetDimension(*da, 2);
    808:   DMDASetSizes(*da, M, N, 1);
    809:   DMDASetNumProcs(*da, m, n, PETSC_DECIDE);
    810:   DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);
    811:   DMDASetDof(*da, dof);
    812:   DMDASetStencilType(*da, stencil_type);
    813:   DMDASetStencilWidth(*da, s);
    814:   DMDASetOwnershipRanges(*da, lx, ly, NULL);
    815:   return(0);
    816: }