xref: /petsc/src/ksp/pc/impls/tfs/xxt.c (revision 792fecdfe9134cce4d631112660ddd34f063bc17)

/*************************************xxt.c************************************
Module Name: xxt
Module Info:

author:  Henry M. Tufo III
e-mail:  hmt@asci.uchicago.edu
contact:
+--------------------------------+--------------------------------+
|MCS Division - Building 221     |Department of Computer Science  |
|Argonne National Laboratory     |Ryerson 152                     |
|9700 S. Cass Avenue             |The University of Chicago       |
|Argonne, IL  60439              |Chicago, IL  60637              |
|(630) 252-5354/5986 ph/fx       |(773) 702-6019/8487 ph/fx       |
+--------------------------------+--------------------------------+

Last Modification: 3.20.01
**************************************xxt.c***********************************/
#include <../src/ksp/pc/impls/tfs/tfs.h>

#define LEFT  -1
#define RIGHT  1
#define BOTH   0

typedef struct xxt_solver_info {
  PetscInt    n, m, n_global, m_global;
  PetscInt    nnz, max_nnz, msg_buf_sz;
  PetscInt    *nsep, *lnsep, *fo, nfo, *stages;
  PetscInt    *col_sz, *col_indices;
  PetscScalar **col_vals, *x, *solve_uu, *solve_w;
  PetscInt    nsolves;
  PetscScalar tot_solve_time;
} xxt_info;

typedef struct matvec_info {
  PetscInt     n, m, n_global, m_global;
  PetscInt     *local2global;
  PCTFS_gs_ADT PCTFS_gs_handle;
  PetscErrorCode (*matvec)(struct matvec_info*,PetscScalar*,PetscScalar*);
  void *grid_data;
} mv_info;

struct xxt_CDT {
  PetscInt id;
  PetscInt ns;
  PetscInt level;
  xxt_info *info;
  mv_info  *mvi;
};

static PetscInt n_xxt        =0;
static PetscInt n_xxt_handles=0;

/* prototypes */
static PetscErrorCode do_xxt_solve(xxt_ADT xxt_handle, PetscScalar *rhs);
static PetscErrorCode check_handle(xxt_ADT xxt_handle);
static PetscErrorCode det_separators(xxt_ADT xxt_handle);
static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u);
static PetscErrorCode xxt_generate(xxt_ADT xxt_handle);
static PetscErrorCode do_xxt_factor(xxt_ADT xxt_handle);
static mv_info *set_mvi(PetscInt *local2global, PetscInt n, PetscInt m, PetscErrorCode (*matvec)(mv_info*,PetscScalar*,PetscScalar*), void *grid_data);

/**************************************xxt.c***********************************/
xxt_ADT XXT_new(void)
{
  xxt_ADT xxt_handle;

  /* rolling count on n_xxt ... pot. problem here */
  n_xxt_handles++;
  xxt_handle       = (xxt_ADT)malloc(sizeof(struct xxt_CDT));
  xxt_handle->id   = ++n_xxt;
  xxt_handle->info = NULL; xxt_handle->mvi  = NULL;

  return(xxt_handle);
}

/**************************************xxt.c***********************************/
PetscErrorCode XXT_factor(xxt_ADT xxt_handle,     /* prev. allocated xxt  handle */
                    PetscInt *local2global, /* global column mapping       */
                    PetscInt n,             /* local num rows              */
                    PetscInt m,             /* local num cols              */
                    PetscErrorCode (*matvec)(void*,PetscScalar*,PetscScalar*), /* b_loc=A_local.x_loc         */
                    void *grid_data)        /* grid data for matvec        */
{
  PCTFS_comm_init();
  check_handle(xxt_handle);

  /* only 2^k for now and all nodes participating */
  PetscCheck((1<<(xxt_handle->level=PCTFS_i_log2_num_nodes))==PCTFS_num_nodes,PETSC_COMM_SELF,PETSC_ERR_PLIB,"only 2^k for now and MPI_COMM_WORLD!!! %d != %d",1<<PCTFS_i_log2_num_nodes,PCTFS_num_nodes);

  /* space for X info */
  xxt_handle->info = (xxt_info*)malloc(sizeof(xxt_info));

  /* set up matvec handles */
  xxt_handle->mvi = set_mvi(local2global, n, m, (PetscErrorCode (*)(mv_info*,PetscScalar*,PetscScalar*))matvec, grid_data);

  /* matrix is assumed to be of full rank */
  /* LATER we can reset to indicate rank def. */
  xxt_handle->ns=0;

  /* determine separators and generate firing order - NB xxt info set here */
  det_separators(xxt_handle);

  return(do_xxt_factor(xxt_handle));
}

/**************************************xxt.c***********************************/
PetscErrorCode XXT_solve(xxt_ADT xxt_handle, PetscScalar *x, PetscScalar *b)
{

  PCTFS_comm_init();
  check_handle(xxt_handle);

  /* need to copy b into x? */
  if (b) PCTFS_rvec_copy(x,b,xxt_handle->mvi->n);
  return do_xxt_solve(xxt_handle,x);
}

/**************************************xxt.c***********************************/
PetscInt XXT_free(xxt_ADT xxt_handle)
{

  PCTFS_comm_init();
  check_handle(xxt_handle);
  n_xxt_handles--;

  free(xxt_handle->info->nsep);
  free(xxt_handle->info->lnsep);
  free(xxt_handle->info->fo);
  free(xxt_handle->info->stages);
  free(xxt_handle->info->solve_uu);
  free(xxt_handle->info->solve_w);
  free(xxt_handle->info->x);
  free(xxt_handle->info->col_vals);
  free(xxt_handle->info->col_sz);
  free(xxt_handle->info->col_indices);
  free(xxt_handle->info);
  free(xxt_handle->mvi->local2global);
  PCTFS_gs_free(xxt_handle->mvi->PCTFS_gs_handle);
  free(xxt_handle->mvi);
  free(xxt_handle);

  /* if the check fails we nuke */
  /* if NULL pointer passed to free we nuke */
  /* if the calls to free fail that's not my problem */
  return(0);
}

/**************************************xxt.c***********************************/
PetscErrorCode XXT_stats(xxt_ADT xxt_handle)
{
  PetscInt       op[]  = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD};
  PetscInt       fop[] = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD};
  PetscInt       vals[9],  work[9];
  PetscScalar    fvals[3], fwork[3];

  PetscFunctionBegin;
  PetscCall(PCTFS_comm_init());
  PetscCall(check_handle(xxt_handle));

  /* if factorization not done there are no stats */
  if (!xxt_handle->info||!xxt_handle->mvi) {
    if (!PCTFS_my_id) PetscCall(PetscPrintf(PETSC_COMM_WORLD,"XXT_stats() :: no stats available!\n"));
    PetscFunctionReturn(1);
  }

  vals[0]=vals[1]=vals[2]=xxt_handle->info->nnz;
  vals[3]=vals[4]=vals[5]=xxt_handle->mvi->n;
  vals[6]=vals[7]=vals[8]=xxt_handle->info->msg_buf_sz;
  PCTFS_giop(vals,work,PETSC_STATIC_ARRAY_LENGTH(op)-1,op);

  fvals[0]=fvals[1]=fvals[2] =xxt_handle->info->tot_solve_time/xxt_handle->info->nsolves++;
  PCTFS_grop(fvals,fwork,PETSC_STATIC_ARRAY_LENGTH(fop)-1,fop);

  if (!PCTFS_my_id) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[0]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[1]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_nnz=%g\n",PCTFS_my_id,(double)(1.0*vals[2]/PCTFS_num_nodes)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: tot   xxt_nnz=%" PetscInt_FMT "\n",PCTFS_my_id,vals[2]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: xxt   C(2d)  =%g\n",PCTFS_my_id,(double)(vals[2]/(PetscPowReal(1.0*vals[5],1.5)))));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: xxt   C(3d)  =%g\n",PCTFS_my_id,(double)(vals[2]/(PetscPowReal(1.0*vals[5],1.6667)))));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[3]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[4]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_n  =%g\n",PCTFS_my_id,(double)(1.0*vals[5]/PCTFS_num_nodes)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: tot   xxt_n  =%" PetscInt_FMT "\n",PCTFS_my_id,vals[5]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_buf=%" PetscInt_FMT "\n",PCTFS_my_id,vals[6]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_buf=%" PetscInt_FMT "\n",PCTFS_my_id,vals[7]));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_buf=%g\n",PCTFS_my_id,(double)(1.0*vals[8]/PCTFS_num_nodes)));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: min   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[0])));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: max   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[1])));
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"%d :: avg   xxt_slv=%g\n",PCTFS_my_id,(double)PetscRealPart(fvals[2]/PCTFS_num_nodes)));
  }
  PetscFunctionReturn(0);
}

/*************************************xxt.c************************************

Description: get A_local, local portion of global coarse matrix which
is a row dist. nxm matrix w/ n<m.
   o my_ml holds address of ML struct associated w/A_local and coarse grid
   o local2global holds global number of column i (i=0,...,m-1)
   o local2global holds global number of row    i (i=0,...,n-1)
   o mylocmatvec performs A_local . vec_local (note that gs is performed using
   PCTFS_gs_init/gop).

mylocmatvec = my_ml->Amat[grid_tag].matvec->external;
mylocmatvec (void :: void *data, double *in, double *out)
**************************************xxt.c***********************************/
static PetscErrorCode do_xxt_factor(xxt_ADT xxt_handle)
{
  return xxt_generate(xxt_handle);
}

/**************************************xxt.c***********************************/
static PetscErrorCode xxt_generate(xxt_ADT xxt_handle)
{
  PetscInt       i,j,k,idex;
  PetscInt       dim, col;
  PetscScalar    *u, *uu, *v, *z, *w, alpha, alpha_w;
  PetscInt       *segs;
  PetscInt       op[] = {GL_ADD,0};
  PetscInt       off, len;
  PetscScalar    *x_ptr;
  PetscInt       *iptr, flag;
  PetscInt       start =0, end, work;
  PetscInt       op2[] = {GL_MIN,0};
  PCTFS_gs_ADT   PCTFS_gs_handle;
  PetscInt       *nsep, *lnsep, *fo;
  PetscInt       a_n            =xxt_handle->mvi->n;
  PetscInt       a_m            =xxt_handle->mvi->m;
  PetscInt       *a_local2global=xxt_handle->mvi->local2global;
  PetscInt       level;
  PetscInt       xxt_nnz=0, xxt_max_nnz=0;
  PetscInt       n, m;
  PetscInt       *col_sz, *col_indices, *stages;
  PetscScalar    **col_vals, *x;
  PetscInt       n_global;
  PetscBLASInt   i1            = 1,dlen;
  PetscScalar    dm1           = -1.0;

  n               = xxt_handle->mvi->n;
  nsep            = xxt_handle->info->nsep;
  lnsep           = xxt_handle->info->lnsep;
  fo              = xxt_handle->info->fo;
  end             = lnsep[0];
  level           = xxt_handle->level;
  PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;

  /* is there a null space? */
  /* LATER add in ability to detect null space by checking alpha */
  for (i=0, j=0; i<=level; i++) j+=nsep[i];

  m = j-xxt_handle->ns;
  if (m!=j) {
    PetscCall(PetscPrintf(PETSC_COMM_WORLD,"xxt_generate() :: null space exists %" PetscInt_FMT " %" PetscInt_FMT " %" PetscInt_FMT "\n",m,j,xxt_handle->ns));
  }

  /* get and initialize storage for x local         */
  /* note that x local is nxm and stored by columns */
  col_sz      = (PetscInt*) malloc(m*sizeof(PetscInt));
  col_indices = (PetscInt*) malloc((2*m+1)*sizeof(PetscInt));
  col_vals    = (PetscScalar**) malloc(m*sizeof(PetscScalar*));
  for (i=j=0; i<m; i++, j+=2) {
    col_indices[j]=col_indices[j+1]=col_sz[i]=-1;
    col_vals[i]   = NULL;
  }
  col_indices[j]=-1;

  /* size of separators for each sub-hc working from bottom of tree to top */
  /* this looks like nsep[]=segments */
  stages = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
  segs   = (PetscInt*) malloc((level+1)*sizeof(PetscInt));
  PCTFS_ivec_zero(stages,level+1);
  PCTFS_ivec_copy(segs,nsep,level+1);
  for (i=0; i<level; i++) segs[i+1] += segs[i];
  stages[0] = segs[0];

  /* temporary vectors  */
  u  = (PetscScalar*) malloc(n*sizeof(PetscScalar));
  z  = (PetscScalar*) malloc(n*sizeof(PetscScalar));
  v  = (PetscScalar*) malloc(a_m*sizeof(PetscScalar));
  uu = (PetscScalar*) malloc(m*sizeof(PetscScalar));
  w  = (PetscScalar*) malloc(m*sizeof(PetscScalar));

  /* extra nnz due to replication of vertices across separators */
  for (i=1, j=0; i<=level; i++) j+=nsep[i];

  /* storage for sparse x values */
  n_global    = xxt_handle->info->n_global;
  xxt_max_nnz = (PetscInt)(2.5*PetscPowReal(1.0*n_global,1.6667) + j*n/2)/PCTFS_num_nodes;
  x           = (PetscScalar*) malloc(xxt_max_nnz*sizeof(PetscScalar));
  xxt_nnz     = 0;

  /* LATER - can embed next sep to fire in gs */
  /* time to make the donuts - generate X factor */
  for (dim=i=j=0; i<m; i++) {
    /* time to move to the next level? */
    while (i==segs[dim]) {
      PetscCheck(dim!=level,PETSC_COMM_SELF,PETSC_ERR_PLIB,"dim about to exceed level");
      stages[dim++]=i;
      end         +=lnsep[dim];
    }
    stages[dim]=i;

    /* which column are we firing? */
    /* i.e. set v_l */
    /* use new seps and do global min across hc to determine which one to fire */
    (start<end) ? (col=fo[start]) : (col=INT_MAX);
    PCTFS_giop_hc(&col,&work,1,op2,dim);

    /* shouldn't need this */
    if (col==INT_MAX) {
      PetscCall(PetscInfo(0,"hey ... col==INT_MAX??\n"));
      continue;
    }

    /* do I own it? I should */
    PCTFS_rvec_zero(v,a_m);
    if (col==fo[start]) {
      start++;
      idex=PCTFS_ivec_linear_search(col, a_local2global, a_n);
      if (idex!=-1) {
        v[idex] = 1.0; j++;
      } else SETERRQ(PETSC_COMM_SELF,PETSC_ERR_PLIB,"NOT FOUND!");
    } else {
      idex=PCTFS_ivec_linear_search(col, a_local2global, a_m);
      if (idex!=-1) v[idex] = 1.0;
    }

    /* perform u = A.v_l */
    PCTFS_rvec_zero(u,n);
    do_matvec(xxt_handle->mvi,v,u);

    /* uu =  X^T.u_l (local portion) */
    /* technically only need to zero out first i entries */
    /* later turn this into an XXT_solve call ? */
    PCTFS_rvec_zero(uu,m);
    x_ptr=x;
    iptr = col_indices;
    for (k=0; k<i; k++) {
      off   = *iptr++;
      len   = *iptr++;
      PetscCall(PetscBLASIntCast(len,&dlen));
      PetscCallBLAS("BLASdot",uu[k] = BLASdot_(&dlen,u+off,&i1,x_ptr,&i1));
      x_ptr+=len;
    }

    /* uu = X^T.u_l (comm portion) */
    PetscCall(PCTFS_ssgl_radd  (uu, w, dim, stages));

    /* z = X.uu */
    PCTFS_rvec_zero(z,n);
    x_ptr=x;
    iptr = col_indices;
    for (k=0; k<i; k++) {
      off  = *iptr++;
      len  = *iptr++;
      PetscCall(PetscBLASIntCast(len,&dlen));
      PetscCallBLAS("BLASaxpy",BLASaxpy_(&dlen,&uu[k],x_ptr,&i1,z+off,&i1));
      x_ptr+=len;
    }

    /* compute v_l = v_l - z */
    PCTFS_rvec_zero(v+a_n,a_m-a_n);
    PetscCall(PetscBLASIntCast(n,&dlen));
    PetscCallBLAS("BLASaxpy",BLASaxpy_(&dlen,&dm1,z,&i1,v,&i1));

    /* compute u_l = A.v_l */
    if (a_n!=a_m) PCTFS_gs_gop_hc(PCTFS_gs_handle,v,"+\0",dim);
    PCTFS_rvec_zero(u,n);
    do_matvec(xxt_handle->mvi,v,u);

    /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - local portion */
    PetscCall(PetscBLASIntCast(n,&dlen));
    PetscCallBLAS("BLASdot",alpha = BLASdot_(&dlen,u,&i1,v,&i1));
    /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - comm portion */
    PCTFS_grop_hc(&alpha, &alpha_w, 1, op, dim);

    alpha = (PetscScalar) PetscSqrtReal((PetscReal)alpha);

    /* check for small alpha                             */
    /* LATER use this to detect and determine null space */
    PetscCheck(PetscAbsScalar(alpha)>=1.0e-14,PETSC_COMM_SELF,PETSC_ERR_PLIB,"bad alpha! %g",(double)PetscAbsScalar(alpha));

    /* compute v_l = v_l/sqrt(alpha) */
    PCTFS_rvec_scale(v,1.0/alpha,n);

    /* add newly generated column, v_l, to X */
    flag = 1;
    off=len=0;
    for (k=0; k<n; k++) {
      if (v[k]!=0.0) {
        len=k;
        if (flag) { off=k; flag=0; }
      }
    }

    len -= (off-1);

    if (len>0) {
      if ((xxt_nnz+len)>xxt_max_nnz) {
        PetscCall(PetscInfo(0,"increasing space for X by 2x!\n"));
        xxt_max_nnz *= 2;
        x_ptr        = (PetscScalar*) malloc(xxt_max_nnz*sizeof(PetscScalar));
        PCTFS_rvec_copy(x_ptr,x,xxt_nnz);
        free(x);
        x     = x_ptr;
        x_ptr+=xxt_nnz;
      }
      xxt_nnz += len;
      PCTFS_rvec_copy(x_ptr,v+off,len);

      col_indices[2*i] = off;
      col_sz[i] = col_indices[2*i+1] = len;
      col_vals[i] = x_ptr;
    }
    else {
      col_indices[2*i] = 0;
      col_sz[i]        = col_indices[2*i+1] = 0;
      col_vals[i]      = x_ptr;
    }
  }

  /* close off stages for execution phase */
  while (dim!=level) {
    stages[dim++] = i;
    PetscCall(PetscInfo(0,"disconnected!!! dim(%" PetscInt_FMT ")!=level(%" PetscInt_FMT ")\n",dim,level));
  }
  stages[dim]=i;

  xxt_handle->info->n              = xxt_handle->mvi->n;
  xxt_handle->info->m              = m;
  xxt_handle->info->nnz            = xxt_nnz;
  xxt_handle->info->max_nnz        = xxt_max_nnz;
  xxt_handle->info->msg_buf_sz     = stages[level]-stages[0];
  xxt_handle->info->solve_uu       = (PetscScalar*) malloc(m*sizeof(PetscScalar));
  xxt_handle->info->solve_w        = (PetscScalar*) malloc(m*sizeof(PetscScalar));
  xxt_handle->info->x              = x;
  xxt_handle->info->col_vals       = col_vals;
  xxt_handle->info->col_sz         = col_sz;
  xxt_handle->info->col_indices    = col_indices;
  xxt_handle->info->stages         = stages;
  xxt_handle->info->nsolves        = 0;
  xxt_handle->info->tot_solve_time = 0.0;

  free(segs);
  free(u);
  free(v);
  free(uu);
  free(z);
  free(w);

  return(0);
}

/**************************************xxt.c***********************************/
static PetscErrorCode do_xxt_solve(xxt_ADT xxt_handle,  PetscScalar *uc)
{
  PetscInt       off, len, *iptr;
  PetscInt       level        = xxt_handle->level;
  PetscInt       n            = xxt_handle->info->n;
  PetscInt       m            = xxt_handle->info->m;
  PetscInt       *stages      = xxt_handle->info->stages;
  PetscInt       *col_indices = xxt_handle->info->col_indices;
  PetscScalar    *x_ptr, *uu_ptr;
  PetscScalar    *solve_uu = xxt_handle->info->solve_uu;
  PetscScalar    *solve_w  = xxt_handle->info->solve_w;
  PetscScalar    *x        = xxt_handle->info->x;
  PetscBLASInt   i1        = 1,dlen;

  PetscFunctionBegin;
  uu_ptr=solve_uu;
  PCTFS_rvec_zero(uu_ptr,m);

  /* x  = X.Y^T.b */
  /* uu = Y^T.b */
  for (x_ptr=x,iptr=col_indices; *iptr!=-1; x_ptr+=len) {
    off       =*iptr++;
    len       =*iptr++;
    PetscCall(PetscBLASIntCast(len,&dlen));
    PetscCallBLAS("BLASdot",*uu_ptr++ = BLASdot_(&dlen,uc+off,&i1,x_ptr,&i1));
  }

  /* comunication of beta */
  uu_ptr=solve_uu;
  if (level) PetscCall(PCTFS_ssgl_radd(uu_ptr, solve_w, level, stages));

  PCTFS_rvec_zero(uc,n);

  /* x = X.uu */
  for (x_ptr=x,iptr=col_indices; *iptr!=-1; x_ptr+=len) {
    off  =*iptr++;
    len  =*iptr++;
    PetscCall(PetscBLASIntCast(len,&dlen));
    PetscCallBLAS("BLASaxpy",BLASaxpy_(&dlen,uu_ptr++,x_ptr,&i1,uc+off,&i1));
  }
  PetscFunctionReturn(0);
}

/**************************************xxt.c***********************************/
static PetscErrorCode check_handle(xxt_ADT xxt_handle)
{
  PetscInt vals[2], work[2], op[] = {NON_UNIFORM,GL_MIN,GL_MAX};

  PetscFunctionBegin;
  PetscCheck(xxt_handle,PETSC_COMM_SELF,PETSC_ERR_PLIB,"check_handle() :: bad handle :: NULL %p",xxt_handle);

  vals[0]=vals[1]=xxt_handle->id;
  PCTFS_giop(vals,work,PETSC_STATIC_ARRAY_LENGTH(op)-1,op);
  PetscCheck(!(vals[0]!=vals[1])&&!(xxt_handle->id<=0),PETSC_COMM_SELF,PETSC_ERR_PLIB,"check_handle() :: bad handle :: id mismatch min/max %" PetscInt_FMT "/%" PetscInt_FMT " %" PetscInt_FMT,vals[0],vals[1], xxt_handle->id);
  PetscFunctionReturn(0);
}

/**************************************xxt.c***********************************/
static PetscErrorCode det_separators(xxt_ADT xxt_handle)
{
  PetscInt     i, ct, id;
  PetscInt     mask, edge, *iptr;
  PetscInt     *dir, *used;
  PetscInt     sum[4], w[4];
  PetscScalar  rsum[4], rw[4];
  PetscInt     op[] = {GL_ADD,0};
  PetscScalar  *lhs, *rhs;
  PetscInt     *nsep, *lnsep, *fo, nfo=0;
  PCTFS_gs_ADT PCTFS_gs_handle = xxt_handle->mvi->PCTFS_gs_handle;
  PetscInt     *local2global   = xxt_handle->mvi->local2global;
  PetscInt     n               = xxt_handle->mvi->n;
  PetscInt     m               = xxt_handle->mvi->m;
  PetscInt     level           = xxt_handle->level;
  PetscInt     shared          = 0;

  PetscFunctionBegin;
  dir  = (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
  nsep = (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
  lnsep= (PetscInt*)malloc(sizeof(PetscInt)*(level+1));
  fo   = (PetscInt*)malloc(sizeof(PetscInt)*(n+1));
  used = (PetscInt*)malloc(sizeof(PetscInt)*n);

  PCTFS_ivec_zero(dir,level+1);
  PCTFS_ivec_zero(nsep,level+1);
  PCTFS_ivec_zero(lnsep,level+1);
  PCTFS_ivec_set (fo,-1,n+1);
  PCTFS_ivec_zero(used,n);

  lhs = (PetscScalar*)malloc(sizeof(PetscScalar)*m);
  rhs = (PetscScalar*)malloc(sizeof(PetscScalar)*m);

  /* determine the # of unique dof */
  PCTFS_rvec_zero(lhs,m);
  PCTFS_rvec_set(lhs,1.0,n);
  PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",level);
  PCTFS_rvec_zero(rsum,2);
  for (i=0; i<n; i++) {
    if (lhs[i]!=0.0) {
      rsum[0]+=1.0/lhs[i]; rsum[1]+=lhs[i];
    }
  }
  PCTFS_grop_hc(rsum,rw,2,op,level);
  rsum[0]+=0.1;
  rsum[1]+=0.1;

  if (PetscAbsScalar(rsum[0]-rsum[1])>EPS) shared=1;

  xxt_handle->info->n_global=xxt_handle->info->m_global=(PetscInt) rsum[0];
  xxt_handle->mvi->n_global =xxt_handle->mvi->m_global =(PetscInt) rsum[0];

  /* determine separator sets top down */
  if (shared) {
    for (iptr=fo+n,id=PCTFS_my_id,mask=PCTFS_num_nodes>>1,edge=level;edge>0;edge--,mask>>=1) {

      /* set rsh of hc, fire, and collect lhs responses */
      (id<mask) ? PCTFS_rvec_zero(lhs,m) : PCTFS_rvec_set(lhs,1.0,m);
      PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge);

      /* set lsh of hc, fire, and collect rhs responses */
      (id<mask) ? PCTFS_rvec_set(rhs,1.0,m) : PCTFS_rvec_zero(rhs,m);
      PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge);

      for (i=0;i<n;i++) {
        if (id< mask) {
          if (lhs[i]!=0.0) lhs[i]=1.0;
        }
        if (id>=mask) {
          if (rhs[i]!=0.0) rhs[i]=1.0;
        }
      }

      if (id< mask) PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge-1);
      else          PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge-1);

      /* count number of dofs I own that have signal and not in sep set */
      PCTFS_rvec_zero(rsum,4);
      for (PCTFS_ivec_zero(sum,4),ct=i=0;i<n;i++) {
        if (!used[i]) {
          /* number of unmarked dofs on node */
          ct++;
          /* number of dofs to be marked on lhs hc */
          if (id< mask) {
            if (lhs[i]!=0.0) { sum[0]++; rsum[0]+=1.0/lhs[i]; }
          }
          /* number of dofs to be marked on rhs hc */
          if (id>=mask) {
            if (rhs[i]!=0.0) { sum[1]++; rsum[1]+=1.0/rhs[i]; }
          }
        }
      }

      /* go for load balance - choose half with most unmarked dofs, bias LHS */
      (id<mask) ? (sum[2]=ct) : (sum[3]=ct);
      (id<mask) ? (rsum[2]=ct) : (rsum[3]=ct);
      PCTFS_giop_hc(sum,w,4,op,edge);
      PCTFS_grop_hc(rsum,rw,4,op,edge);
      rsum[0]+=0.1; rsum[1]+=0.1; rsum[2]+=0.1; rsum[3]+=0.1;

      if (id<mask) {
        /* mark dofs I own that have signal and not in sep set */
        for (ct=i=0;i<n;i++) {
          if ((!used[i])&&(lhs[i]!=0.0)) {
            ct++; nfo++;

            PetscCheck(nfo<=n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"nfo about to exceed n");

            *--iptr = local2global[i];
            used[i] = edge;
          }
        }
        if (ct>1) PCTFS_ivec_sort(iptr,ct);

        lnsep[edge]=ct;
        nsep[edge]=(PetscInt) rsum[0];
        dir [edge]=LEFT;
      }

      if (id>=mask) {
        /* mark dofs I own that have signal and not in sep set */
        for (ct=i=0;i<n;i++) {
          if ((!used[i])&&(rhs[i]!=0.0)) {
            ct++; nfo++;

            PetscCheck(nfo<=n,PETSC_COMM_SELF,PETSC_ERR_PLIB,"nfo about to exceed n");

            *--iptr = local2global[i];
            used[i] = edge;
          }
        }
        if (ct>1) PCTFS_ivec_sort(iptr,ct);

        lnsep[edge] = ct;
        nsep[edge]  = (PetscInt) rsum[1];
        dir [edge]  = RIGHT;
      }

      /* LATER or we can recur on these to order seps at this level */
      /* do we need full set of separators for this?                */

      /* fold rhs hc into lower */
      if (id>=mask) id-=mask;
    }
  } else {
    for (iptr=fo+n,id=PCTFS_my_id,mask=PCTFS_num_nodes>>1,edge=level;edge>0;edge--,mask>>=1) {
      /* set rsh of hc, fire, and collect lhs responses */
      (id<mask) ? PCTFS_rvec_zero(lhs,m) : PCTFS_rvec_set(lhs,1.0,m);
      PCTFS_gs_gop_hc(PCTFS_gs_handle,lhs,"+\0",edge);

      /* set lsh of hc, fire, and collect rhs responses */
      (id<mask) ? PCTFS_rvec_set(rhs,1.0,m) : PCTFS_rvec_zero(rhs,m);
      PCTFS_gs_gop_hc(PCTFS_gs_handle,rhs,"+\0",edge);

      /* count number of dofs I own that have signal and not in sep set */
      for (PCTFS_ivec_zero(sum,4),ct=i=0;i<n;i++) {
        if (!used[i]) {
          /* number of unmarked dofs on node */
          ct++;
          /* number of dofs to be marked on lhs hc */
          if ((id< mask)&&(lhs[i]!=0.0)) sum[0]++;
          /* number of dofs to be marked on rhs hc */
          if ((id>=mask)&&(rhs[i]!=0.0)) sum[1]++;
        }
      }

      /* go for load balance - choose half with most unmarked dofs, bias LHS */
      (id<mask) ? (sum[2]=ct) : (sum[3]=ct);
      PCTFS_giop_hc(sum,w,4,op,edge);

      /* lhs hc wins */
      if (sum[2]>=sum[3]) {
        if (id<mask) {
          /* mark dofs I own that have signal and not in sep set */
          for (ct=i=0;i<n;i++) {
            if ((!used[i])&&(lhs[i]!=0.0)) {
              ct++; nfo++;
              *--iptr = local2global[i];
              used[i]=edge;
            }
          }
          if (ct>1) PCTFS_ivec_sort(iptr,ct);
          lnsep[edge]=ct;
        }
        nsep[edge]=sum[0];
        dir [edge]=LEFT;
      } else { /* rhs hc wins */
        if (id>=mask) {
          /* mark dofs I own that have signal and not in sep set */
          for (ct=i=0;i<n;i++) {
            if ((!used[i])&&(rhs[i]!=0.0)) {
              ct++; nfo++;
              *--iptr = local2global[i];
              used[i]=edge;
            }
          }
          if (ct>1) PCTFS_ivec_sort(iptr,ct);
          lnsep[edge]=ct;
        }
        nsep[edge]=sum[1];
        dir [edge]=RIGHT;
      }
      /* LATER or we can recur on these to order seps at this level */
      /* do we need full set of separators for this?                */

      /* fold rhs hc into lower */
      if (id>=mask) id-=mask;
    }
  }

  /* level 0 is on processor case - so mark the remainder */
  for (ct=i=0; i<n; i++) {
    if (!used[i]) {
      ct++; nfo++;
      *--iptr = local2global[i];
      used[i] = edge;
    }
  }
  if (ct>1) PCTFS_ivec_sort(iptr,ct);
  lnsep[edge]=ct;
  nsep [edge]=ct;
  dir  [edge]=LEFT;

  xxt_handle->info->nsep  = nsep;
  xxt_handle->info->lnsep = lnsep;
  xxt_handle->info->fo    = fo;
  xxt_handle->info->nfo   = nfo;

  free(dir);
  free(lhs);
  free(rhs);
  free(used);
  PetscFunctionReturn(0);
}

/**************************************xxt.c***********************************/
static mv_info *set_mvi(PetscInt *local2global,PetscInt n,PetscInt m,PetscErrorCode (*matvec)(mv_info*,PetscScalar*,PetscScalar*),void *grid_data)
{
  mv_info *mvi;

  mvi               = (mv_info*)malloc(sizeof(mv_info));
  mvi->n            = n;
  mvi->m            = m;
  mvi->n_global     = -1;
  mvi->m_global     = -1;
  mvi->local2global = (PetscInt*)malloc((m+1)*sizeof(PetscInt));
  PCTFS_ivec_copy(mvi->local2global,local2global,m);
  mvi->local2global[m] = INT_MAX;
  mvi->matvec          = matvec;
  mvi->grid_data       = grid_data;

  /* set xxt communication handle to perform restricted matvec */
  mvi->PCTFS_gs_handle = PCTFS_gs_init(local2global, m, PCTFS_num_nodes);

  return(mvi);
}

/**************************************xxt.c***********************************/
static PetscErrorCode do_matvec(mv_info *A, PetscScalar *v, PetscScalar *u)
{
  PetscFunctionBegin;
  A->matvec((mv_info*)A->grid_data,v,u);
  PetscFunctionReturn(0);
}