C++ AllocateWorkSpace函數代碼示例

void METIS_NodeRefine(int nvtxs, idxtype *xadj, idxtype *vwgt, idxtype *adjncy, 
           idxtype *adjwgt, idxtype *where, idxtype *hmarker, float ubfactor)
{
  GraphType *graph;
  CtrlType ctrl;

  ctrl.dbglvl    = ONMETIS_DBGLVL;
  ctrl.optype    = OP_ONMETIS;

  graph = CreateGraph();
  SetUpGraph(graph, OP_ONMETIS, nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);

  AllocateWorkSpace(&ctrl, graph, 2);

  Allocate2WayNodePartitionMemory(&ctrl, graph);
  idxcopy(nvtxs, where, graph->where);

  Compute2WayNodePartitionParams(&ctrl, graph);

  FM_2WayNodeRefine_OneSidedP(&ctrl, graph, hmarker, ubfactor, 10); 
  /* FM_2WayNodeRefine_TwoSidedP(&ctrl, graph, hmarker, ubfactor, 10); */

  FreeWorkSpace(&ctrl, graph);

  idxcopy(nvtxs, graph->where, where);

  FreeGraph(graph);

}

/*************************************************************************
* This function is the entry point for OEMETIS
**************************************************************************/
void METIS_EdgeND(int *nvtxs, idxtype *xadj, idxtype *adjncy, int *numflag, int *options, 
                  idxtype *perm, idxtype *iperm) 
{
  int i, j;
  GraphType graph;
  CtrlType ctrl;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_OEMETIS, *nvtxs, 1, xadj, adjncy, NULL, NULL, 0);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = OEMETIS_CTYPE;
    ctrl.IType = OEMETIS_ITYPE;
    ctrl.RType = OEMETIS_RTYPE;
    ctrl.dbglvl = OEMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }
  ctrl.oflags  = 0;
  ctrl.pfactor = -1;
  ctrl.nseps   = 1;

  ctrl.optype = OP_OEMETIS;
  ctrl.CoarsenTo = 20;
  ctrl.maxvwgt = 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);

  InitRandom(-1);

  AllocateWorkSpace(&ctrl, &graph, 2);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, *nvtxs);

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

  for (i=0; i<*nvtxs; i++)
    perm[iperm[i]] = i;

  FreeWorkSpace(&ctrl, &graph);

  if (*numflag == 1)
    Change2FNumberingOrder(*nvtxs, xadj, adjncy, perm, iperm);
}

/*************************************************************************
* This function is the entry point for PWMETIS that accepts exact weights
* for the target partitions
**************************************************************************/
void METIS_WPartGraphRecursive(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt, 
                               idxtype *adjwgt, int *wgtflag, int *numflag, int *nparts, 
                               floattype *tpwgts, int *options, int *edgecut, idxtype *part)
{
  int i, j;
  GraphType graph;
  CtrlType ctrl;
  floattype *mytpwgts;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_PMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, *wgtflag);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = PMETIS_CTYPE;
    ctrl.IType = PMETIS_ITYPE;
    ctrl.RType = PMETIS_RTYPE;
    ctrl.dbglvl = PMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }
  ctrl.optype = OP_PMETIS;
  ctrl.CoarsenTo = 20;
  ctrl.maxvwgt = 1.5*(idxsum(*nvtxs, graph.vwgt)/ctrl.CoarsenTo);

  mytpwgts = fmalloc(*nparts, "PWMETIS: mytpwgts");
  for (i=0; i<*nparts; i++) 
    mytpwgts[i] = tpwgts[i];

  InitRandom(-1);

  AllocateWorkSpace(&ctrl, &graph, *nparts);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  *edgecut = MlevelRecursiveBisection(&ctrl, &graph, *nparts, part, mytpwgts, 1.000, 0);

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

  FreeWorkSpace(&ctrl, &graph);
  free(mytpwgts);

  if (*numflag == 1)
    Change2FNumbering(*nvtxs, xadj, adjncy, part);
}

/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_NodeComputeSeparator(int *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt, 
           idxtype *adjwgt, float *ubfactor, int *options, int *sepsize, idxtype *part) 
{
  int i, j, tvwgt, tpwgts[2];
  GraphType graph;
  CtrlType ctrl;

  SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
  tvwgt = idxsum(*nvtxs, graph.vwgt);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType  = ONMETIS_CTYPE;
    ctrl.IType  = ONMETIS_ITYPE;
    ctrl.RType  = ONMETIS_RTYPE;
    ctrl.dbglvl = ONMETIS_DBGLVL;
  }
  else {
    ctrl.CType  = options[OPTION_CTYPE];
    ctrl.IType  = options[OPTION_ITYPE];
    ctrl.RType  = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }

  ctrl.oflags    = OFLAG_COMPRESS; /* For by-passing the pre-coarsening for multiple runs */
  ctrl.RType     = 2;  /* Standard 1-sided node refinement code */
  ctrl.pfactor   = 0;
  ctrl.nseps     = 5;  /* This should match NUM_INIT_MSECTIONS in ParMETISLib/defs.h */
  ctrl.optype    = OP_ONMETIS;

  InitRandom(options[7]);

  AllocateWorkSpace(&ctrl, &graph, 2);

  /*============================================================
   * Perform the bisection
   *============================================================*/ 
  tpwgts[0] = tvwgt/2;
  tpwgts[1] = tvwgt-tpwgts[0];

  MlevelNodeBisectionMultiple(&ctrl, &graph, tpwgts, *ubfactor*.95);

  *sepsize = graph.pwgts[2];
  idxcopy(*nvtxs, graph.where, part);

  GKfree((void **)&graph.gdata, &graph.rdata, &graph.label, LTERM);


  FreeWorkSpace(&ctrl, &graph);

}

/*************************************************************************
* This function is the entry point for ONWMETIS. It requires weights on the
* vertices. It is for the case that the matrix has been pre-compressed.
**************************************************************************/
void METIS_NodeComputeSeparator(idxtype *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt, 
           idxtype *adjwgt, idxtype *options, idxtype *sepsize, idxtype *part) 
{
  idxtype i, j, tvwgt, tpwgts[2];
  GraphType graph;
  CtrlType ctrl;

  SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, 3);
  tvwgt = idxsum(*nvtxs, graph.vwgt, 1);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = ONMETIS_CTYPE;
    ctrl.IType = ONMETIS_ITYPE;
    ctrl.RType = ONMETIS_RTYPE;
    ctrl.dbglvl = ONMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }

  ctrl.oflags  = 0;
  ctrl.pfactor = 0;
  ctrl.nseps = 3;
  ctrl.optype = OP_ONMETIS;
  ctrl.CoarsenTo = amin(100, *nvtxs-1);
  ctrl.maxvwgt = 1.5*tvwgt/ctrl.CoarsenTo;

  InitRandom(options[7]);

  AllocateWorkSpace(&ctrl, &graph, 2);

  /*============================================================
   * Perform the bisection
   *============================================================*/ 
  tpwgts[0] = tvwgt/2;
  tpwgts[1] = tvwgt-tpwgts[0];

  MlevelNodeBisectionMultiple(&ctrl, &graph, tpwgts, 1.02);

  *sepsize = graph.pwgts[2];
  idxcopy(*nvtxs, graph.where, part);

  FreeGraph(&graph, 0);

  FreeWorkSpace(&ctrl, &graph);

}

/*************************************************************************
* This function is the entry point for KWMETIS
**************************************************************************/
void METIS_mCPartGraphKway(int *nvtxs, int *ncon, idxtype *xadj, idxtype *adjncy, 
                          idxtype *vwgt, idxtype *adjwgt, int *wgtflag, int *numflag, 
                          int *nparts, floattype *rubvec, int *options, int *edgecut, 
                          idxtype *part)
{
  int i, j;
  GraphType graph;
  CtrlType ctrl;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_KMETIS, *nvtxs, *ncon, xadj, adjncy, vwgt, adjwgt, *wgtflag);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType  = McKMETIS_CTYPE;
    ctrl.IType  = McKMETIS_ITYPE;
    ctrl.RType  = McKMETIS_RTYPE;
    ctrl.dbglvl = McKMETIS_DBGLVL;
  }
  else {
    ctrl.CType  = options[OPTION_CTYPE];
    ctrl.IType  = options[OPTION_ITYPE];
    ctrl.RType  = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }
  ctrl.optype = OP_KMETIS;
  ctrl.CoarsenTo = amax((*nvtxs)/(20*log2Int(*nparts)), 30*(*nparts));

  ctrl.nmaxvwgt = 1.5/(1.0*ctrl.CoarsenTo);

  InitRandom(-1);

  AllocateWorkSpace(&ctrl, &graph, *nparts);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  ASSERT(CheckGraph(&graph));
  *edgecut = MCMlevelKWayPartitioning(&ctrl, &graph, *nparts, part, rubvec);

  IFSET(ctrl.dbglvl, DBG_TIME, stoptimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

  FreeWorkSpace(&ctrl, &graph);

  if (*numflag == 1)
    Change2FNumbering(*nvtxs, xadj, adjncy, part);
}

/*************************************************************************
* This function is the entry point for KWMETIS with seed specification
* in options[7] 
**************************************************************************/
void METIS_WPartGraphKway2(idxtype *nvtxs, idxtype *xadj, idxtype *adjncy, idxtype *vwgt, 
                          idxtype *adjwgt, idxtype *wgtflag, idxtype *numflag, idxtype *nparts, 
                          float *tpwgts, idxtype *options, idxtype *edgecut, idxtype *part)
{
  idxtype i, j;
  GraphType graph;
  CtrlType ctrl;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  SetUpGraph(&graph, OP_KMETIS, *nvtxs, 1, xadj, adjncy, vwgt, adjwgt, *wgtflag);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType = KMETIS_CTYPE;
    ctrl.IType = KMETIS_ITYPE;
    ctrl.RType = KMETIS_RTYPE;
    ctrl.dbglvl = KMETIS_DBGLVL;
  }
  else {
    ctrl.CType = options[OPTION_CTYPE];
    ctrl.IType = options[OPTION_ITYPE];
    ctrl.RType = options[OPTION_RTYPE];
    ctrl.dbglvl = options[OPTION_DBGLVL];
  }
  ctrl.optype = OP_KMETIS;
  ctrl.CoarsenTo = 20*(*nparts);
  ctrl.maxvwgt = 1.5*((graph.vwgt ? idxsum(*nvtxs, graph.vwgt, 1) : (*nvtxs))/ctrl.CoarsenTo);

  InitRandom(options[7]);

  AllocateWorkSpace(&ctrl, &graph, *nparts);

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, gk_startcputimer(ctrl.TotalTmr));

  *edgecut = MlevelKWayPartitioning(&ctrl, &graph, *nparts, part, tpwgts, 1.03);

  IFSET(ctrl.dbglvl, DBG_TIME, gk_stopcputimer(ctrl.TotalTmr));
  IFSET(ctrl.dbglvl, DBG_TIME, PrintTimers(&ctrl));

  FreeWorkSpace(&ctrl, &graph);

  if (*numflag == 1)
    Change2FNumbering(*nvtxs, xadj, adjncy, part);
}

int METIS_PartGraphKway(idx_t *nvtxs, idx_t *ncon, idx_t *xadj, idx_t *adjncy, 
          idx_t *vwgt, idx_t *vsize, idx_t *adjwgt, idx_t *nparts, 
          real_t *tpwgts, real_t *ubvec, idx_t *options, idx_t *objval, 
          idx_t *part)
{
  int sigrval=0, renumber=0;
  graph_t *graph;
  ctrl_t *ctrl;

  /* set up malloc cleaning code and signal catchers */
  if (!gk_malloc_init()) 
    return METIS_ERROR_MEMORY;

  gk_sigtrap();

  if ((sigrval = gk_sigcatch()) != 0)
    goto SIGTHROW;


  /* set up the run parameters */
  ctrl = SetupCtrl(METIS_OP_KMETIS, options, *ncon, *nparts, tpwgts, ubvec);
  if (!ctrl) {
    gk_siguntrap();
    return METIS_ERROR_INPUT;
  }

  /* if required, change the numbering to 0 */
  if (ctrl->numflag == 1) {
    Change2CNumbering(*nvtxs, xadj, adjncy);
    renumber = 1;
  }

  /* set up the graph */
  graph = SetupGraph(ctrl, *nvtxs, *ncon, xadj, adjncy, vwgt, vsize, adjwgt);

  /* set up multipliers for making balance computations easier */
  SetupKWayBalMultipliers(ctrl, graph);

  /* set various run parameters that depend on the graph */
  if (ctrl->iptype == METIS_IPTYPE_METISRB) {
    ctrl->CoarsenTo = gk_max((*nvtxs)/(40*gk_log2(*nparts)), 30*(*nparts));
    ctrl->CoarsenTo = 10*(*nparts);
    ctrl->nIparts   = (ctrl->CoarsenTo == 30*(*nparts) ? 4 : 5);
  }
  else {
    ctrl->CoarsenTo = 10*(*nparts);
    ctrl->nIparts   = 10;
  }

  /* take care contiguity requests for disconnected graphs */
  if (ctrl->contig && !IsConnected(graph, 0)) 
    gk_errexit(SIGERR, "METIS Error: A contiguous partition is requested for a non-contiguous input graph.\n");
    
  /* allocate workspace memory */  
  AllocateWorkSpace(ctrl, graph);

  /* start the partitioning */
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, InitTimers(ctrl));
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startwctimer(ctrl->TotalTmr));

  *objval = MlevelKWayPartitioning(ctrl, graph, part);

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopwctimer(ctrl->TotalTmr));
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, PrintTimers(ctrl));

  /* clean up */
  FreeCtrl(&ctrl);

SIGTHROW:
  /* if required, change the numbering back to 1 */
  if (renumber)
    Change2FNumbering(*nvtxs, xadj, adjncy, part);

  gk_siguntrap();
  gk_malloc_cleanup(0);

  return metis_rcode(sigrval);
}

idx_t MlevelKWayPartitioning(ctrl_t *ctrl, graph_t *graph, idx_t *part)
{
  idx_t i, objval=0, curobj=0, bestobj=0;
  real_t curbal=0.0, bestbal=0.0;
  graph_t *cgraph;


  for (i=0; i<ctrl->ncuts; i++) {
    cgraph = CoarsenGraph(ctrl, graph);

    IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startwctimer(ctrl->InitPartTmr));
    AllocateKWayPartitionMemory(ctrl, cgraph);

    /* Compute the initial partitioning */
    switch (ctrl->iptype) {
      case METIS_IPTYPE_METISRB:
        FreeWorkSpace(ctrl); /* Release the work space, for the recursive metis call */
        InitKWayPartitioningRB(ctrl, cgraph);
        AllocateWorkSpace(ctrl, graph); /* Re-allocate the work space */
        break;

      case METIS_IPTYPE_GROW:
        AllocateRefinementWorkSpace(ctrl, 2*cgraph->nedges);
        InitKWayPartitioningGrow(ctrl, cgraph);
        break;

      default:
        gk_errexit(SIGERR, "Unknown iptype: %d\n", ctrl->iptype);
    }

    IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_stopwctimer(ctrl->InitPartTmr));
    IFSET(ctrl->dbglvl, METIS_DBG_IPART, printf("Initial %"PRIDX \
          "-way partitioning cut: %"PRIDX"\n", ctrl->nparts, objval));

    RefineKWay(ctrl, graph, cgraph);

    switch (ctrl->objtype) {
      case METIS_OBJTYPE_CUT:
        curobj = graph->mincut;
        break;

      case METIS_OBJTYPE_VOL:
        curobj = graph->minvol;
        break;

      default:
        gk_errexit(SIGERR, "Unknown objtype: %d\n", ctrl->objtype);
    }

    curbal = ComputeLoadImbalanceDiff(graph, ctrl->nparts, ctrl->pijbm, ctrl->ubfactors);

    if (i == 0 
        || (curbal <= 0.0005 && bestobj > curobj)
        || (bestbal > 0.0005 && curbal < bestbal)) {
      icopy(graph->nvtxs, graph->where, part);
      bestobj = curobj;
      bestbal = curbal;
    }

    FreeRData(graph);

    if (bestobj == 0)
      break;
  }

  FreeGraph(&graph);

  return bestobj;
}

int METIS_NodeND(idx_t *nvtxs, idx_t *xadj, idx_t *adjncy, idx_t *vwgt,
          idx_t *options, idx_t *perm, idx_t *iperm) 
{
  int sigrval=0, renumber=0;
  idx_t i, ii, j, l, nnvtxs=0;
  graph_t *graph=NULL;
  ctrl_t *ctrl;
  idx_t *cptr, *cind, *piperm;
  int numflag = 0;

  /* set up malloc cleaning code and signal catchers */
  if (!gk_malloc_init()) 
    return METIS_ERROR_MEMORY;

  gk_sigtrap();

  if ((sigrval = gk_sigcatch()) != 0) 
    goto SIGTHROW;


  /* set up the run time parameters */
  ctrl = SetupCtrl(METIS_OP_OMETIS, options, 1, 3, NULL, NULL);
  if (!ctrl) {
    gk_siguntrap();
    return METIS_ERROR_INPUT;
  }

  /* if required, change the numbering to 0 */
  if (ctrl->numflag == 1) {
    Change2CNumbering(*nvtxs, xadj, adjncy);
    renumber = 1;
  }

  IFSET(ctrl->dbglvl, METIS_DBG_TIME, InitTimers(ctrl));
  IFSET(ctrl->dbglvl, METIS_DBG_TIME, gk_startcputimer(ctrl->TotalTmr));

  /* prune the dense columns */
  if (ctrl->pfactor > 0.0) { 
    piperm = imalloc(*nvtxs, "OMETIS: piperm");

    graph = PruneGraph(ctrl, *nvtxs, xadj, adjncy, vwgt, piperm, ctrl->pfactor);
    if (graph == NULL) {
      /* if there was no prunning, cleanup the pfactor */
      gk_free((void **)&piperm, LTERM);
      ctrl->pfactor = 0.0;
    }
    else {
      nnvtxs = graph->nvtxs;
      ctrl->compress = 0;  /* disable compression if prunning took place */
    }
  }

  /* compress the graph; note that compression only happens if not prunning 
     has taken place. */
  if (ctrl->compress) { 
    cptr = imalloc(*nvtxs+1, "OMETIS: cptr");
    cind = imalloc(*nvtxs, "OMETIS: cind");

    graph = CompressGraph(ctrl, *nvtxs, xadj, adjncy, vwgt, cptr, cind);
    if (graph == NULL) {
      /* if there was no compression, cleanup the compress flag */
      gk_free((void **)&cptr, &cind, LTERM);
      ctrl->compress = 0; 
    }
    else {
      nnvtxs = graph->nvtxs;
      ctrl->cfactor = 1.0*(*nvtxs)/nnvtxs;
      if (ctrl->cfactor > 1.5 && ctrl->nseps == 1)
        ctrl->nseps = 2;
      //ctrl->nseps = (idx_t)(ctrl->cfactor*ctrl->nseps);
    }
  }

  /* if no prunning and no compression, setup the graph in the normal way. */
  if (ctrl->pfactor == 0.0 && ctrl->compress == 0) 
    graph = SetupGraph(ctrl, *nvtxs, 1, xadj, adjncy, vwgt, NULL, NULL);

  ASSERT(CheckGraph(graph, ctrl->numflag, 1));

  /* allocate workspace memory */
  AllocateWorkSpace(ctrl, graph);

  /* do the nested dissection ordering  */
  if (ctrl->ccorder) 
    MlevelNestedDissectionCC(ctrl, graph, iperm, graph->nvtxs);
  else
    MlevelNestedDissection(ctrl, graph, iperm, graph->nvtxs);


  if (ctrl->pfactor > 0.0) { /* Order any prunned vertices */
    icopy(nnvtxs, iperm, perm);  /* Use perm as an auxiliary array */
    for (i=0; i<nnvtxs; i++)
      iperm[piperm[i]] = perm[i];
    for (i=nnvtxs; i<*nvtxs; i++)
      iperm[piperm[i]] = i;

    gk_free((void **)&piperm, LTERM);
  }
  else if (ctrl->compress) { /* Uncompress the ordering */
    /* construct perm from iperm */
//.........這裏部分代碼省略.........

/*************************************************************************
* This function is the entry point for ONCMETIS
**************************************************************************/
void METIS_NodeND(int *nvtxs, idxtype *xadj, idxtype *adjncy, int *numflag, int *options, 
                  idxtype *perm, idxtype *iperm) 
{
  int i, ii, j, l, wflag, nflag;
  GraphType graph;
  CtrlType ctrl;
  idxtype *cptr, *cind, *piperm;

  if (*numflag == 1)
    Change2CNumbering(*nvtxs, xadj, adjncy);

  if (options[0] == 0) {  /* Use the default parameters */
    ctrl.CType   = ONMETIS_CTYPE;
    ctrl.IType   = ONMETIS_ITYPE;
    ctrl.RType   = ONMETIS_RTYPE;
    ctrl.dbglvl  = ONMETIS_DBGLVL;
    ctrl.oflags  = ONMETIS_OFLAGS;
    ctrl.pfactor = ONMETIS_PFACTOR;
    ctrl.nseps   = ONMETIS_NSEPS;
  }
  else {
    ctrl.CType   = options[OPTION_CTYPE];
    ctrl.IType   = options[OPTION_ITYPE];
    ctrl.RType   = options[OPTION_RTYPE];
    ctrl.dbglvl  = options[OPTION_DBGLVL];
    ctrl.oflags  = options[OPTION_OFLAGS];
    ctrl.pfactor = options[OPTION_PFACTOR];
    ctrl.nseps   = options[OPTION_NSEPS];
  }
  if (ctrl.nseps < 1)
    ctrl.nseps = 1;

  ctrl.optype = OP_ONMETIS;
  ctrl.CoarsenTo = 100;

  IFSET(ctrl.dbglvl, DBG_TIME, InitTimers(&ctrl));
  IFSET(ctrl.dbglvl, DBG_TIME, starttimer(ctrl.TotalTmr));

  InitRandom(-1);

  if (ctrl.pfactor > 0) { 
    /*============================================================
    * Prune the dense columns
    ==============================================================*/
    piperm = idxmalloc(*nvtxs, "ONMETIS: piperm");

    PruneGraph(&ctrl, &graph, *nvtxs, xadj, adjncy, piperm, (float)(0.1*ctrl.pfactor));
  }
  else if (ctrl.oflags&OFLAG_COMPRESS) {
    /*============================================================
    * Compress the graph 
    ==============================================================*/
    cptr = idxmalloc(*nvtxs+1, "ONMETIS: cptr");
    cind = idxmalloc(*nvtxs, "ONMETIS: cind");

    CompressGraph(&ctrl, &graph, *nvtxs, xadj, adjncy, cptr, cind);

    if (graph.nvtxs >= COMPRESSION_FRACTION*(*nvtxs)) {
      ctrl.oflags--; /* We actually performed no compression */
      GKfree(&cptr, &cind, LTERM);
    }
    else if (2*graph.nvtxs < *nvtxs && ctrl.nseps == 1)
      ctrl.nseps = 2;
  }
  else {
    SetUpGraph(&graph, OP_ONMETIS, *nvtxs, 1, xadj, adjncy, NULL, NULL, 0);
  }


  /*=============================================================
  * Do the nested dissection ordering 
  --=============================================================*/
  ctrl.maxvwgt = 1.5*(idxsum(graph.nvtxs, graph.vwgt)/ctrl.CoarsenTo);
  AllocateWorkSpace(&ctrl, &graph, 2);

  if (ctrl.oflags&OFLAG_CCMP) 
    MlevelNestedDissectionCC(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, graph.nvtxs);
  else
    MlevelNestedDissection(&ctrl, &graph, iperm, ORDER_UNBALANCE_FRACTION, graph.nvtxs);

  FreeWorkSpace(&ctrl, &graph);

  if (ctrl.pfactor > 0) { /* Order any prunned vertices */
    if (graph.nvtxs < *nvtxs) { 
      idxcopy(graph.nvtxs, iperm, perm);  /* Use perm as an auxiliary array */
      for (i=0; i<graph.nvtxs; i++)
        iperm[piperm[i]] = perm[i];
      for (i=graph.nvtxs; i<*nvtxs; i++)
        iperm[piperm[i]] = i;
    }

    GKfree(&piperm, LTERM);
  }
  else if (ctrl.oflags&OFLAG_COMPRESS) { /* Uncompress the ordering */
    if (graph.nvtxs < COMPRESSION_FRACTION*(*nvtxs)) { 
      /* construct perm from iperm */
      for (i=0; i<graph.nvtxs; i++)
//.........這裏部分代碼省略.........

/**************************************************************************
* mexFunction: gateway routine for MATLAB interface.
***************************************************************************/
void mexFunction
(int nlhs, mxArray *plhs[], int nrhs, const mxArray *prhs[])
{
    
    // Argument checking
    if (nrhs != 5)
        mexErrMsgIdAndTxt(FUNC_NAME, "Wrong input.");
    if (nlhs != 3)
        mexErrMsgIdAndTxt(FUNC_NAME, "Wrong output.");
    
    // Input and output variables
    idx_t nvtxs = (idx_t) mxGetScalar(nvtxs_in);
    idx_t *xadj; GetIdxArray(xadj_in,&xadj);
    idx_t *adjncy; GetIdxArray(adjncy_in,&adjncy);
    idx_t *vwgt; GetIdxArray(vwgt_in,&vwgt);
    idx_t options[METIS_NOPTIONS];
    GetOptions(options_in, options);
    idx_t *sepidx;
    idx_t *lgraphidx;
    idx_t *rgraphidx;
    
    // Metis main function
    idx_t i, nnvtxs=0;
    idx_t ptlgraph, ptrgraph, ptsep;
    graph_t *graph=NULL;
    ctrl_t *ctrl;
    idx_t *piperm;
    idx_t snvtxs[3];
    idx_t *where;

    /* set up malloc cleaning code and signal catchers */
    if (!gk_malloc_init()) 
        CheckReturn( METIS_ERROR_MEMORY, FUNC_NAME );

    // set up the run time parameters
    ctrl = SetupCtrl(METIS_OP_OMETIS, options, 1, 3, NULL, NULL);

    // prune the dense columns
    if (ctrl->pfactor > 0.0)
    { 
        piperm = imalloc(nvtxs, "OMETIS: piperm");

        graph = PruneGraph(ctrl, nvtxs, xadj, adjncy, vwgt,
                piperm, ctrl->pfactor);
        if (graph == NULL)
        {
            // if there was no prunning, cleanup the pfactor
            gk_free((void **)&piperm, LTERM);
            ctrl->pfactor = 0.0;
        }
        else
        {
            nnvtxs = graph->nvtxs;
            // disable compression if prunning took place
            ctrl->compress = 0;
        }
    }

    // compress the graph
    if (ctrl->compress)
        ctrl->compress = 0; 

    // if no prunning and no compression, setup the graph in the normal way.
    if (ctrl->pfactor == 0.0 && ctrl->compress == 0) 
        graph = SetupGraph(ctrl, nvtxs, 1, xadj, adjncy, vwgt, NULL, NULL);

    ASSERT(CheckGraph(graph, ctrl->numflag, 1));

    /* allocate workspace memory */
    AllocateWorkSpace(ctrl, graph);

    MlevelNodeBisectionMultiple(ctrl, graph);

    snvtxs[0] = 0;
    snvtxs[1] = 0;
    snvtxs[2] = 0;

    if (ctrl->pfactor > 0.0)
        snvtxs[2] += nvtxs-nnvtxs;

    where = graph->where;
    for (i=0; i<graph->nvtxs; i++)
        snvtxs[where[i]]++;

    lgraphidx = (idx_t*) mxCalloc (snvtxs[0], sizeof(idx_t));
    rgraphidx = (idx_t*) mxCalloc (snvtxs[1], sizeof(idx_t));
    sepidx    = (idx_t*) mxCalloc (snvtxs[2], sizeof(idx_t));

    ptlgraph = 0;
    ptrgraph = 0;
    ptsep    = 0;

    if (ctrl->pfactor > 0.0)
    {
        for (i=0; i<graph->nvtxs; i++)
            if (where[i] == 0)
                lgraphidx[ptlgraph++] = piperm[i];
//.........這裏部分代碼省略.........