Date: 2015-10-02T22:12:59+00:00

Actual source code: da2.c
petsc-3.6.2 2015-10-02
Report Typos and Errors

      2: #include <petsc/private/dmdaimpl.h>    /*I   "petscdmda.h"   I*/
      3: #include <petscdraw.h>

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

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

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

     29:     PetscViewerGetFormat(viewer, &format);
     30:     if (format != PETSC_VIEWER_ASCII_VTK && format != PETSC_VIEWER_ASCII_VTK_CELL) {
     31:       DMDALocalInfo info;
     32:       DMDAGetLocalInfo(da,&info);
     33:       PetscViewerASCIISynchronizedAllow(viewer,PETSC_TRUE);
     34:       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);
     35:       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);
     36:       PetscViewerFlush(viewer);
     37:       PetscViewerASCIISynchronizedAllow(viewer,PETSC_FALSE);
     38:     } else {
     39:       DMView_DA_VTK(da,viewer);
     40:     }
     41:   } else if (isdraw) {
     42:     PetscDraw      draw;
     43:     double         ymin = -1*dd->s-1,ymax = dd->N+dd->s;
     44:     double         xmin = -1*dd->s-1,xmax = dd->M+dd->s;
     45:     double         x,y;
     46:     PetscInt       base;
     47:     const PetscInt *idx;
     48:     char           node[10];
     49:     PetscBool      isnull;

     51:     PetscViewerDrawGetDraw(viewer,0,&draw);
     52:     PetscDrawIsNull(draw,&isnull); if (isnull) return(0);
     53:     if (!da->coordinates) {
     54:       PetscDrawSetCoordinates(draw,xmin,ymin,xmax,ymax);
     55:     }
     56:     PetscDrawSynchronizedClear(draw);

     58:     /* first processor draw all node lines */
     59:     if (!rank) {
     60:       ymin = 0.0; ymax = dd->N - 1;
     61:       for (xmin=0; xmin<dd->M; xmin++) {
     62:         PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_BLACK);
     63:       }
     64:       xmin = 0.0; xmax = dd->M - 1;
     65:       for (ymin=0; ymin<dd->N; ymin++) {
     66:         PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_BLACK);
     67:       }
     68:     }
     69:     PetscDrawSynchronizedFlush(draw);
     70:     PetscDrawPause(draw);

     72:     /* draw my box */
     73:     ymin = dd->ys; ymax = dd->ye - 1; xmin = dd->xs/dd->w;
     74:     xmax =(dd->xe-1)/dd->w;
     75:     PetscDrawLine(draw,xmin,ymin,xmax,ymin,PETSC_DRAW_RED);
     76:     PetscDrawLine(draw,xmin,ymin,xmin,ymax,PETSC_DRAW_RED);
     77:     PetscDrawLine(draw,xmin,ymax,xmax,ymax,PETSC_DRAW_RED);
     78:     PetscDrawLine(draw,xmax,ymin,xmax,ymax,PETSC_DRAW_RED);

     80:     /* put in numbers */
     81:     base = (dd->base)/dd->w;
     82:     for (y=ymin; y<=ymax; y++) {
     83:       for (x=xmin; x<=xmax; x++) {
     84:         sprintf(node,"%d",(int)base++);
     85:         PetscDrawString(draw,x,y,PETSC_DRAW_BLACK,node);
     86:       }
     87:     }

     89:     PetscDrawSynchronizedFlush(draw);
     90:     PetscDrawPause(draw);
     91:     /* overlay ghost numbers, useful for error checking */
     92:     /* put in numbers */

     94:     base = 0;
     95:     ISLocalToGlobalMappingGetBlockIndices(da->ltogmap,&idx);
     96:     ymin = dd->Ys; ymax = dd->Ye; xmin = dd->Xs; xmax = dd->Xe;
     97:     for (y=ymin; y<ymax; y++) {
     98:       for (x=xmin; x<xmax; x++) {
     99:         if ((base % dd->w) == 0) {
    100:           sprintf(node,"%d",(int)(idx[base/dd->w]));
    101:           PetscDrawString(draw,x/dd->w,y,PETSC_DRAW_BLUE,node);
    102:         }
    103:         base++;
    104:       }
    105:     }
    106:     ISLocalToGlobalMappingRestoreBlockIndices(da->ltogmap,&idx);
    107:     PetscDrawSynchronizedFlush(draw);
    108:     PetscDrawPause(draw);
    109:   } else if (isbinary) {
    110:     DMView_DA_Binary(da,viewer);
    111: #if defined(PETSC_HAVE_MATLAB_ENGINE)
    112:   } else if (ismatlab) {
    113:     DMView_DA_Matlab(da,viewer);
    114: #endif
    115:   }
    116:   return(0);
    117: }

    119: /*
    120:       M is number of grid points
    121:       m is number of processors

    123: */
    126: PetscErrorCode  DMDASplitComm2d(MPI_Comm comm,PetscInt M,PetscInt N,PetscInt sw,MPI_Comm *outcomm)
    127: {
    129:   PetscInt       m,n = 0,x = 0,y = 0;
    130:   PetscMPIInt    size,csize,rank;

    133:   MPI_Comm_size(comm,&size);
    134:   MPI_Comm_rank(comm,&rank);

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

    141:     m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)csize)/((PetscReal)N)));
    142:     if (!m) m = 1;
    143:     while (m > 0) {
    144:       n = csize/m;
    145:       if (m*n == csize) break;
    146:       m--;
    147:     }
    148:     if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}

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

    157:     MPI_Comm_group(comm,&entire_group);
    158:     PetscMalloc1(csize,&groupies);
    159:     for (i=0; i<csize; i++) {
    160:       groupies[i] = (rank/csize)*csize + i;
    161:     }
    162:     MPI_Group_incl(entire_group,csize,groupies,&sub_group);
    163:     PetscFree(groupies);
    164:     MPI_Comm_create(comm,sub_group,outcomm);
    165:     MPI_Group_free(&entire_group);
    166:     MPI_Group_free(&sub_group);
    167:     PetscInfo1(0,"DMDASplitComm2d:Creating redundant coarse problems of size %d\n",csize);
    168:   } else {
    169:     *outcomm = comm;
    170:   }
    171:   return(0);
    172: }

    174: #if defined(new)
    177: /*
    178:   DMDAGetDiagonal_MFFD - Gets the diagonal for a matrix free matrix where local
    179:     function lives on a DMDA

    181:         y ~= (F(u + ha) - F(u))/h,
    182:   where F = nonlinear function, as set by SNESSetFunction()
    183:         u = current iterate
    184:         h = difference interval
    185: */
    186: PetscErrorCode DMDAGetDiagonal_MFFD(DM da,Vec U,Vec a)
    187: {
    188:   PetscScalar    h,*aa,*ww,v;
    189:   PetscReal      epsilon = PETSC_SQRT_MACHINE_EPSILON,umin = 100.0*PETSC_SQRT_MACHINE_EPSILON;
    191:   PetscInt       gI,nI;
    192:   MatStencil     stencil;
    193:   DMDALocalInfo  info;

    196:   (*ctx->func)(0,U,a,ctx->funcctx);
    197:   (*ctx->funcisetbase)(U,ctx->funcctx);

    199:   VecGetArray(U,&ww);
    200:   VecGetArray(a,&aa);

    202:   nI = 0;
    203:   h  = ww[gI];
    204:   if (h == 0.0) h = 1.0;
    205:   if (PetscAbsScalar(h) < umin && PetscRealPart(h) >= 0.0) h = umin;
    206:   else if (PetscRealPart(h) < 0.0 && PetscAbsScalar(h) < umin) h = -umin;
    207:   h *= epsilon;

    209:   ww[gI] += h;
    210:   (*ctx->funci)(i,w,&v,ctx->funcctx);
    211:   aa[nI]  = (v - aa[nI])/h;
    212:   ww[gI] -= h;
    213:   nI++;

    215:   VecRestoreArray(U,&ww);
    216:   VecRestoreArray(a,&aa);
    217:   return(0);
    218: }
    219: #endif

    223: PetscErrorCode  DMSetUp_DA_2D(DM da)
    224: {
    225:   DM_DA            *dd = (DM_DA*)da->data;
    226:   const PetscInt   M            = dd->M;
    227:   const PetscInt   N            = dd->N;
    228:   PetscInt         m            = dd->m;
    229:   PetscInt         n            = dd->n;
    230:   const PetscInt   dof          = dd->w;
    231:   const PetscInt   s            = dd->s;
    232:   DMBoundaryType   bx           = dd->bx;
    233:   DMBoundaryType   by           = dd->by;
    234:   DMDAStencilType  stencil_type = dd->stencil_type;
    235:   PetscInt         *lx          = dd->lx;
    236:   PetscInt         *ly          = dd->ly;
    237:   MPI_Comm         comm;
    238:   PetscMPIInt      rank,size;
    239:   PetscInt         xs,xe,ys,ye,x,y,Xs,Xe,Ys,Ye,IXs,IXe,IYs,IYe;
    240:   PetscInt         up,down,left,right,i,n0,n1,n2,n3,n5,n6,n7,n8,*idx,nn;
    241:   PetscInt         xbase,*bases,*ldims,j,x_t,y_t,s_t,base,count;
    242:   PetscInt         s_x,s_y; /* s proportionalized to w */
    243:   PetscInt         sn0 = 0,sn2 = 0,sn6 = 0,sn8 = 0;
    244:   Vec              local,global;
    245:   VecScatter       gtol;
    246:   IS               to,from;
    247:   PetscErrorCode   ierr;

    250:   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");
    251:   PetscObjectGetComm((PetscObject)da,&comm);
    252: #if !defined(PETSC_USE_64BIT_INDICES)
    253:   if (((Petsc64bitInt) M)*((Petsc64bitInt) N)*((Petsc64bitInt) dof) > (Petsc64bitInt) PETSC_MPI_INT_MAX) SETERRQ3(comm,PETSC_ERR_INT_OVERFLOW,"Mesh of %D by %D by %D (dof) is too large for 32 bit indices",M,N,dof);
    254: #endif

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

    259:   MPI_Comm_size(comm,&size);
    260:   MPI_Comm_rank(comm,&rank);

    262:   dd->p = 1;
    263:   if (m != PETSC_DECIDE) {
    264:     if (m < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in X direction: %D",m);
    265:     else if (m > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in X direction: %D %d",m,size);
    266:   }
    267:   if (n != PETSC_DECIDE) {
    268:     if (n < 1) SETERRQ1(comm,PETSC_ERR_ARG_OUTOFRANGE,"Non-positive number of processors in Y direction: %D",n);
    269:     else if (n > size) SETERRQ2(comm,PETSC_ERR_ARG_OUTOFRANGE,"Too many processors in Y direction: %D %d",n,size);
    270:   }

    272:   if (m == PETSC_DECIDE || n == PETSC_DECIDE) {
    273:     if (n != PETSC_DECIDE) {
    274:       m = size/n;
    275:     } else if (m != PETSC_DECIDE) {
    276:       n = size/m;
    277:     } else {
    278:       /* try for squarish distribution */
    279:       m = (PetscInt)(0.5 + PetscSqrtReal(((PetscReal)M)*((PetscReal)size)/((PetscReal)N)));
    280:       if (!m) m = 1;
    281:       while (m > 0) {
    282:         n = size/m;
    283:         if (m*n == size) break;
    284:         m--;
    285:       }
    286:       if (M > N && m < n) {PetscInt _m = m; m = n; n = _m;}
    287:     }
    288:     if (m*n != size) SETERRQ(comm,PETSC_ERR_PLIB,"Unable to create partition, check the size of the communicator and input m and n ");
    289:   } else if (m*n != size) SETERRQ(comm,PETSC_ERR_ARG_OUTOFRANGE,"Given Bad partition");

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

    294:   /*
    295:      Determine locally owned region
    296:      xs is the first local node number, x is the number of local nodes
    297:   */
    298:   if (!lx) {
    299:     PetscMalloc1(m, &dd->lx);
    300:     lx   = dd->lx;
    301:     for (i=0; i<m; i++) {
    302:       lx[i] = M/m + ((M % m) > i);
    303:     }
    304:   }
    305:   x  = lx[rank % m];
    306:   xs = 0;
    307:   for (i=0; i<(rank % m); i++) {
    308:     xs += lx[i];
    309:   }
    310: #if defined(PETSC_USE_DEBUG)
    311:   left = xs;
    312:   for (i=(rank % m); i<m; i++) {
    313:     left += lx[i];
    314:   }
    315:   if (left != M) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of lx across processors not equal to M: %D %D",left,M);
    316: #endif

    318:   /*
    319:      Determine locally owned region
    320:      ys is the first local node number, y is the number of local nodes
    321:   */
    322:   if (!ly) {
    323:     PetscMalloc1(n, &dd->ly);
    324:     ly   = dd->ly;
    325:     for (i=0; i<n; i++) {
    326:       ly[i] = N/n + ((N % n) > i);
    327:     }
    328:   }
    329:   y  = ly[rank/m];
    330:   ys = 0;
    331:   for (i=0; i<(rank/m); i++) {
    332:     ys += ly[i];
    333:   }
    334: #if defined(PETSC_USE_DEBUG)
    335:   left = ys;
    336:   for (i=(rank/m); i<n; i++) {
    337:     left += ly[i];
    338:   }
    339:   if (left != N) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_ARG_OUTOFRANGE,"Sum of ly across processors not equal to N: %D %D",left,N);
    340: #endif

    342:   /*
    343:    check if the scatter requires more than one process neighbor or wraps around
    344:    the domain more than once
    345:   */
    346:   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);
    347:   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);
    348:   xe = xs + x;
    349:   ye = ys + y;

    351:   /* determine ghost region (Xs) and region scattered into (IXs)  */
    352:   if (xs-s > 0) {
    353:     Xs = xs - s; IXs = xs - s;
    354:   } else {
    355:     if (bx) {
    356:       Xs = xs - s;
    357:     } else {
    358:       Xs = 0;
    359:     }
    360:     IXs = 0;
    361:   }
    362:   if (xe+s <= M) {
    363:     Xe = xe + s; IXe = xe + s;
    364:   } else {
    365:     if (bx) {
    366:       Xs = xs - s; Xe = xe + s;
    367:     } else {
    368:       Xe = M;
    369:     }
    370:     IXe = M;
    371:   }

    373:   if (bx == DM_BOUNDARY_PERIODIC || bx == DM_BOUNDARY_MIRROR) {
    374:     IXs = xs - s;
    375:     IXe = xe + s;
    376:     Xs  = xs - s;
    377:     Xe  = xe + s;
    378:   }

    380:   if (ys-s > 0) {
    381:     Ys = ys - s; IYs = ys - s;
    382:   } else {
    383:     if (by) {
    384:       Ys = ys - s;
    385:     } else {
    386:       Ys = 0;
    387:     }
    388:     IYs = 0;
    389:   }
    390:   if (ye+s <= N) {
    391:     Ye = ye + s; IYe = ye + s;
    392:   } else {
    393:     if (by) {
    394:       Ye = ye + s;
    395:     } else {
    396:       Ye = N;
    397:     }
    398:     IYe = N;
    399:   }

    401:   if (by == DM_BOUNDARY_PERIODIC || by == DM_BOUNDARY_MIRROR) {
    402:     IYs = ys - s;
    403:     IYe = ye + s;
    404:     Ys  = ys - s;
    405:     Ye  = ye + s;
    406:   }

    408:   /* stencil length in each direction */
    409:   s_x = s;
    410:   s_y = s;

    412:   /* determine starting point of each processor */
    413:   nn       = x*y;
    414:   PetscMalloc2(size+1,&bases,size,&ldims);
    415:   MPI_Allgather(&nn,1,MPIU_INT,ldims,1,MPIU_INT,comm);
    416:   bases[0] = 0;
    417:   for (i=1; i<=size; i++) {
    418:     bases[i] = ldims[i-1];
    419:   }
    420:   for (i=1; i<=size; i++) {
    421:     bases[i] += bases[i-1];
    422:   }
    423:   base = bases[rank]*dof;

    425:   /* allocate the base parallel and sequential vectors */
    426:   dd->Nlocal = x*y*dof;
    427:   VecCreateMPIWithArray(comm,dof,dd->Nlocal,PETSC_DECIDE,NULL,&global);
    428:   dd->nlocal = (Xe-Xs)*(Ye-Ys)*dof;
    429:   VecCreateSeqWithArray(PETSC_COMM_SELF,dof,dd->nlocal,NULL,&local);

    431:   /* generate appropriate vector scatters */
    432:   /* local to global inserts non-ghost point region into global */
    433:   PetscMalloc1((IXe-IXs)*(IYe-IYs),&idx);
    434:   left  = xs - Xs; right = left + x;
    435:   down  = ys - Ys; up = down + y;
    436:   count = 0;
    437:   for (i=down; i<up; i++) {
    438:     for (j=left; j<right; j++) {
    439:       idx[count++] = i*(Xe-Xs) + j;
    440:     }
    441:   }

    443:   /* global to local must include ghost points within the domain,
    444:      but not ghost points outside the domain that aren't periodic */
    445:   if (stencil_type == DMDA_STENCIL_BOX) {
    446:     left  = IXs - Xs; right = left + (IXe-IXs);
    447:     down  = IYs - Ys; up = down + (IYe-IYs);
    448:     count = 0;
    449:     for (i=down; i<up; i++) {
    450:       for (j=left; j<right; j++) {
    451:         idx[count++] = j + i*(Xe-Xs);
    452:       }
    453:     }
    454:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);

    456:   } else {
    457:     /* must drop into cross shape region */
    458:     /*       ---------|
    459:             |  top    |
    460:          |---         ---| up
    461:          |   middle      |
    462:          |               |
    463:          ----         ---- down
    464:             | bottom  |
    465:             -----------
    466:          Xs xs        xe Xe */
    467:     left  = xs - Xs; right = left + x;
    468:     down  = ys - Ys; up = down + y;
    469:     count = 0;
    470:     /* bottom */
    471:     for (i=(IYs-Ys); i<down; i++) {
    472:       for (j=left; j<right; j++) {
    473:         idx[count++] = j + i*(Xe-Xs);
    474:       }
    475:     }
    476:     /* middle */
    477:     for (i=down; i<up; i++) {
    478:       for (j=(IXs-Xs); j<(IXe-Xs); j++) {
    479:         idx[count++] = j + i*(Xe-Xs);
    480:       }
    481:     }
    482:     /* top */
    483:     for (i=up; i<up+IYe-ye; i++) {
    484:       for (j=left; j<right; j++) {
    485:         idx[count++] = j + i*(Xe-Xs);
    486:       }
    487:     }
    488:     ISCreateBlock(comm,dof,count,idx,PETSC_OWN_POINTER,&to);
    489:   }

    492:   /* determine who lies on each side of us stored in    n6 n7 n8
    493:                                                         n3    n5
    494:                                                         n0 n1 n2
    495:   */

    497:   /* Assume the Non-Periodic Case */
    498:   n1 = rank - m;
    499:   if (rank % m) {
    500:     n0 = n1 - 1;
    501:   } else {
    502:     n0 = -1;
    503:   }
    504:   if ((rank+1) % m) {
    505:     n2 = n1 + 1;
    506:     n5 = rank + 1;
    507:     n8 = rank + m + 1; if (n8 >= m*n) n8 = -1;
    508:   } else {
    509:     n2 = -1; n5 = -1; n8 = -1;
    510:   }
    511:   if (rank % m) {
    512:     n3 = rank - 1;
    513:     n6 = n3 + m; if (n6 >= m*n) n6 = -1;
    514:   } else {
    515:     n3 = -1; n6 = -1;
    516:   }
    517:   n7 = rank + m; if (n7 >= m*n) n7 = -1;

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

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

    535:     /* Handle Left and Right Sides */
    536:     if (n3 < 0) n3 = rank + (m-1);
    537:     if (n5 < 0) n5 = rank - (m-1);
    538:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    539:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    540:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    541:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    542:   } else if (by == DM_BOUNDARY_PERIODIC) {  /* Handle Top and Bottom Sides */
    543:     if (n1 < 0) n1 = rank + m * (n-1);
    544:     if (n7 < 0) n7 = rank - m * (n-1);
    545:     if ((n3 >= 0) && (n0 < 0)) n0 = size - m + rank - 1;
    546:     if ((n3 >= 0) && (n6 < 0)) n6 = (rank%m)-1;
    547:     if ((n5 >= 0) && (n2 < 0)) n2 = size - m + rank + 1;
    548:     if ((n5 >= 0) && (n8 < 0)) n8 = (rank%m)+1;
    549:   } else if (bx == DM_BOUNDARY_PERIODIC) { /* Handle Left and Right Sides */
    550:     if (n3 < 0) n3 = rank + (m-1);
    551:     if (n5 < 0) n5 = rank - (m-1);
    552:     if ((n1 >= 0) && (n0 < 0)) n0 = rank-1;
    553:     if ((n1 >= 0) && (n2 < 0)) n2 = rank-2*m+1;
    554:     if ((n7 >= 0) && (n6 < 0)) n6 = rank+2*m-1;
    555:     if ((n7 >= 0) && (n8 < 0)) n8 = rank+1;
    556:   }

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

    560:   dd->neighbors[0] = n0;
    561:   dd->neighbors[1] = n1;
    562:   dd->neighbors[2] = n2;
    563:   dd->neighbors[3] = n3;
    564:   dd->neighbors[4] = rank;
    565:   dd->neighbors[5] = n5;
    566:   dd->neighbors[6] = n6;
    567:   dd->neighbors[7] = n7;
    568:   dd->neighbors[8] = n8;

    570:   if (stencil_type == DMDA_STENCIL_STAR) {
    571:     /* save corner processor numbers */
    572:     sn0 = n0; sn2 = n2; sn6 = n6; sn8 = n8;
    573:     n0  = n2 = n6 = n8 = -1;
    574:   }

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

    578:   nn = 0;
    579:   xbase = bases[rank];
    580:   for (i=1; i<=s_y; i++) {
    581:     if (n0 >= 0) { /* left below */
    582:       x_t = lx[n0 % m];
    583:       y_t = ly[(n0/m)];
    584:       s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    585:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    586:     }

    588:     if (n1 >= 0) { /* directly below */
    589:       x_t = x;
    590:       y_t = ly[(n1/m)];
    591:       s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    592:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    593:     } else if (by == DM_BOUNDARY_MIRROR) {
    594:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    595:     }

    597:     if (n2 >= 0) { /* right below */
    598:       x_t = lx[n2 % m];
    599:       y_t = ly[(n2/m)];
    600:       s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    601:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    602:     }
    603:   }

    605:   for (i=0; i<y; i++) {
    606:     if (n3 >= 0) { /* directly left */
    607:       x_t = lx[n3 % m];
    608:       /* y_t = y; */
    609:       s_t = bases[n3] + (i+1)*x_t - s_x;
    610:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    611:     } else if (bx == DM_BOUNDARY_MIRROR) {
    612:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    613:     }

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

    617:     if (n5 >= 0) { /* directly right */
    618:       x_t = lx[n5 % m];
    619:       /* y_t = y; */
    620:       s_t = bases[n5] + (i)*x_t;
    621:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    622:     } else if (bx == DM_BOUNDARY_MIRROR) {
    623:       for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    624:     }
    625:   }

    627:   for (i=1; i<=s_y; i++) {
    628:     if (n6 >= 0) { /* left above */
    629:       x_t = lx[n6 % m];
    630:       /* y_t = ly[(n6/m)]; */
    631:       s_t = bases[n6] + (i)*x_t - s_x;
    632:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    633:     }

    635:     if (n7 >= 0) { /* directly above */
    636:       x_t = x;
    637:       /* y_t = ly[(n7/m)]; */
    638:       s_t = bases[n7] + (i-1)*x_t;
    639:       for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    640:     } else if (by == DM_BOUNDARY_MIRROR) {
    641:       for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    642:     }

    644:     if (n8 >= 0) { /* right above */
    645:       x_t = lx[n8 % m];
    646:       /* y_t = ly[(n8/m)]; */
    647:       s_t = bases[n8] + (i-1)*x_t;
    648:       for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    649:     }
    650:   }

    652:   ISCreateBlock(comm,dof,nn,idx,PETSC_USE_POINTER,&from);
    653:   VecScatterCreate(global,from,local,to,&gtol);
    654:   PetscLogObjectParent((PetscObject)da,(PetscObject)gtol);
    655:   ISDestroy(&to);
    656:   ISDestroy(&from);

    658:   if (stencil_type == DMDA_STENCIL_STAR) {
    659:     n0 = sn0; n2 = sn2; n6 = sn6; n8 = sn8;
    660:   }

    662:   if (((stencil_type == DMDA_STENCIL_STAR)  ||
    663:        (bx && bx != DM_BOUNDARY_PERIODIC) ||
    664:        (by && by != DM_BOUNDARY_PERIODIC))) {
    665:     /*
    666:         Recompute the local to global mappings, this time keeping the
    667:       information about the cross corner processor numbers and any ghosted
    668:       but not periodic indices.
    669:     */
    670:     nn    = 0;
    671:     xbase = bases[rank];
    672:     for (i=1; i<=s_y; i++) {
    673:       if (n0 >= 0) { /* left below */
    674:         x_t = lx[n0 % m];
    675:         y_t = ly[(n0/m)];
    676:         s_t = bases[n0] + x_t*y_t - (s_y-i)*x_t - s_x;
    677:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    678:       } else if (xs-Xs > 0 && ys-Ys > 0) {
    679:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    680:       }
    681:       if (n1 >= 0) { /* directly below */
    682:         x_t = x;
    683:         y_t = ly[(n1/m)];
    684:         s_t = bases[n1] + x_t*y_t - (s_y+1-i)*x_t;
    685:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    686:       } else if (ys-Ys > 0) {
    687:         if (by == DM_BOUNDARY_MIRROR) {
    688:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(s_y - i + 1)  + j;
    689:         } else {
    690:           for (j=0; j<x; j++) idx[nn++] = -1;
    691:         }
    692:       }
    693:       if (n2 >= 0) { /* right below */
    694:         x_t = lx[n2 % m];
    695:         y_t = ly[(n2/m)];
    696:         s_t = bases[n2] + x_t*y_t - (s_y+1-i)*x_t;
    697:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    698:       } else if (Xe-xe> 0 && ys-Ys > 0) {
    699:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    700:       }
    701:     }

    703:     for (i=0; i<y; i++) {
    704:       if (n3 >= 0) { /* directly left */
    705:         x_t = lx[n3 % m];
    706:         /* y_t = y; */
    707:         s_t = bases[n3] + (i+1)*x_t - s_x;
    708:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    709:       } else if (xs-Xs > 0) {
    710:         if (bx == DM_BOUNDARY_MIRROR) {
    711:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*i + s_x - j;
    712:         } else {
    713:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    714:         }
    715:       }

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

    719:       if (n5 >= 0) { /* directly right */
    720:         x_t = lx[n5 % m];
    721:         /* y_t = y; */
    722:         s_t = bases[n5] + (i)*x_t;
    723:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    724:       } else if (Xe-xe > 0) {
    725:         if (bx == DM_BOUNDARY_MIRROR) {
    726:           for (j=0; j<s_x; j++) idx[nn++] = bases[rank] + x*(i + 1) - 2 - j;
    727:         } else {
    728:           for (j=0; j<s_x; j++) idx[nn++] = -1;
    729:         }
    730:       }
    731:     }

    733:     for (i=1; i<=s_y; i++) {
    734:       if (n6 >= 0) { /* left above */
    735:         x_t = lx[n6 % m];
    736:         /* y_t = ly[(n6/m)]; */
    737:         s_t = bases[n6] + (i)*x_t - s_x;
    738:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    739:       } else if (xs-Xs > 0 && Ye-ye > 0) {
    740:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    741:       }
    742:       if (n7 >= 0) { /* directly above */
    743:         x_t = x;
    744:         /* y_t = ly[(n7/m)]; */
    745:         s_t = bases[n7] + (i-1)*x_t;
    746:         for (j=0; j<x_t; j++) idx[nn++] = s_t++;
    747:       } else if (Ye-ye > 0) {
    748:         if (by == DM_BOUNDARY_MIRROR) {
    749:           for (j=0; j<x; j++) idx[nn++] = bases[rank] + x*(y - i - 1)  + j;
    750:         } else {
    751:           for (j=0; j<x; j++) idx[nn++] = -1;
    752:         }
    753:       }
    754:       if (n8 >= 0) { /* right above */
    755:         x_t = lx[n8 % m];
    756:         /* y_t = ly[(n8/m)]; */
    757:         s_t = bases[n8] + (i-1)*x_t;
    758:         for (j=0; j<s_x; j++) idx[nn++] = s_t++;
    759:       } else if (Xe-xe > 0 && Ye-ye > 0) {
    760:         for (j=0; j<s_x; j++) idx[nn++] = -1;
    761:       }
    762:     }
    763:   }
    764:   /*
    765:      Set the local to global ordering in the global vector, this allows use
    766:      of VecSetValuesLocal().
    767:   */
    768:   ISLocalToGlobalMappingCreate(comm,dof,nn,idx,PETSC_OWN_POINTER,&da->ltogmap);
    769:   PetscLogObjectParent((PetscObject)da,(PetscObject)da->ltogmap);

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

    777:   VecDestroy(&local);
    778:   VecDestroy(&global);

    780:   dd->gtol      = gtol;
    781:   dd->base      = base;
    782:   da->ops->view = DMView_DA_2d;
    783:   dd->ltol      = NULL;
    784:   dd->ao        = NULL;
    785:   return(0);
    786: }

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

    794:    Collective on MPI_Comm

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

    813:    Output Parameter:
    814: .  da - the resulting distributed array object

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

    827:    Level: beginner

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

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

    838: .keywords: distributed array, create, two-dimensional

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

    844: @*/

    846: PetscErrorCode  DMDACreate2d(MPI_Comm comm,DMBoundaryType bx,DMBoundaryType by,DMDAStencilType stencil_type,
    847:                           PetscInt M,PetscInt N,PetscInt m,PetscInt n,PetscInt dof,PetscInt s,const PetscInt lx[],const PetscInt ly[],DM *da)
    848: {

    852:   DMDACreate(comm, da);
    853:   DMSetDimension(*da, 2);
    854:   DMDASetSizes(*da, M, N, 1);
    855:   DMDASetNumProcs(*da, m, n, PETSC_DECIDE);
    856:   DMDASetBoundaryType(*da, bx, by, DM_BOUNDARY_NONE);
    857:   DMDASetDof(*da, dof);
    858:   DMDASetStencilType(*da, stencil_type);
    859:   DMDASetStencilWidth(*da, s);
    860:   DMDASetOwnershipRanges(*da, lx, ly, NULL);
    861:   /* This violates the behavior for other classes, but right now users expect negative dimensions to be handled this way */
    862:   DMSetFromOptions(*da);
    863:   DMSetUp(*da);
    864:   return(0);
    865: }