xref: /petsc/src/ksp/pc/impls/gamg/geo.c (revision 71959b99bcd666003eb379f9f9f233414e2b9990)

/*
 GAMG geometric-algebric multiogrid PC - Mark Adams 2011
 */

#include <../src/ksp/pc/impls/gamg/gamg.h>        /*I "petscpc.h" I*/
#include <petsc-private/kspimpl.h>

#if defined(PETSC_HAVE_TRIANGLE)
#define REAL PetscReal
#include <triangle.h>
#endif

#include <petscblaslapack.h>

/* Private context for the GAMG preconditioner */
typedef struct {
  PetscInt lid;            /* local vertex index */
  PetscInt degree;         /* vertex degree */
} GAMGNode;

int petsc_geo_mg_compare(const void *a, const void *b)
{
  return (((GAMGNode*)a)->degree - ((GAMGNode*)b)->degree);
}

/* -------------------------------------------------------------------------- */
/*
   PCSetCoordinates_GEO

   Input Parameter:
   .  pc - the preconditioner context
*/
EXTERN_C_BEGIN
#undef __FUNCT__
#define __FUNCT__ "PCSetCoordinates_GEO"
PetscErrorCode PCSetCoordinates_GEO(PC pc, PetscInt ndm, PetscInt a_nloc, PetscReal *coords)
{
  PC_MG          *mg      = (PC_MG*)pc->data;
  PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
  PetscErrorCode ierr;
  PetscInt       arrsz,bs,my0,kk,ii,nloc,Iend;
  Mat            Amat = pc->pmat;

  PetscFunctionBegin;
  PetscValidHeaderSpecific(Amat, MAT_CLASSID, 1);
  ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);

  ierr = MatGetOwnershipRange(Amat, &my0, &Iend);CHKERRQ(ierr);
  nloc = (Iend-my0)/bs;

  if (nloc!=a_nloc) SETERRQ2(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Stokes not supported nloc = %d %d.",a_nloc,nloc);
  if ((Iend-my0)%bs!=0) SETERRQ1(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Bad local size %d.",nloc);

  pc_gamg->data_cell_rows = 1;
  if (coords==0 && nloc > 0) SETERRQ(((PetscObject)Amat)->comm,PETSC_ERR_ARG_WRONG, "Need coordinates for pc_gamg_type 'geo'.");
  pc_gamg->data_cell_cols = ndm; /* coordinates */

  arrsz = nloc*pc_gamg->data_cell_rows*pc_gamg->data_cell_cols;

  /* create data - syntactic sugar that should be refactored at some point */
  if (pc_gamg->data==0 || (pc_gamg->data_sz != arrsz)) {
    ierr = PetscFree(pc_gamg->data);CHKERRQ(ierr);
    ierr = PetscMalloc((arrsz+1)*sizeof(PetscReal), &pc_gamg->data);CHKERRQ(ierr);
  }
  for (kk=0; kk<arrsz; kk++) pc_gamg->data[kk] = -999.;
  pc_gamg->data[arrsz] = -99.;
  /* copy data in - column oriented */
  for (kk = 0; kk < nloc; kk++) {
    for (ii = 0; ii < ndm; ii++) {
      pc_gamg->data[ii*nloc + kk] =  coords[kk*ndm + ii];
    }
  }
  if (pc_gamg->data[arrsz] != -99.) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"pc_gamg->data[arrsz %D] %g != -99.",arrsz,pc_gamg->data[arrsz]);
  pc_gamg->data_sz = arrsz;
  PetscFunctionReturn(0);
}
EXTERN_C_END

/* -------------------------------------------------------------------------- */
/*
   PCSetData_GEO

  Input Parameter:
   . pc -
*/
#undef __FUNCT__
#define __FUNCT__ "PCSetData_GEO"
PetscErrorCode PCSetData_GEO(PC pc, Mat m)
{
  PetscFunctionBegin;
  SETERRQ(((PetscObject)pc)->comm,PETSC_ERR_PLIB,"GEO MG needs coordinates");
}

/* -------------------------------------------------------------------------- */
/*
   PCSetFromOptions_GEO

  Input Parameter:
   . pc -
*/
#undef __FUNCT__
#define __FUNCT__ "PCSetFromOptions_GEO"
PetscErrorCode PCSetFromOptions_GEO(PC pc)
{
  PetscErrorCode ierr;
  PC_MG          *mg      = (PC_MG*)pc->data;
  PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;

  PetscFunctionBegin;
  ierr = PetscOptionsHead("GAMG-GEO options");CHKERRQ(ierr);
  {
    /* -pc_gamg_sa_nsmooths */
    /* pc_gamg_sa->smooths = 0; */
    /* ierr = PetscOptionsInt("-pc_gamg_agg_nsmooths", */
    /*                        "smoothing steps for smoothed aggregation, usually 1 (0)", */
    /*                        "PCGAMGSetNSmooths_AGG", */
    /*                        pc_gamg_sa->smooths, */
    /*                        &pc_gamg_sa->smooths, */
    /*                        &flag);  */
    /* CHKERRQ(ierr); */
  }
  ierr = PetscOptionsTail();CHKERRQ(ierr);

  /* call base class */
  ierr = PCSetFromOptions_GAMG(pc);CHKERRQ(ierr);

  if (pc_gamg->verbose) {
    MPI_Comm wcomm = ((PetscObject)pc)->comm;
    PetscPrintf(wcomm,"[%d]%s done\n",0,__FUNCT__);
  }
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
 triangulateAndFormProl

   Input Parameter:
   . selected_2 - list of selected local ID, includes selected ghosts
   . data_stride -
   . coords[2*data_stride] - column vector of local coordinates w/ ghosts
   . nselected_1 - selected IDs that go with base (1) graph
   . clid_lid_1[nselected_1] - lids of selected (c) nodes   ???????????
   . agg_lists_1 - list of aggregates
   . crsGID[selected.size()] - global index for prolongation operator
   . bs - block size
  Output Parameter:
   . a_Prol - prolongation operator
   . a_worst_best - measure of worst missed fine vertex, 0 is no misses
*/
#undef __FUNCT__
#define __FUNCT__ "triangulateAndFormProl"
static PetscErrorCode triangulateAndFormProl(IS  selected_2, /* list of selected local ID, includes selected ghosts */
                                             const PetscInt data_stride,
                                             const PetscReal coords[], /* column vector of local coordinates w/ ghosts */
                                             const PetscInt nselected_1, /* list of selected local ID, includes selected ghosts */
                                             const PetscInt clid_lid_1[],
                                             const PetscCoarsenData *agg_lists_1, /* selected_1 vertices of aggregate unselected vertices */
                                             const PetscInt crsGID[],
                                             const PetscInt bs,
                                             Mat a_Prol, /* prolongation operator (output) */
                                             PetscReal *a_worst_best) /* measure of worst missed fine vertex, 0 is no misses */
{
#if defined(PETSC_HAVE_TRIANGLE)
  PetscErrorCode       ierr;
  PetscInt             jj,tid,tt,idx,nselected_2;
  struct triangulateio in,mid;
  const PetscInt       *selected_idx_2;
  PetscMPIInt          rank,size;
  PetscInt             Istart,Iend,nFineLoc,myFine0;
  int                  kk,nPlotPts,sid;
  MPI_Comm             wcomm = ((PetscObject)a_Prol)->comm;
  PetscReal            tm;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
  ierr = ISGetSize(selected_2, &nselected_2);CHKERRQ(ierr);
  if (nselected_2 == 1 || nselected_2 == 2) { /* 0 happens on idle processors */
    *a_worst_best = 100.0; /* this will cause a stop, but not globalized (should not happen) */
  } else *a_worst_best = 0.0;
  ierr = MPI_Allreduce(a_worst_best, &tm, 1, MPIU_REAL, MPIU_MAX, wcomm);CHKERRQ(ierr);
  if (tm > 0.0) {
    *a_worst_best = 100.0;
    PetscFunctionReturn(0);
  }
  ierr     = MatGetOwnershipRange(a_Prol, &Istart, &Iend);CHKERRQ(ierr);
  nFineLoc = (Iend-Istart)/bs; myFine0 = Istart/bs;
  nPlotPts = nFineLoc; /* locals */
  /* traingle */
  /* Define input points - in*/
  in.numberofpoints          = nselected_2;
  in.numberofpointattributes = 0;
  /* get nselected points */
  ierr = PetscMalloc(2*(nselected_2)*sizeof(REAL), &in.pointlist);CHKERRQ(ierr);
  ierr = ISGetIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);

  for (kk=0,sid=0; kk<nselected_2; kk++,sid += 2) {
    PetscInt lid = selected_idx_2[kk];
    in.pointlist[sid]   = coords[lid];
    in.pointlist[sid+1] = coords[data_stride + lid];
    if (lid>=nFineLoc) nPlotPts++;
  }
  if (sid != 2*nselected_2) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != 2*nselected_2 %D",sid,nselected_2);

  in.numberofsegments      = 0;
  in.numberofedges         = 0;
  in.numberofholes         = 0;
  in.numberofregions       = 0;
  in.trianglelist          = 0;
  in.segmentmarkerlist     = 0;
  in.pointattributelist    = 0;
  in.pointmarkerlist       = 0;
  in.triangleattributelist = 0;
  in.trianglearealist      = 0;
  in.segmentlist           = 0;
  in.holelist              = 0;
  in.regionlist            = 0;
  in.edgelist              = 0;
  in.edgemarkerlist        = 0;
  in.normlist              = 0;

  /* triangulate */
  mid.pointlist = 0;            /* Not needed if -N switch used. */
  /* Not needed if -N switch used or number of point attributes is zero: */
  mid.pointattributelist = 0;
  mid.pointmarkerlist    = 0; /* Not needed if -N or -B switch used. */
  mid.trianglelist       = 0;    /* Not needed if -E switch used. */
  /* Not needed if -E switch used or number of triangle attributes is zero: */
  mid.triangleattributelist = 0;
  mid.neighborlist          = 0; /* Needed only if -n switch used. */
  /* Needed only if segments are output (-p or -c) and -P not used: */
  mid.segmentlist = 0;
  /* Needed only if segments are output (-p or -c) and -P and -B not used: */
  mid.segmentmarkerlist = 0;
  mid.edgelist          = 0;    /* Needed only if -e switch used. */
  mid.edgemarkerlist    = 0; /* Needed if -e used and -B not used. */
  mid.numberoftriangles = 0;

  /* Triangulate the points.  Switches are chosen to read and write a  */
  /*   PSLG (p), preserve the convex hull (c), number everything from  */
  /*   zero (z), assign a regional attribute to each element (A), and  */
  /*   produce an edge list (e), a Voronoi diagram (v), and a triangle */
  /*   neighbor list (n).                                            */
  if (nselected_2 != 0) { /* inactive processor */
    char args[] = "npczQ"; /* c is needed ? */
    triangulate(args, &in, &mid, (struct triangulateio*) NULL);
    /* output .poly files for 'showme' */
    if (!PETSC_TRUE) {
      static int level = 1;
      FILE       *file; char fname[32];

      sprintf(fname,"C%d_%d.poly",level,rank); file = fopen(fname, "w");
      /*First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)>*/
      fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0);
      /*Following lines: <vertex #> <x> <y> */
      for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid += 2) {
        fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
      }
      /*One line: <# of segments> <# of boundary markers (0 or 1)> */
      fprintf(file, "%d  %d\n",0,0);
      /*Following lines: <segment #> <endpoint> <endpoint> [boundary marker] */
      /* One line: <# of holes> */
      fprintf(file, "%d\n",0);
      /* Following lines: <hole #> <x> <y> */
      /* Optional line: <# of regional attributes and/or area constraints> */
      /* Optional following lines: <region #> <x> <y> <attribute> <maximum area> */
      fclose(file);

      /* elems */
      sprintf(fname,"C%d_%d.ele",level,rank); file = fopen(fname, "w");
      /* First line: <# of triangles> <nodes per triangle> <# of attributes> */
      fprintf(file, "%d %d %d\n",mid.numberoftriangles,3,0);
      /* Remaining lines: <triangle #> <node> <node> <node> ... [attributes] */
      for (kk=0,sid=0; kk<mid.numberoftriangles; kk++,sid += 3) {
        fprintf(file, "%d %d %d %d\n",kk,mid.trianglelist[sid],mid.trianglelist[sid+1],mid.trianglelist[sid+2]);
      }
      fclose(file);

      sprintf(fname,"C%d_%d.node",level,rank); file = fopen(fname, "w");
      /* First line: <# of vertices> <dimension (must be 2)> <# of attributes> <# of boundary markers (0 or 1)> */
      /* fprintf(file, "%d  %d  %d  %d\n",in.numberofpoints,2,0,0); */
      fprintf(file, "%d  %d  %d  %d\n",nPlotPts,2,0,0);
      /*Following lines: <vertex #> <x> <y> */
      for (kk=0,sid=0; kk<in.numberofpoints; kk++,sid+=2) {
        fprintf(file, "%d %e %e\n",kk,in.pointlist[sid],in.pointlist[sid+1]);
      }

      sid /= 2;
      for (jj=0; jj<nFineLoc; jj++) {
        PetscBool sel = PETSC_TRUE;
        for (kk=0; kk<nselected_2 && sel; kk++) {
          PetscInt lid = selected_idx_2[kk];
          if (lid == jj) sel = PETSC_FALSE;
        }
        if (sel) fprintf(file, "%d %e %e\n",sid++,coords[jj],coords[data_stride + jj]);
      }
      fclose(file);
      if (sid != nPlotPts) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"sid %D != nPlotPts %D",sid,nPlotPts);
      level++;
    }
  }
#if defined PETSC_GAMG_USE_LOG
  ierr = PetscLogEventBegin(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
#endif
  { /* form P - setup some maps */
    PetscInt clid,mm,*nTri,*node_tri;

    ierr = PetscMalloc(nselected_2*sizeof(PetscInt), &node_tri);CHKERRQ(ierr);
    ierr = PetscMalloc(nselected_2*sizeof(PetscInt), &nTri);CHKERRQ(ierr);

    /* need list of triangles on node */
    for (kk=0; kk<nselected_2; kk++) nTri[kk] = 0;
    for (tid=0,kk=0; tid<mid.numberoftriangles; tid++) {
      for (jj=0; jj<3; jj++) {
        PetscInt cid = mid.trianglelist[kk++];
        if (nTri[cid] == 0) node_tri[cid] = tid;
        nTri[cid]++;
      }
    }
#define EPS 1.e-12
    /* find points and set prolongation */
    for (mm = clid = 0; mm < nFineLoc; mm++) {
      PetscBool ise;
      ierr = PetscCDEmptyAt(agg_lists_1,mm,&ise);CHKERRQ(ierr);
      if (!ise) {
        const PetscInt lid = mm;
        /* for (clid_iterator=0;clid_iterator<nselected_1;clid_iterator++) { */
        PetscScalar  AA[3][3];
        PetscBLASInt N=3,NRHS=1,LDA=3,IPIV[3],LDB=3,INFO;
        PetscCDPos   pos;
        ierr = PetscCDGetHeadPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);
        while (pos) {
          PetscInt flid;
          ierr = PetscLLNGetID(pos, &flid);CHKERRQ(ierr);
          ierr = PetscCDGetNextPos(agg_lists_1,lid,&pos);CHKERRQ(ierr);

          if (flid < nFineLoc) {  /* could be a ghost */
            PetscInt       bestTID = -1; PetscReal best_alpha = 1.e10;
            const PetscInt fgid    = flid + myFine0;
            /* compute shape function for gid */
            const PetscReal fcoord[3] = {coords[flid],coords[data_stride+flid],1.0};
            PetscBool       haveit    =PETSC_FALSE; PetscScalar alpha[3]; PetscInt clids[3];

            /* look for it */
            for (tid = node_tri[clid], jj=0;
                 jj < 5 && !haveit && tid != -1;
                 jj++) {
              for (tt=0; tt<3; tt++) {
                PetscInt cid2 = mid.trianglelist[3*tid + tt];
                PetscInt lid2 = selected_idx_2[cid2];
                AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
                clids[tt] = cid2; /* store for interp */
              }

              for (tt=0; tt<3; tt++) alpha[tt] = (PetscScalar)fcoord[tt];

              /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
              PetscStackCall("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
              {
                PetscBool have=PETSC_TRUE;  PetscReal lowest=1.e10;
                for (tt = 0, idx = 0; tt < 3; tt++) {
                  if (PetscRealPart(alpha[tt]) > (1.0+EPS) || PetscRealPart(alpha[tt]) < -EPS) have = PETSC_FALSE;
                  if (PetscRealPart(alpha[tt]) < lowest) {
                    lowest = PetscRealPart(alpha[tt]);
                    idx    = tt;
                  }
                }
                haveit = have;
              }
              tid = mid.neighborlist[3*tid + idx];
            }

            if (!haveit) {
              /* brute force */
              for (tid=0; tid<mid.numberoftriangles && !haveit; tid++) {
                for (tt=0; tt<3; tt++) {
                  PetscInt cid2 = mid.trianglelist[3*tid + tt];
                  PetscInt lid2 = selected_idx_2[cid2];
                  AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
                  clids[tt] = cid2; /* store for interp */
                }
                for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
                /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
                PetscStackCall("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
                {
                  PetscBool have=PETSC_TRUE;  PetscReal worst=0.0, v;
                  for (tt=0; tt<3 && have; tt++) {
                    if (PetscRealPart(alpha[tt]) > 1.0+EPS || PetscRealPart(alpha[tt]) < -EPS) have=PETSC_FALSE;
                    if ((v=PetscAbs(PetscRealPart(alpha[tt])-0.5)) > worst) worst = v;
                  }
                  if (worst < best_alpha) {
                    best_alpha = worst; bestTID = tid;
                  }
                  haveit = have;
                }
              }
            }
            if (!haveit) {
              if (best_alpha > *a_worst_best) *a_worst_best = best_alpha;
              /* use best one */
              for (tt=0; tt<3; tt++) {
                PetscInt cid2 = mid.trianglelist[3*bestTID + tt];
                PetscInt lid2 = selected_idx_2[cid2];
                AA[tt][0] = coords[lid2]; AA[tt][1] = coords[data_stride + lid2]; AA[tt][2] = 1.0;
                clids[tt] = cid2; /* store for interp */
              }
              for (tt=0; tt<3; tt++) alpha[tt] = fcoord[tt];
              /* SUBROUTINE DGESV(N, NRHS, A, LDA, IPIV, B, LDB, INFO) */
              PetscStackCall("LAPACKgesv",LAPACKgesv_(&N, &NRHS, (PetscScalar*)AA, &LDA, IPIV, alpha, &LDB, &INFO));
            }

            /* put in row of P */
            for (idx=0; idx<3; idx++) {
              PetscScalar shp = alpha[idx];
              if (PetscAbs(PetscRealPart(shp)) > 1.e-6) {
                PetscInt cgid = crsGID[clids[idx]];
                PetscInt jj   = cgid*bs, ii = fgid*bs; /* need to gloalize */
                for (tt=0; tt < bs; tt++, ii++, jj++) {
                  ierr = MatSetValues(a_Prol,1,&ii,1,&jj,&shp,INSERT_VALUES);CHKERRQ(ierr);
                }
              }
            }
          }
        } /* aggregates iterations */
        clid++;
      } /* a coarse agg */
    } /* for all fine nodes */

    ierr = ISRestoreIndices(selected_2, &selected_idx_2);CHKERRQ(ierr);
    ierr = MatAssemblyBegin(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);
    ierr = MatAssemblyEnd(a_Prol,MAT_FINAL_ASSEMBLY);CHKERRQ(ierr);

    ierr = PetscFree(node_tri);CHKERRQ(ierr);
    ierr = PetscFree(nTri);CHKERRQ(ierr);
  }
#if defined PETSC_GAMG_USE_LOG
  ierr = PetscLogEventEnd(petsc_gamg_setup_events[FIND_V],0,0,0,0);CHKERRQ(ierr);
#endif
  free(mid.trianglelist);
  free(mid.neighborlist);
  ierr = PetscFree(in.pointlist);CHKERRQ(ierr);
  PetscFunctionReturn(0);
#else
  SETERRQ(((PetscObject)a_Prol)->comm,PETSC_ERR_PLIB,"configure with TRIANGLE to use geometric MG");
#endif
}
/* -------------------------------------------------------------------------- */
/*
   getGIDsOnSquareGraph - square graph, get

   Input Parameter:
   . nselected_1 - selected local indices (includes ghosts in input Gmat1)
   . clid_lid_1 - [nselected_1] lids of selected nodes
   . Gmat1 - graph that goes with 'selected_1'
   Output Parameter:
   . a_selected_2 - selected local indices (includes ghosts in output a_Gmat_2)
   . a_Gmat_2 - graph that is squared of 'Gmat_1'
   . a_crsGID[a_selected_2.size()] - map of global IDs of coarse grid nodes
*/
#undef __FUNCT__
#define __FUNCT__ "getGIDsOnSquareGraph"
static PetscErrorCode getGIDsOnSquareGraph(const PetscInt nselected_1,const PetscInt clid_lid_1[],const Mat Gmat1,IS *a_selected_2,Mat *a_Gmat_2,PetscInt **a_crsGID)
{
  PetscErrorCode ierr;
  PetscMPIInt    rank,size;
  PetscInt       *crsGID, kk,my0,Iend,nloc;
  MPI_Comm       wcomm = ((PetscObject)Gmat1)->comm;

  PetscFunctionBegin;
  ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(Gmat1,&my0,&Iend);CHKERRQ(ierr); /* AIJ */
  nloc = Iend - my0; /* this does not change */

  if (size == 1) { /* not much to do in serial */
    ierr = PetscMalloc(nselected_1*sizeof(PetscInt), &crsGID);CHKERRQ(ierr);
    for (kk=0; kk<nselected_1; kk++) crsGID[kk] = kk;
    *a_Gmat_2 = 0;
    ierr      = ISCreateGeneral(PETSC_COMM_SELF,nselected_1,clid_lid_1,PETSC_COPY_VALUES,a_selected_2);CHKERRQ(ierr);
  } else {
    PetscInt    idx,num_fine_ghosts,num_crs_ghost,myCrs0;
    Mat_MPIAIJ  *mpimat2;
    Mat         Gmat2;
    Vec         locState;
    PetscScalar *cpcol_state;

    /* scan my coarse zero gid, set 'lid_state' with coarse GID */
    kk = nselected_1;
    MPI_Scan(&kk, &myCrs0, 1, MPIU_INT, MPIU_SUM, wcomm);
    myCrs0 -= nselected_1;

    if (a_Gmat_2) { /* output */
      /* grow graph to get wider set of selected vertices to cover fine grid, invalidates 'llist' */
      ierr      = MatTransposeMatMult(Gmat1, Gmat1, MAT_INITIAL_MATRIX, PETSC_DEFAULT, &Gmat2);CHKERRQ(ierr);
      *a_Gmat_2 = Gmat2; /* output */
    } else Gmat2 = Gmat1;  /* use local to get crsGIDs at least */
    /* get coarse grid GIDS for selected (locals and ghosts) */
    mpimat2 = (Mat_MPIAIJ*)Gmat2->data;
    ierr    = MatGetVecs(Gmat2, &locState, 0);CHKERRQ(ierr);
    ierr    = VecSet(locState, (PetscScalar)(PetscReal)(-1));CHKERRQ(ierr); /* set with UNKNOWN state */
    for (kk=0; kk<nselected_1; kk++) {
      PetscInt    fgid = clid_lid_1[kk] + my0;
      PetscScalar v    = (PetscScalar)(kk+myCrs0);
      ierr = VecSetValues(locState, 1, &fgid, &v, INSERT_VALUES);CHKERRQ(ierr); /* set with PID */
    }
    ierr = VecAssemblyBegin(locState);CHKERRQ(ierr);
    ierr = VecAssemblyEnd(locState);CHKERRQ(ierr);
    ierr = VecScatterBegin(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr =   VecScatterEnd(mpimat2->Mvctx,locState,mpimat2->lvec,INSERT_VALUES,SCATTER_FORWARD);CHKERRQ(ierr);
    ierr = VecGetLocalSize(mpimat2->lvec, &num_fine_ghosts);CHKERRQ(ierr);
    ierr = VecGetArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
    for (kk=0,num_crs_ghost=0; kk<num_fine_ghosts; kk++) {
      if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) num_crs_ghost++;
    }
    ierr = PetscMalloc((nselected_1+num_crs_ghost)*sizeof(PetscInt), &crsGID);CHKERRQ(ierr); /* output */
    {
      PetscInt *selected_set;
      ierr = PetscMalloc((nselected_1+num_crs_ghost)*sizeof(PetscInt), &selected_set);CHKERRQ(ierr);
      /* do ghost of 'crsGID' */
      for (kk=0,idx=nselected_1; kk<num_fine_ghosts; kk++) {
        if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
          PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
          selected_set[idx] = nloc + kk;
          crsGID[idx++]     = cgid;
        }
      }
      if (idx != (nselected_1+num_crs_ghost)) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != (nselected_1 %D + num_crs_ghost %D)",idx,nselected_1,num_crs_ghost);
      ierr = VecRestoreArray(mpimat2->lvec, &cpcol_state);CHKERRQ(ierr);
      /* do locals in 'crsGID' */
      ierr = VecGetArray(locState, &cpcol_state);CHKERRQ(ierr);
      for (kk=0,idx=0; kk<nloc; kk++) {
        if ((PetscInt)PetscRealPart(cpcol_state[kk]) != -1) {
          PetscInt cgid = (PetscInt)PetscRealPart(cpcol_state[kk]);
          selected_set[idx] = kk;
          crsGID[idx++]     = cgid;
        }
      }
      if (idx != nselected_1) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"idx %D != nselected_1 %D",idx,nselected_1);
      ierr = VecRestoreArray(locState, &cpcol_state);CHKERRQ(ierr);

      if (a_selected_2 != 0) { /* output */
        ierr = ISCreateGeneral(PETSC_COMM_SELF,(nselected_1+num_crs_ghost),selected_set,PETSC_OWN_POINTER,a_selected_2);CHKERRQ(ierr);
      } else {
        ierr = PetscFree(selected_set);CHKERRQ(ierr);
      }
    }
    ierr = VecDestroy(&locState);CHKERRQ(ierr);
  }
  *a_crsGID = crsGID; /* output */
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
   PCGAMGgraph_GEO

  Input Parameter:
   . pc - this
   . Amat - matrix on this fine level
  Output Parameter:
   . a_Gmat
*/
#undef __FUNCT__
#define __FUNCT__ "PCGAMGgraph_GEO"
PetscErrorCode PCGAMGgraph_GEO(PC pc,const Mat Amat,Mat *a_Gmat)
{
  PetscErrorCode  ierr;
  PC_MG           *mg      = (PC_MG*)pc->data;
  PC_GAMG         *pc_gamg = (PC_GAMG*)mg->innerctx;
  const PetscInt  verbose  = pc_gamg->verbose;
  const PetscReal vfilter  = pc_gamg->threshold;
  PetscMPIInt     rank,size;
  MPI_Comm        wcomm = ((PetscObject)Amat)->comm;
  Mat             Gmat;
  PetscBool       set,flg,symm;

  PetscFunctionBegin;
#if defined PETSC_USE_LOG
  ierr = PetscLogEventBegin(PC_GAMGGgraph_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  ierr = MPI_Comm_rank(wcomm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(wcomm, &size);CHKERRQ(ierr);

  ierr = MatIsSymmetricKnown(Amat, &set, &flg);CHKERRQ(ierr);
  symm = (PetscBool)!(set && flg);

  ierr = PCGAMGCreateGraph(Amat, &Gmat);CHKERRQ(ierr);
  ierr = PCGAMGFilterGraph(&Gmat, vfilter, symm, verbose);CHKERRQ(ierr);

  *a_Gmat = Gmat;
#if defined PETSC_USE_LOG
  ierr = PetscLogEventEnd(PC_GAMGGgraph_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
   PCGAMGcoarsen_GEO

  Input Parameter:
   . a_pc - this
   . a_Gmat - graph
  Output Parameter:
   . a_llist_parent - linked list from selected indices for data locality only
*/
#undef __FUNCT__
#define __FUNCT__ "PCGAMGcoarsen_GEO"
PetscErrorCode PCGAMGcoarsen_GEO(PC a_pc,Mat *a_Gmat,PetscCoarsenData **a_llist_parent)
{
  PetscErrorCode ierr;
  PC_MG          *mg      = (PC_MG*)a_pc->data;
  PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
  PetscInt       Istart,Iend,nloc,kk,Ii,ncols;
  PetscMPIInt    rank,size;
  IS             perm;
  GAMGNode       *gnodes;
  PetscInt       *permute;
  Mat            Gmat  = *a_Gmat;
  MPI_Comm       wcomm = ((PetscObject)Gmat)->comm;
  MatCoarsen     crs;

  PetscFunctionBegin;
#if defined PETSC_USE_LOG
  ierr = PetscLogEventBegin(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  ierr = MPI_Comm_rank(wcomm, &rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(wcomm, &size);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(Gmat, &Istart, &Iend);CHKERRQ(ierr);
  nloc = (Iend-Istart);

  /* create random permutation with sort for geo-mg */
  ierr = PetscMalloc(nloc*sizeof(GAMGNode), &gnodes);CHKERRQ(ierr);
  ierr = PetscMalloc(nloc*sizeof(PetscInt), &permute);CHKERRQ(ierr);

  for (Ii=Istart; Ii<Iend; Ii++) { /* locals only? */
    ierr = MatGetRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
    {
      PetscInt lid = Ii - Istart;
      gnodes[lid].lid    = lid;
      gnodes[lid].degree = ncols;
    }
    ierr = MatRestoreRow(Gmat,Ii,&ncols,0,0);CHKERRQ(ierr);
  }
  /* randomize */
  srand(1); /* make deterministic */
  if (PETSC_TRUE) {
    PetscBool *bIndexSet;
    ierr = PetscMalloc(nloc*sizeof(PetscBool), &bIndexSet);CHKERRQ(ierr);
    for (Ii = 0; Ii < nloc; Ii++) bIndexSet[Ii] = PETSC_FALSE;
    for (Ii = 0; Ii < nloc; Ii++) {
      PetscInt iSwapIndex = rand()%nloc;
      if (!bIndexSet[iSwapIndex] && iSwapIndex != Ii) {
        GAMGNode iTemp = gnodes[iSwapIndex];
        gnodes[iSwapIndex]    = gnodes[Ii];
        gnodes[Ii]            = iTemp;
        bIndexSet[Ii]         = PETSC_TRUE;
        bIndexSet[iSwapIndex] = PETSC_TRUE;
      }
    }
    ierr = PetscFree(bIndexSet);CHKERRQ(ierr);
  }
  /* only sort locals */
  qsort(gnodes, nloc, sizeof(GAMGNode), petsc_geo_mg_compare);
  /* create IS of permutation */
  for (kk=0; kk<nloc; kk++) permute[kk] = gnodes[kk].lid; /* locals only */
  ierr = ISCreateGeneral(PETSC_COMM_SELF, nloc, permute, PETSC_OWN_POINTER, &perm);CHKERRQ(ierr);

  ierr = PetscFree(gnodes);CHKERRQ(ierr);

  /* get MIS aggs */

  ierr = MatCoarsenCreate(wcomm, &crs);CHKERRQ(ierr);
  ierr = MatCoarsenSetType(crs, MATCOARSENMIS);CHKERRQ(ierr);
  ierr = MatCoarsenSetGreedyOrdering(crs, perm);CHKERRQ(ierr);
  ierr = MatCoarsenSetAdjacency(crs, Gmat);CHKERRQ(ierr);
  ierr = MatCoarsenSetVerbose(crs, pc_gamg->verbose);CHKERRQ(ierr);
  ierr = MatCoarsenSetStrictAggs(crs, PETSC_FALSE);CHKERRQ(ierr);
  ierr = MatCoarsenApply(crs);CHKERRQ(ierr);
  ierr = MatCoarsenGetData(crs, a_llist_parent);CHKERRQ(ierr);
  ierr = MatCoarsenDestroy(&crs);CHKERRQ(ierr);

  ierr = ISDestroy(&perm);CHKERRQ(ierr);
#if defined PETSC_USE_LOG
  ierr = PetscLogEventEnd(PC_GAMGCoarsen_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
 PCGAMGProlongator_GEO

 Input Parameter:
 . pc - this
 . Amat - matrix on this fine level
 . Graph - used to get ghost data for nodes in
 . selected_1 - [nselected]
 . agg_lists - [nselected]
 Output Parameter:
 . a_P_out - prolongation operator to the next level
 */
#undef __FUNCT__
#define __FUNCT__ "PCGAMGProlongator_GEO"
PetscErrorCode PCGAMGProlongator_GEO(PC pc,const Mat Amat,const Mat Gmat,PetscCoarsenData *agg_lists,Mat *a_P_out)
{
  PC_MG          *mg      = (PC_MG*)pc->data;
  PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;
  const PetscInt verbose  = pc_gamg->verbose;
  const PetscInt dim      = pc_gamg->data_cell_cols, data_cols = pc_gamg->data_cell_cols;
  PetscErrorCode ierr;
  PetscInt       Istart,Iend,nloc,my0,jj,kk,ncols,nLocalSelected,bs,*clid_flid;
  Mat            Prol;
  PetscMPIInt    rank, size;
  MPI_Comm       wcomm = ((PetscObject)Amat)->comm;
  IS             selected_2,selected_1;
  const PetscInt *selected_idx;

  PetscFunctionBegin;
#if defined PETSC_USE_LOG
  ierr = PetscLogEventBegin(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  ierr = MPI_Comm_rank(wcomm,&rank);CHKERRQ(ierr);
  ierr = MPI_Comm_size(wcomm,&size);CHKERRQ(ierr);
  ierr = MatGetOwnershipRange(Amat, &Istart, &Iend);CHKERRQ(ierr);
  ierr = MatGetBlockSize(Amat, &bs);CHKERRQ(ierr);
  nloc = (Iend-Istart)/bs; my0 = Istart/bs;
  if ((Iend-Istart) % bs) SETERRQ3(PETSC_COMM_SELF,PETSC_ERR_PLIB,"(Iend %D - Istart %D) % bs %D",Iend,Istart,bs);

  /* get 'nLocalSelected' */
  ierr = PetscCDGetMIS(agg_lists, &selected_1);CHKERRQ(ierr);
  ierr = ISGetSize(selected_1, &jj);CHKERRQ(ierr);
  ierr = PetscMalloc(jj*sizeof(PetscInt), &clid_flid);CHKERRQ(ierr);
  ierr = ISGetIndices(selected_1, &selected_idx);CHKERRQ(ierr);
  for (kk=0,nLocalSelected=0; kk<jj; kk++) {
    PetscInt lid = selected_idx[kk];
    if (lid<nloc) {
      ierr = MatGetRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
      if (ncols>1) clid_flid[nLocalSelected++] = lid; /* fiter out singletons */
      ierr = MatRestoreRow(Gmat,lid+my0,&ncols,0,0);CHKERRQ(ierr);
    }
  }
  ierr = ISRestoreIndices(selected_1, &selected_idx);CHKERRQ(ierr);
  ierr = ISDestroy(&selected_1);CHKERRQ(ierr); /* this is selected_1 in serial */

  /* create prolongator, create P matrix */
  ierr = MatCreate(wcomm, &Prol);CHKERRQ(ierr);
  ierr = MatSetSizes(Prol,nloc*bs,nLocalSelected*bs,PETSC_DETERMINE,PETSC_DETERMINE);CHKERRQ(ierr);
  ierr = MatSetBlockSizes(Prol, bs, bs);CHKERRQ(ierr);
  ierr = MatSetType(Prol, MATAIJ);CHKERRQ(ierr);
  ierr = MatSeqAIJSetPreallocation(Prol,3*data_cols,NULL);CHKERRQ(ierr);
  ierr = MatMPIAIJSetPreallocation(Prol,3*data_cols,NULL,3*data_cols,NULL);CHKERRQ(ierr);
  /* ierr = MatCreateAIJ(wcomm,  */
  /*                      nloc*bs, nLocalSelected*bs, */
  /*                      PETSC_DETERMINE, PETSC_DETERMINE, */
  /*                      3*data_cols, NULL,  */
  /*                      3*data_cols, NULL, */
  /*                      &Prol); */
  /* CHKERRQ(ierr); */

  /* can get all points "removed" - but not on geomg */
  ierr =  MatGetSize(Prol, &kk, &jj);CHKERRQ(ierr);
  if (jj==0) {
    if (verbose) PetscPrintf(wcomm,"[%d]%s ERROE: no selected points on coarse grid\n",rank,__FUNCT__);
    ierr = PetscFree(clid_flid);CHKERRQ(ierr);
    ierr = MatDestroy(&Prol);CHKERRQ(ierr);
    *a_P_out = NULL;  /* out */
    PetscFunctionReturn(0);
  }

  {
    PetscReal *coords;
    PetscInt  data_stride;
    PetscInt  *crsGID = NULL;
    Mat       Gmat2;

    if (dim != data_cols) SETERRQ2(PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim %D != data_cols %D",dim,data_cols);
    /* grow ghost data for better coarse grid cover of fine grid */
#if defined PETSC_GAMG_USE_LOG
    ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
#endif
    /* messy method, squares graph and gets some data */
    ierr = getGIDsOnSquareGraph(nLocalSelected, clid_flid, Gmat, &selected_2, &Gmat2, &crsGID);CHKERRQ(ierr);
    /* llist is now not valid wrt squared graph, but will work as iterator in 'triangulateAndFormProl' */
#if defined PETSC_GAMG_USE_LOG
    ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET5],0,0,0,0);CHKERRQ(ierr);
#endif
    /* create global vector of coorindates in 'coords' */
    if (size > 1) {
      ierr = PCGAMGGetDataWithGhosts(Gmat2, dim, pc_gamg->data, &data_stride, &coords);CHKERRQ(ierr);
    } else {
      coords      = (PetscReal*)pc_gamg->data;
      data_stride = pc_gamg->data_sz/pc_gamg->data_cell_cols;
    }
    ierr = MatDestroy(&Gmat2);CHKERRQ(ierr);

    /* triangulate */
    if (dim == 2) {
      PetscReal metric,tm;
#if defined PETSC_GAMG_USE_LOG
      ierr = PetscLogEventBegin(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
#endif
      ierr = triangulateAndFormProl(selected_2, data_stride, coords,nLocalSelected, clid_flid, agg_lists, crsGID, bs, Prol, &metric);CHKERRQ(ierr);
#if defined PETSC_GAMG_USE_LOG
      ierr = PetscLogEventEnd(petsc_gamg_setup_events[SET6],0,0,0,0);CHKERRQ(ierr);
#endif
      ierr = PetscFree(crsGID);CHKERRQ(ierr);

      /* clean up and create coordinates for coarse grid (output) */
      if (size > 1) ierr = PetscFree(coords);CHKERRQ(ierr);

      ierr = MPI_Allreduce(&metric, &tm, 1, MPIU_REAL, MPIU_MAX, wcomm);CHKERRQ(ierr);
      if (tm > 1.) { /* needs to be globalized - should not happen */
        if (verbose) PetscPrintf(wcomm,"[%d]%s failed metric for coarse grid %e\n",rank,__FUNCT__,tm);
        ierr = MatDestroy(&Prol);CHKERRQ(ierr);
        Prol = NULL;
      } else if (metric > .0) {
        if (verbose) PetscPrintf(wcomm,"[%d]%s worst metric for coarse grid = %e\n",rank,__FUNCT__,metric);
      }
    } else SETERRQ(wcomm,PETSC_ERR_PLIB,"3D not implemented for 'geo' AMG");
    { /* create next coords - output */
      PetscReal *crs_crds;
      ierr = PetscMalloc(dim*nLocalSelected*sizeof(PetscReal), &crs_crds);CHKERRQ(ierr);
      for (kk=0; kk<nLocalSelected; kk++) { /* grab local select nodes to promote - output */
        PetscInt lid = clid_flid[kk];
        for (jj=0; jj<dim; jj++) crs_crds[jj*nLocalSelected + kk] = pc_gamg->data[jj*nloc + lid];
      }

      ierr             = PetscFree(pc_gamg->data);CHKERRQ(ierr);
      pc_gamg->data    = crs_crds; /* out */
      pc_gamg->data_sz = dim*nLocalSelected;
    }
    ierr = ISDestroy(&selected_2);CHKERRQ(ierr);
  }

  *a_P_out = Prol;  /* out */
  ierr     = PetscFree(clid_flid);CHKERRQ(ierr);
#if defined PETSC_USE_LOG
  ierr = PetscLogEventEnd(PC_GAMGProlongator_GEO,0,0,0,0);CHKERRQ(ierr);
#endif
  PetscFunctionReturn(0);
}

/* -------------------------------------------------------------------------- */
/*
 PCCreateGAMG_GEO

  Input Parameter:
   . pc -
*/
#undef __FUNCT__
#define __FUNCT__ "PCCreateGAMG_GEO"
PetscErrorCode  PCCreateGAMG_GEO(PC pc)
{
  PetscErrorCode ierr;
  PC_MG          *mg      = (PC_MG*)pc->data;
  PC_GAMG        *pc_gamg = (PC_GAMG*)mg->innerctx;

  PetscFunctionBegin;
  pc->ops->setfromoptions = PCSetFromOptions_GEO;
  /* pc->ops->destroy        = PCDestroy_GEO; */
  /* reset does not do anything; setup not virtual */

  /* set internal function pointers */
  pc_gamg->graph       = PCGAMGgraph_GEO;
  pc_gamg->coarsen     = PCGAMGcoarsen_GEO;
  pc_gamg->prolongator = PCGAMGProlongator_GEO;
  pc_gamg->optprol     = 0;
  pc_gamg->formkktprol = 0;

  pc_gamg->createdefaultdata = PCSetData_GEO;

  ierr = PetscObjectComposeFunctionDynamic((PetscObject)pc,
                                           "PCSetCoordinates_C",
                                           "PCSetCoordinates_GEO",
                                           PCSetCoordinates_GEO);CHKERRQ(ierr);
  PetscFunctionReturn(0);
}