impls/tfs/xxt.c

/*************************************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***********************************/


/*************************************xxt.c************************************
NOTES ON USAGE:

**************************************xxt.c***********************************/
#include <stdio.h>
#include <stdlib.h>
#include <limits.h>
#include <float.h>
#include <math.h>
#if   defined NXSRC
#include <nx.h>
#elif defined MPISRC
#include <mpi.h>
#endif

#include "const.h"
#include "types.h"
#include "comm.h"
#include "error.h"
#include "ivec.h"
#include "bss_malloc.h"
#include "queue.h"
#include "gs.h"
#ifdef MLSRC
#include "ml_include.h"
#endif
#include "blas.h"
#include "xxt.h"

#define LEFT  -1
#define RIGHT  1
#define BOTH   0
#define MAX_FORTRAN_HANDLES  10

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

typedef struct matvec_info {
  int n, m, n_global, m_global;
  int *local2global;
  gs_ADT gs_handle;
  PetscErrorCode (*matvec)(struct matvec_info*,REAL*,REAL*);
  void *grid_data;
} mv_info;

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

static int n_xxt=0;
static int n_xxt_handles=0;

/* prototypes */
static void do_xxt_solve(xxt_ADT xxt_handle, REAL *rhs);
static void check_init(void);
static void check_handle(xxt_ADT xxt_handle);
static void det_separators(xxt_ADT xxt_handle);
static void do_matvec(mv_info *A, REAL *v, REAL *u);
static int xxt_generate(xxt_ADT xxt_handle);
static int do_xxt_factor(xxt_ADT xxt_handle);
static mv_info *set_mvi(int *local2global, int n, int m, void *matvec, void *grid_data);
#ifdef MLSRC
void ML_XXT_solve(xxt_ADT xxt_handle, int lx, double *x, int lb, double *b);
int  ML_XXT_factor(xxt_ADT xxt_handle, int *local2global, int n, int m,
		   void *matvec, void *grid_data, int grid_tag, ML *my_ml);
#endif


/*************************************xxt.c************************************
Function: XXT_new()

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
xxt_ADT
XXT_new(void)
{
  xxt_ADT xxt_handle;


#ifdef DEBUG
  error_msg_warning("XXT_new() :: start %d\n",n_xxt_handles);
#endif

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

#ifdef DEBUG
  error_msg_warning("XXT_new() :: end   %d\n",n_xxt_handles);
#endif

  return(xxt_handle);
}


/*************************************xxt.c************************************
Function: XXT_factor()

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
int
XXT_factor(xxt_ADT xxt_handle, /* prev. allocated xxt  handle */
	   int *local2global,  /* global column mapping       */
	   int n,              /* local num rows              */
	   int m,              /* local num cols              */
	   void *matvec,       /* b_loc=A_local.x_loc         */
	   void *grid_data     /* grid data for matvec        */
	   )
{
#ifdef DEBUG
  int flag;


  error_msg_warning("XXT_factor() :: start %d\n",n_xxt_handles);
#endif

  check_init();
  check_handle(xxt_handle);

  /* only 2^k for now and all nodes participating */
  if ((1<<(xxt_handle->level=i_log2_num_nodes))!=num_nodes)
    {error_msg_fatal("only 2^k for now and MPI_COMM_WORLD!!! %d != %d\n",1<<i_log2_num_nodes,num_nodes);}

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

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

#ifdef DEBUG
  flag = do_xxt_factor(xxt_handle);
  error_msg_warning("XXT_factor() :: end   %d (flag=%d)\n",n_xxt_handles,flag);
  return(flag);
#else
  return(do_xxt_factor(xxt_handle));
#endif
}


/*************************************xxt.c************************************
Function: XXT_solve

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
int
XXT_solve(xxt_ADT xxt_handle, double *x, double *b)
{
#if defined(NXSRC) && defined(TIMING)
  double dclock(),    time=0.0;
#elif defined(MPISRC) && defined(TIMING)
  double MPI_Wtime(), time=0.0;
#endif
#ifdef INFO
  REAL vals[3], work[3];
  int op[] = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD};
#endif


#ifdef DEBUG
  error_msg_warning("XXT_solve() :: start %d\n",n_xxt_handles);
#endif

  check_init();
  check_handle(xxt_handle);

#if defined(NXSRC) && defined(TIMING)
  time = dclock();
#elif defined(MPISRC) && defined(TIMING)
  time = MPI_Wtime();
#endif

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

#if defined(NXSRC) && defined(TIMING)
  time = dclock() - time;
#elif defined(MPISRC) && defined(TIMING)
  time = MPI_Wtime() - time;
#endif

#ifdef TIMING
  xxt_handle->info->nsolves++;
  xxt_handle->info->tot_solve_time+=time;

#ifdef INFO
  vals[0]=vals[1]=vals[2]= (REAL) time;
  grop(vals,work,sizeof(op)/sizeof(op[0])-1,op);
  if (!my_id)
    {
      printf("%d :: min   xxt_slv=%g\n",my_id,vals[0]);
      printf("%d :: max   xxt_slv=%g\n",my_id,vals[1]);
      printf("%d :: avg   xxt_slv=%g\n",my_id,vals[2]/num_nodes);
    }
#endif
#endif

#ifdef DEBUG
  error_msg_warning("XXT_solve() :: end   %d\n",n_xxt_handles);
#endif

  return(0);
}


/*************************************xxt.c************************************
Function: XXT_free()

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
int
XXT_free(xxt_ADT xxt_handle)
{
#ifdef DEBUG
  error_msg_warning("XXT_free() :: start %d\n",n_xxt_handles);
#endif

  check_init();
  check_handle(xxt_handle);
  n_xxt_handles--;

  bss_free(xxt_handle->info->nsep);
  bss_free(xxt_handle->info->lnsep);
  bss_free(xxt_handle->info->fo);
  bss_free(xxt_handle->info->stages);
  bss_free(xxt_handle->info->solve_uu);
  bss_free(xxt_handle->info->solve_w);
  bss_free(xxt_handle->info->x);
  bss_free(xxt_handle->info->col_vals);
  bss_free(xxt_handle->info->col_sz);
  bss_free(xxt_handle->info->col_indices);
  bss_free(xxt_handle->info);
  bss_free(xxt_handle->mvi->local2global);
   gs_free(xxt_handle->mvi->gs_handle);
  bss_free(xxt_handle->mvi);
  bss_free(xxt_handle);


#ifdef DEBUG
  error_msg_warning("perm frees = %d\n",perm_frees());
  error_msg_warning("perm calls = %d\n",perm_calls());
  error_msg_warning("bss frees  = %d\n",bss_frees());
  error_msg_warning("bss calls  = %d\n",bss_calls());
  error_msg_warning("XXT_free() :: end   %d\n",n_xxt_handles);
#endif

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


#ifdef MLSRC
/*************************************xxt.c************************************
Function: ML_XXT_factor()

Input :
Output:
Return:
Description:

ML requires that the solver call be checked in
**************************************xxt.c***********************************/
PetscErrorCode
ML_XXT_factor(xxt_ADT xxt_handle,  /* prev. allocated xxt  handle */
		int *local2global, /* global column mapping       */
		int n,             /* local num rows              */
		int m,             /* local num cols              */
		void *matvec,      /* b_loc=A_local.x_loc         */
		void *grid_data,   /* grid data for matvec        */
		int grid_tag,      /* grid tag for ML_Set_CSolve  */
		ML *my_ml          /* ML handle                   */
		)
{
#ifdef DEBUG
  int flag;
#endif


#ifdef DEBUG
  error_msg_warning("ML_XXT_factor() :: start %d\n",n_xxt_handles);
#endif

  check_init();
  check_handle(xxt_handle);
  if (my_ml->comm->ML_mypid!=my_id)
    {error_msg_fatal("ML_XXT_factor bad my_id %d\t%d\n",
		     my_ml->comm->ML_mypid,my_id);}
  if (my_ml->comm->ML_nprocs!=num_nodes)
    {error_msg_fatal("ML_XXT_factor bad np %d\t%d\n",
		     my_ml->comm->ML_nprocs,num_nodes);}

  my_ml->SingleLevel[grid_tag].csolve->func->external = ML_XXT_solve;
  my_ml->SingleLevel[grid_tag].csolve->func->ML_id = ML_EXTERNAL;
  my_ml->SingleLevel[grid_tag].csolve->data = xxt_handle;

  /* done ML specific stuff ... back to reg sched pgm */
#ifdef DEBUG
  flag = XXT_factor(xxt_handle, local2global, n, m, matvec, grid_data);
  error_msg_warning("ML_XXT_factor() :: end   %d (flag=%d)\n",n_xxt_handles,flag);
  return(flag);
#else
  return(XXT_factor(xxt_handle, local2global, n, m, matvec, grid_data));
#endif
}


/*************************************xxt.c************************************
Function: ML_XXT_solve

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
void
ML_XXT_solve(xxt_ADT xxt_handle, int lx, double *sol, int lb, double *rhs)
{
  XXT_solve(xxt_handle, sol, rhs);
}
#endif


/*************************************xxt.c************************************
Function:

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
int
XXT_stats(xxt_ADT xxt_handle)
{
  int  op[] = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD,GL_MIN,GL_MAX,GL_ADD};
  int fop[] = {NON_UNIFORM,GL_MIN,GL_MAX,GL_ADD};
  int   vals[9],  work[9];
  REAL fvals[3], fwork[3];


#ifdef DEBUG
  error_msg_warning("xxt_stats() :: begin\n");
#endif

  check_init();
  check_handle(xxt_handle);

  /* if factorization not done there are no stats */
  if (!xxt_handle->info||!xxt_handle->mvi)
    {
      if (!my_id)
	{printf("XXT_stats() :: no stats available!\n");}
      return 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;
  giop(vals,work,sizeof(op)/sizeof(op[0])-1,op);

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

  if (!my_id)
    {
      printf("%d :: min   xxt_nnz=%d\n",my_id,vals[0]);
      printf("%d :: max   xxt_nnz=%d\n",my_id,vals[1]);
      printf("%d :: avg   xxt_nnz=%g\n",my_id,1.0*vals[2]/num_nodes);
      printf("%d :: tot   xxt_nnz=%d\n",my_id,vals[2]);
      printf("%d :: xxt   C(2d)  =%g\n",my_id,vals[2]/(pow(1.0*vals[5],1.5)));
      printf("%d :: xxt   C(3d)  =%g\n",my_id,vals[2]/(pow(1.0*vals[5],1.6667)));
      printf("%d :: min   xxt_n  =%d\n",my_id,vals[3]);
      printf("%d :: max   xxt_n  =%d\n",my_id,vals[4]);
      printf("%d :: avg   xxt_n  =%g\n",my_id,1.0*vals[5]/num_nodes);
      printf("%d :: tot   xxt_n  =%d\n",my_id,vals[5]);
      printf("%d :: min   xxt_buf=%d\n",my_id,vals[6]);
      printf("%d :: max   xxt_buf=%d\n",my_id,vals[7]);
      printf("%d :: avg   xxt_buf=%g\n",my_id,1.0*vals[8]/num_nodes);
      printf("%d :: min   xxt_slv=%g\n",my_id,fvals[0]);
      printf("%d :: max   xxt_slv=%g\n",my_id,fvals[1]);
      printf("%d :: avg   xxt_slv=%g\n",my_id,fvals[2]/num_nodes);
    }

#ifdef DEBUG
  error_msg_warning("xxt_stats() :: end\n");
#endif

  return(0);
}


/*************************************xxt.c************************************
Function: do_xxt_factor

Input :
Output:
Return:
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
   gs_init/gop).

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


#ifdef DEBUG
  error_msg_warning("do_xxt_factor() :: begin\n");
#endif

  flag=xxt_generate(xxt_handle);

#ifdef INFO
  XXT_stats(xxt_handle);
  bss_stats();
  perm_stats();
#endif

#ifdef DEBUG
  error_msg_warning("do_xxt_factor() :: end\n");
#endif

  return(flag);
}


/*************************************xxt.c************************************
Function:

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
static
int
xxt_generate(xxt_ADT xxt_handle)
{
  int i,j,k,idex;
  int dim, col;
  REAL *u, *uu, *v, *z, *w, alpha, alpha_w;
  int *segs;
  int op[] = {GL_ADD,0};
  int off, len;
  REAL *x_ptr;
  int *iptr, flag;
  int start=0, end, work;
  int op2[] = {GL_MIN,0};
  gs_ADT gs_handle;
  int *nsep, *lnsep, *fo;
  int a_n=xxt_handle->mvi->n;
  int a_m=xxt_handle->mvi->m;
  int *a_local2global=xxt_handle->mvi->local2global;
  int level;
  int xxt_nnz=0, xxt_max_nnz=0;
  int n, m;
  int *col_sz, *col_indices, *stages;
  REAL **col_vals, *x;
  int n_global;
  int xxt_zero_nnz=0;
  int xxt_zero_nnz_0=0;


#ifdef DEBUG
  error_msg_warning("xxt_generate() :: begin\n");
#endif

  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;
  gs_handle=xxt_handle->mvi->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)
    {printf("xxt_generate() :: null space exists %d %d %d\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 = (int*) bss_malloc(m*INT_LEN);
  col_indices = (int*) bss_malloc((2*m+1)*sizeof(int));
  col_vals = (REAL **) bss_malloc(m*sizeof(REAL *));
  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 = (int*) bss_malloc((level+1)*INT_LEN);
  segs   = (int*) bss_malloc((level+1)*INT_LEN);
  ivec_zero(stages,level+1);
  ivec_copy(segs,nsep,level+1);
  for (i=0; i<level; i++)
    {segs[i+1] += segs[i];}
  stages[0] = segs[0];

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

  /* 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 = (int)(2.5*pow(1.0*n_global,1.6667) + j*n/2)/num_nodes;
  x = (REAL *) bss_malloc(xxt_max_nnz*sizeof(REAL));
  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])
	{
#ifdef SAFE
	  if (dim==level)
	    {error_msg_fatal("dim about to exceed level\n"); break;}
#endif

	  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);
      giop_hc(&col,&work,1,op2,dim);

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

      /* do I own it? I should */
      rvec_zero(v ,a_m);
      if (col==fo[start])
	{
	  start++;
	  idex=ivec_linear_search(col, a_local2global, a_n);
	  if (idex!=-1)
	    {v[idex] = 1.0; j++;}
	  else
	    {error_msg_fatal("NOT FOUND!\n");}
	}
      else
	{
	  idex=ivec_linear_search(col, a_local2global, a_m);
	  if (idex!=-1)
	    {v[idex] = 1.0;}
	}

      /* perform u = A.v_l */
      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 ? */
      rvec_zero(uu,m);
      x_ptr=x;
      iptr = col_indices;
      for (k=0; k<i; k++)
	{
	  off = *iptr++;
	  len = *iptr++;

#if   BLAS||CBLAS
	  uu[k] = dot(len,u+off,1,x_ptr,1);
#else
	  uu[k] = rvec_dot(u+off,x_ptr,len);
#endif
	  x_ptr+=len;
	}


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

      /* z = X.uu */
      rvec_zero(z,n);
      x_ptr=x;
      iptr = col_indices;
      for (k=0; k<i; k++)
	{
	  off = *iptr++;
	  len = *iptr++;

#if   BLAS||CBLAS
	  axpy(len,uu[k],x_ptr,1,z+off,1);
#else
	  rvec_axpy(z+off,x_ptr,uu[k],len);
#endif
	  x_ptr+=len;
	}

      /* compute v_l = v_l - z */
      rvec_zero(v+a_n,a_m-a_n);
#if   BLAS&&CBLAS
      axpy(n,-1.0,z,1,v,1);
#else
      rvec_axpy(v,z,-1.0,n);
#endif

      /* compute u_l = A.v_l */
      if (a_n!=a_m)
	{gs_gop_hc(gs_handle,v,"+\0",dim);}
      rvec_zero(u,n);
      do_matvec(xxt_handle->mvi,v,u);

      /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - local portion */
#if   BLAS&&CBLAS
      alpha = dot(n,u,1,v,1);
#else
      alpha = rvec_dot(u,v,n);
#endif
      /* compute sqrt(alpha) = sqrt(v_l^T.u_l) - comm portion */
      grop_hc(&alpha, &alpha_w, 1, op, dim);

      alpha = (REAL) sqrt((double)alpha);

      /* check for small alpha                             */
      /* LATER use this to detect and determine null space */
#ifdef r8
      if (fabs(alpha)<1.0e-14)
	{error_msg_fatal("bad alpha! %g\n",alpha);}
#else
      if (fabs((double) alpha) < 1.0e-6)
	{error_msg_fatal("bad alpha! %g\n",alpha);}
#endif

      /* compute v_l = v_l/sqrt(alpha) */
      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)
	    {
	      error_msg_warning("increasing space for X by 2x!\n");
	      xxt_max_nnz *= 2;
	      x_ptr = (REAL *) bss_malloc(xxt_max_nnz*sizeof(REAL));
	      rvec_copy(x_ptr,x,xxt_nnz);
	      bss_free(x);
	      x = x_ptr;
	      x_ptr+=xxt_nnz;
	    }
	  xxt_nnz += len;
	  rvec_copy(x_ptr,v+off,len);

          /* keep track of number of zeros */
	  if (dim)
	    {
	      for (k=0; k<len; k++)
		{
		  if (x_ptr[k]==0.0)
		    {xxt_zero_nnz++;}
		}
	    }
	  else
	    {
	      for (k=0; k<len; k++)
		{
		  if (x_ptr[k]==0.0)
		    {xxt_zero_nnz_0++;}
		}
	    }
	  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;
      error_msg_warning("disconnected!!! dim(%d)!=level(%d)\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 = (REAL *) bss_malloc(m*sizeof(REAL));
  xxt_handle->info->solve_w  = (REAL *) bss_malloc(m*sizeof(REAL));
  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;

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

#ifdef DEBUG
  error_msg_warning("xxt_generate() :: end\n");
#endif

  return(0);
}


/*************************************xxt.c************************************
Function:

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
static
void
do_xxt_solve(xxt_ADT xxt_handle, register REAL *uc)
{
  register int off, len, *iptr;
  int level       =xxt_handle->level;
  int n           =xxt_handle->info->n;
  int m           =xxt_handle->info->m;
  int *stages     =xxt_handle->info->stages;
  int *col_indices=xxt_handle->info->col_indices;
  register REAL *x_ptr, *uu_ptr;
#if   BLAS||CBLAS
  REAL zero=0.0;
#endif
  REAL *solve_uu=xxt_handle->info->solve_uu;
  REAL *solve_w =xxt_handle->info->solve_w;
  REAL *x       =xxt_handle->info->x;

#ifdef DEBUG
  error_msg_warning("do_xxt_solve() :: begin\n");
#endif

  uu_ptr=solve_uu;
#if   BLAS||CBLAS
  copy(m,&zero,0,uu_ptr,1);
#else
  rvec_zero(uu_ptr,m);
#endif

  /* 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++;
#if   BLAS||CBLAS
      *uu_ptr++ = dot(len,uc+off,1,x_ptr,1);
#else
      *uu_ptr++ = rvec_dot(uc+off,x_ptr,len);
#endif
    }

  /* comunication of beta */
  uu_ptr=solve_uu;
  if (level) {ssgl_radd(uu_ptr, solve_w, level, stages);}

#if   BLAS||CBLAS
  copy(n,&zero,0,uc,1);
#else
  rvec_zero(uc,n);
#endif

  /* x = X.uu */
  for (x_ptr=x,iptr=col_indices; *iptr!=-1; x_ptr+=len)
    {
      off=*iptr++; len=*iptr++;
#if   BLAS||CBLAS
      axpy(len,*uu_ptr++,x_ptr,1,uc+off,1);
#else
      rvec_axpy(uc+off,x_ptr,*uu_ptr++,len);
#endif
    }

#ifdef DEBUG
  error_msg_warning("do_xxt_solve() :: end\n");
#endif
}


/*************************************Xxt.c************************************
Function: check_init

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
static
void
check_init(void)
{
#ifdef DEBUG
  error_msg_warning("check_init() :: start %d\n",n_xxt_handles);
#endif

  comm_init();
  /*
  perm_init();
  bss_init();
  */

#ifdef DEBUG
  error_msg_warning("check_init() :: end   %d\n",n_xxt_handles);
#endif
}


/*************************************xxt.c************************************
Function: check_handle()

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
static
void
check_handle(xxt_ADT xxt_handle)
{
#ifdef SAFE
  int vals[2], work[2], op[] = {NON_UNIFORM,GL_MIN,GL_MAX};
#endif


#ifdef DEBUG
  error_msg_warning("check_handle() :: start %d\n",n_xxt_handles);
#endif

  if (xxt_handle==NULL)
    {error_msg_fatal("check_handle() :: bad handle :: NULL %d\n",xxt_handle);}

#ifdef SAFE
  vals[0]=vals[1]=xxt_handle->id;
  giop(vals,work,sizeof(op)/sizeof(op[0])-1,op);
  if ((vals[0]!=vals[1])||(xxt_handle->id<=0))
    {error_msg_fatal("check_handle() :: bad handle :: id mismatch min/max %d/%d %d\n",
		     vals[0],vals[1], xxt_handle->id);}
#endif

#ifdef DEBUG
  error_msg_warning("check_handle() :: end   %d\n",n_xxt_handles);
#endif
}


/*************************************xxt.c************************************
Function: det_separators

Input :
Output:
Return:
Description:
  det_separators(xxt_handle, local2global, n, m, mylocmatvec, grid_data);
**************************************xxt.c***********************************/
static
void
det_separators(xxt_ADT xxt_handle)
{
  int i, ct, id;
  int mask, edge, *iptr;
  int *dir, *used;
  int sum[4], w[4];
  REAL rsum[4], rw[4];
  int op[] = {GL_ADD,0};
  REAL *lhs, *rhs;
  int *nsep, *lnsep, *fo, nfo=0;
  gs_ADT gs_handle=xxt_handle->mvi->gs_handle;
  int *local2global=xxt_handle->mvi->local2global;
  int  n=xxt_handle->mvi->n;
  int  m=xxt_handle->mvi->m;
  int level=xxt_handle->level;
  int shared=FALSE;

#ifdef DEBUG
  error_msg_warning("det_separators() :: start %d %d %d\n",level,n,m);
#endif

  dir  = (int*)bss_malloc(INT_LEN*(level+1));
  nsep = (int*)bss_malloc(INT_LEN*(level+1));
  lnsep= (int*)bss_malloc(INT_LEN*(level+1));
  fo   = (int*)bss_malloc(INT_LEN*(n+1));
  used = (int*)bss_malloc(INT_LEN*n);

  ivec_zero(dir  ,level+1);
  ivec_zero(nsep ,level+1);
  ivec_zero(lnsep,level+1);
  ivec_set (fo   ,-1,n+1);
  ivec_zero(used,n);

  lhs  = (double*)bss_malloc(REAL_LEN*m);
  rhs  = (double*)bss_malloc(REAL_LEN*m);

  /* determine the # of unique dof */
  rvec_zero(lhs,m);
  rvec_set(lhs,1.0,n);
  gs_gop_hc(gs_handle,lhs,"+\0",level);
  rvec_zero(rsum,2);
  for (ct=i=0;i<n;i++)
    {
      if (lhs[i]!=0.0)
	{rsum[0]+=1.0/lhs[i]; rsum[1]+=lhs[i];}
    }
  grop_hc(rsum,rw,2,op,level);
  rsum[0]+=0.1;
  rsum[1]+=0.1;
  /*  if (!my_id)
    {
      printf("xxt n unique = %d (%g)\n",(int) rsum[0], rsum[0]);
      printf("xxt n shared = %d (%g)\n",(int) rsum[1], rsum[1]);
      }*/

  if (fabs(rsum[0]-rsum[1])>EPS)
    {shared=TRUE;}

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

  /* determine separator sets top down */
  if (shared)
    {
      for (iptr=fo+n,id=my_id,mask=num_nodes>>1,edge=level;edge>0;edge--,mask>>=1)
	{
	  /* set rsh of hc, fire, and collect lhs responses */
	  (id<mask) ? rvec_zero(lhs,m) : rvec_set(lhs,1.0,m);
	  gs_gop_hc(gs_handle,lhs,"+\0",edge);

	  /* set lsh of hc, fire, and collect rhs responses */
	  (id<mask) ? rvec_set(rhs,1.0,m) : rvec_zero(rhs,m);
	  gs_gop_hc(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)
	    {gs_gop_hc(gs_handle,lhs,"+\0",edge-1);}
	  else
	    {gs_gop_hc(gs_handle,rhs,"+\0",edge-1);}

	  /* count number of dofs I own that have signal and not in sep set */
	  rvec_zero(rsum,4);
	  for (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);
	  giop_hc(sum,w,4,op,edge);
	  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++;

		      if (nfo>n)
			{error_msg_fatal("nfo about to exceed n\n");}

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

	      lnsep[edge]=ct;
	      nsep[edge]=(int) 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++;

		      if (nfo>n)
			{error_msg_fatal("nfo about to exceed n\n");}

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

	      lnsep[edge]=ct;
	      nsep[edge]= (int) 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=my_id,mask=num_nodes>>1,edge=level;edge>0;edge--,mask>>=1)
	{
	  /* set rsh of hc, fire, and collect lhs responses */
	  (id<mask) ? rvec_zero(lhs,m) : rvec_set(lhs,1.0,m);
	  gs_gop_hc(gs_handle,lhs,"+\0",edge);

	  /* set lsh of hc, fire, and collect rhs responses */
	  (id<mask) ? rvec_set(rhs,1.0,m) : rvec_zero(rhs,m);
	  gs_gop_hc(gs_handle,rhs,"+\0",edge);

	  /* count number of dofs I own that have signal and not in sep set */
	  for (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);
	  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) {ivec_sort(iptr,ct);}
		  lnsep[edge]=ct;
		}
	      nsep[edge]=sum[0];
	      dir [edge]=LEFT;
	    }
	  /* rhs hc wins */
	  else
	    {
	      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) {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) {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;

  bss_free(dir);
  bss_free(lhs);
  bss_free(rhs);
  bss_free(used);

#ifdef DEBUG
  error_msg_warning("det_separators() :: end\n");
#endif
}


/*************************************xxt.c************************************
Function: set_mvi

Input :
Output:
Return:
Description:
**************************************xxt.c***********************************/
static
mv_info *set_mvi(int *local2global, int n, int m, void *matvec, void *grid_data)
{
  mv_info *mvi;


#ifdef DEBUG
  error_msg_warning("set_mvi() :: start\n");
#endif

  mvi = (mv_info*)bss_malloc(sizeof(mv_info));
  mvi->n=n;
  mvi->m=m;
  mvi->n_global=-1;
  mvi->m_global=-1;
  mvi->local2global=(int*)bss_malloc((m+1)*INT_LEN);
  ivec_copy(mvi->local2global,local2global,m);
  mvi->local2global[m] = INT_MAX;
  mvi->matvec=(PetscErrorCode (*)(mv_info*,REAL*,REAL*))matvec;
  mvi->grid_data=grid_data;

  /* set xxt communication handle to perform restricted matvec */
  mvi->gs_handle = gs_init(local2global, m, num_nodes);

#ifdef DEBUG
  error_msg_warning("set_mvi() :: end   \n");
#endif

  return(mvi);
}


/*************************************xxt.c************************************
Function: set_mvi

Input :
Output:
Return:
Description:

      computes u = A.v
      do_matvec(xxt_handle->mvi,v,u);
**************************************xxt.c***********************************/
static
void do_matvec(mv_info *A, REAL *v, REAL *u)
{
  A->matvec((mv_info*)A->grid_data,v,u);
}