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Nefpart.c

#include "Global.h"
#include "Nef.h"

#define GL_Long        Long
#ifndef CEQ_Nmax
#define CEQ_Nmax       EQUA_Nmax  
#endif

/*   ===============        Typedefs and Headers      ===================  */

int  GLZ_Make_Trian_NF(Long X[][VERT_Nmax], int *n, int *nv,
                   GL_Long G[][POLY_Dmax]);   /* current=best */

void Poly_Sym(PolyPointList *_P, VertexNumList *_V, EqList *_F, int *sym_num,
            int V_perm[][VERT_Nmax]);

/*   ===============    local Typedefs and Headers    ===================  */

typedef struct {
  int ne; 
  Equation e[CEQ_Nmax];
} CEqList;

typedef struct {
  int nv;                /*   #vertices of face */ 
  int v[VERT_Nmax];      /*   vertices of face */
} VList; 

typedef struct {
  int Nv;                /*   #vertices */
  int nf;                /*   #facets */
  VList *vl;             /*   vertices of facets */
} FVList;

typedef struct {
  int f;
  int v;
} Step;

typedef struct {
  int s[VERT_Nmax];
} V_Flag;

typedef struct {
  int m[FACE_Nmax];
} M_Rank;

typedef struct {          
  int M[POLY_Dmax][POLY_Dmax];
  int d;
  int codim;
} MMatrix;

typedef struct {
  int d;
  int nv;
  Long X[POLY_Dmax][VERT_Nmax];
} XMatrix;

typedef struct {
  int d;
  GL_Long G[POLY_Dmax][POLY_Dmax];
} GMatrix;

typedef struct {
  int Vp[SYM_Nmax][VERT_Nmax];
  int ns;
} SYM;

typedef struct {
  int A[POLY_Dmax];
  int m;
  int M;
} Subset;

int GLZ_Start_Simplex(PolyPointList *_P, VertexNumList *_V, CEqList *_C);


/*   ===============    End of Typedefs and Headers   ===================  */

void Print_FVl(FVList *_FVl, const char *comment){
  int i,j;

  fprintf(outFILE,"%s\n",comment);
  for (i = 0; i < _FVl->nf; i++){
    for (j = 0; j < _FVl->vl[i].nv; j++)
      fprintf(outFILE, "  %d  ", _FVl->vl[i].v[j]);
    fprintf(outFILE, "nv: %d\n",_FVl->vl[i].nv);fflush(0);
  }
}

void Print_M(MMatrix *_M, int *_nf, const char *comment){
  int i, j, k;

  fprintf(outFILE,"%s\n",comment);
  for (i = 0; i < *_nf; i++){
    fprintf(outFILE, "\n\n facet %d:\n", i);
    for(j = 0; j < _M[i].codim; j++){
      fprintf(outFILE, "m[%d]: ",j);
      for(k = 0; k < _M[i].d; k++)
      fprintf(outFILE, "%d ",_M[i].M[k][j]);
      fprintf(outFILE,"\n");
    }
  }
}

void Dir_Product(PartList *_PTL, VertexNumList *_V, PolyPointList *_P){

  int i, j, k, d, rank;
  
  CEqList CEtemp;
  VertexNumList Vtemp;

  PolyPointList *_PV = (PolyPointList *) malloc(sizeof(PolyPointList));
  if(_PV == NULL) Die("Unable to alloc space for PolyPointList _PV");

  _PV->n = _P->n;
  for(i = 0; i < _PTL->n; i++){
    rank = 0;
    for(j = 0; j < _PTL->codim; j++){
      _PV->np = 0; 
      for(k = 0; k < _PTL->nv; k++)
                        if(_PTL->S[i][k] == j){
                              for(d = 0; d < _P->n; d++)
                                    _PV->x[_PV->np][d] = _P->x[_V->v[k]][d];
                              _PV->np += 1;
                        }
      for(d = 0; d < _P->n; d++)
                        _PV->x[_PV->np][d] = 0;
      _PV->np += 1;
      rank += GLZ_Start_Simplex(_PV, &Vtemp, &CEtemp); 
    }
    if(rank == _P->n)
      _PTL->DirProduct[i] = 1;
    else
      _PTL->DirProduct[i] = 0;
  }
  free(_PV);
}

void Set_To_Vlist(int *_S, VertexNumList *_V, PolyPointList *_P, PolyPointList 
              *_PV, Subset *_Pset){
  int i, d;

  _PV->n = _P->n; _PV->np = 0; 
  for(i = 0; i < _V->nv; i++)
    if( _Pset->A[_S[i]] == 1){
      for(d = 0; d < _P->n; d++)
                        _PV->x[_PV->np][d] = _P->x[_V->v[i]][d];
      _PV->np ++;
    }
  for(d = 0; d < _P->n; d++)
    _PV->x[_PV->np][d] = 0;
  _PV->np += 1;
}

int New_Set(int i, Subset *_Pset, Subset *_CPset){
  
  if(_Pset->A[i] == 0){
    _Pset->A[i] = 1; _Pset->m++;
    _CPset->A[i] = 0; _CPset->m--;
    return 1;
  }
  else
    return 0;
}

void Old_Set(int i, Subset *_Pset, Subset *_CPset){
  _Pset->A[i] = 0; _Pset->m--;
  _CPset->A[i] = 1; _CPset->m++;
}

void Select_Set(int *_S, VertexNumList *_V, PolyPointList *_P, PolyPointList *_PV, 
            CEqList *_CEtemp, VertexNumList *_Vtemp, int * _DirFlag, Subset 
            *_Pset, Subset *_CPset, int nmax_old){
  int rank, nmax;

  Set_To_Vlist(_S, _V, _P, _PV, _Pset); 
  rank = GLZ_Start_Simplex(_PV, _Vtemp, _CEtemp);
  Set_To_Vlist(_S, _V, _P, _PV, _CPset);
  rank += GLZ_Start_Simplex(_PV, _Vtemp, _CEtemp);

  /*{int i; for(i=0;i<_Pset->M;i++) printf("   %d",_Pset->A[i]); printf("\n");}*/
  if(rank == _P->n) 
    *_DirFlag = 1;
  else{
    if(_Pset->m < (_Pset->M/2 + (_Pset->M % 2))){
      nmax = (nmax_old + 1);
      while(!*_DirFlag && (nmax < _Pset->M)){
                        /*printf("aaa");*/
                        if (New_Set(nmax, _Pset, _CPset)){
                              Select_Set(_S, _V, _P, _PV, _CEtemp, _Vtemp, _DirFlag, _Pset, _CPset,
                                                             nmax);
                              Old_Set(nmax, _Pset, _CPset);
                        }
                        nmax++;
      }
    }
  }
}

void REC_Dir_Product(PartList *_PTL, VertexNumList *_V, PolyPointList *_P){

  int i, j, k;
  CEqList *_CEtemp;
  VertexNumList *_Vtemp;
  PolyPointList *_PV;
  Subset Pset, CPset;

  _PV = (PolyPointList *) malloc(sizeof(PolyPointList));
  if(_PV == NULL) Die("Unable to alloc space for PolyPointList _PV");
  _CEtemp = (CEqList *) malloc(sizeof(CEqList));
  if(_CEtemp == NULL) Die("Unable to alloc space for CEqList _CEtemp");
  _Vtemp = (VertexNumList *) malloc(sizeof(VertexNumList));
  if(_Vtemp == NULL) Die("Unable to alloc space for VertexNumList _Vtemp");
  
  for(i = 0; i < _PTL->n; i++){
    _PTL->DirProduct[i] = 0; j = 0;
    /*printf("\n*********************************\n");*/
    while((j < _PTL->codim) && !_PTL->DirProduct[i]){
      for(k = 0; k < _PTL->codim; k++){
                        if(k == j){
                              Pset.A[k] = 1; CPset.A[k] = 0;
                        }
                        else{
                              Pset.A[k] = 0; CPset.A[k] = 1;
                        }
      }
      Pset.m = 1; Pset.M = _PTL->codim;
      CPset.m = (_PTL->codim - 1); CPset.M = _PTL->codim;
      Select_Set(_PTL->S[i], _V, _P, _PV, _CEtemp, _Vtemp, &_PTL->DirProduct[i], 
                                                 &Pset, &CPset, 0);
      j++;
    }
  }
  free(_Vtemp); free(_CEtemp); free(_PV);
}

int COMP_S(int SA[], int SB[], int *_nv){

  int eq_flag = 1, i = 0;

  while((i < *_nv) && eq_flag){
    if((SA[i] > SB[i]) || (SA[i] < SB[i]))
      eq_flag = 0;
    i++;
  }
  if(eq_flag) 
    return 0;
  else{ 
    if(SA[i-1] > SB[i-1])
      return 1;
    else
      return -1;
  }
}

void NForm_S(int S[], int *_nv){

  int s[POLY_Dmax], d=0, n_flag, i, j;
      
  for(i = 0; i < *_nv; i++){
    n_flag = 1; j = 0;
    while((j < i) && n_flag){
      if(S[j] == S[i])
                        n_flag = 0;
      j++;
    }
    if(n_flag){
      s[S[i]] = d;
      d++;
    }
  }
  for(i = 0; i < *_nv; i++)
    S[i] = s[S[i]];
}

int Bisection_PTL(PartList *_PTL, int s[], int S[]){
      
  int min_pos = -1, max_pos = _PTL->n, pos = 1, c = 1;

  while((max_pos - min_pos ) > 1){
    pos = (max_pos + min_pos) / 2;
    c = COMP_S(S, _PTL->S[s[pos]], &_PTL->nv);
    if (c == 1)
      min_pos = pos;
    else if (c == -1)
      max_pos = pos;
    else 
      min_pos =  max_pos;
  }
  assert (c == 0);
  return s[pos];
}

void Bubble_PTL(PartList *_PTL, int s[]){

  int i, j, diff=0;

  for(i = 0; i < _PTL->n; i++)
    s[i] = i;
  for(i = 0; i < _PTL->n - 1; ++i)
    for(j = _PTL->n - 1; j > i; --j)
      if(COMP_S(_PTL->S[s[j-1]], _PTL->S[s[j]], &_PTL->nv) == 1)
      swap(&s[j-1], &s[j]);
  for(i = 1; i < _PTL->n; i++){
    if(COMP_S(_PTL->S[s[i-1]], _PTL->S[s[i]], &_PTL->nv) == 0)
      diff += 1;
    else
      s[i - diff] = s[i];
  }
  _PTL->n =  _PTL->n - diff;
}

void Remove_Sym(SYM *_VP, PartList *_PTL, PartList *_S_PTL){

  int *_s, *_s_sym, *_p;
  int n=1, i, j, k;
  PartList *_SYM_PTL;
  
  _s = (int*) calloc(_PTL->n, sizeof(int));
  assert(_s != NULL);
  _s_sym = (int*) calloc(_VP->ns, sizeof(int));
  assert(_s_sym != NULL);
  _p = (int*) calloc(_PTL->n, sizeof(int));
  assert(_p != NULL);
  _SYM_PTL = (PartList*) malloc(sizeof(PartList));
  assert(_SYM_PTL != NULL);
  
  if(Nef_Max < SYM_Nmax) Die("\nNeed Nef_Max >= SYM_Nmax!!!\n");
  for(i = 0; i < _PTL->n; i++){
    _p[i] = 0; _s[i] = 0;
  }
  for(i = 0; i < _PTL->n; i++)
    NForm_S(_PTL->S[i], &_PTL->nv);
  Bubble_PTL(_PTL, _s);
  for(i = 0; i < _PTL->n; i++){
    if(_p[_s[i]] == 0){
      _p[_s[i]] = n;
      for(j = 0; j < _VP->ns; j++){
      for(k = 0; k < _PTL->nv; k++)
      _SYM_PTL->S[j][k] = _PTL->S[_s[i]][_VP->Vp[j][k]];
      }
      _SYM_PTL->n = _VP->ns; _SYM_PTL->nv = _PTL->nv;
      for(j = 0; j < _VP->ns; j++)
      NForm_S(_SYM_PTL->S[j], &_SYM_PTL->nv);
      Bubble_PTL(_SYM_PTL, _s_sym);
      for(j = 1; j < _VP->ns; j++)
      if(COMP_S(_SYM_PTL->S[_s_sym[j]], _SYM_PTL->S[_s_sym[j-1]], &_PTL->nv) != 0)
        _p[Bisection_PTL(_PTL, _s, _SYM_PTL->S[_s_sym[j]])] = n;
      n++;
    }
  }
  n--; _S_PTL->nv = _PTL->nv; _S_PTL->n = 0; _S_PTL->codim = _PTL->codim;
  while(n  >  0){
    i = 0;
    while(_p[_s[i]] != n)
      i++;
    for(j = 0; j < _PTL->nv; j ++)
      _S_PTL->S[_S_PTL->n][j] = _PTL->S[_s[i]][j];
    _S_PTL->n += 1;
    n--;
    }
  free(_s);free(_s_sym);free(_p);free(_SYM_PTL);
}

void M_TO_MM(MMatrix *_M, MMatrix *_MM, GMatrix *_G, int *_nf){

  int i, l, c, j;

  for(i = 0; i < *_nf; i++){
    for(l = 0; l < _M[i].d; l++)
      for(c = 0; c < _M[i].codim; c++){
                        _MM[i].M[l][c] = 0;
                        for(j = 0; j < _M[i].d; j++)
                              _MM[i].M[l][c] += _G[i].G[j][l] * _M[i].M[j][c];
      }
    _MM[i].d = _M[i].d; _MM[i].codim =_M[i].codim; 
  }
}

int Convex_Check(MMatrix *_M, GMatrix *_G, XMatrix *_X, int S[], FVList *_FVl,
             NEF_Flags *_F){ 
  MMatrix *_MM;
  int c_flag = 1, i, j, k, l, d, IP;

  if (_F->noconvex) return 1;

  _MM = (MMatrix *) calloc(_FVl->nf, sizeof(MMatrix)); 
  assert(_MM != NULL);

  M_TO_MM(_M, _MM, _G, &_FVl->nf);
 
  i = 0;
  while((i < _FVl->nf) && c_flag){
    j = 0;
    while((j < _FVl->nf) && c_flag){
      if(i != j){
                        k = 0;
                        while((k < _MM[i].codim) && c_flag){
                              l = 0;
                              while((l < _X[i].nv) && c_flag){
                                    if(S[_FVl->vl[i].v[l]] == k)
                                          IP = 1;
                                    else
                                          IP = 0;
                                    for(d = 0; d < _MM[i].d; d++)
                                          IP += - _X[i].X[d][l] * _MM[j].M[d][k]; 
                                    if (IP < 0)
                                          c_flag = 0;
                                    l++;
                              }
                              k++;
                        }
      }
      j++;
    }
    i++;
  }
  if (c_flag && _F->Test)
            Print_M(_MM, &_FVl->nf, "M-Matrix:");
  free(_MM);
  return c_flag;
}

int Codim_Check(int S[], int *_codim, int *_Nv){

  int gp[POLY_Dmax] = {0}, gp_flag = 1, i, j=0;

  while( (j < *_codim) && gp_flag){
    i = 0;
    while( (i < *_Nv) && (gp[j] == 0)){
      if (S[i] == j)
                        gp[j] = 1;
      i++;
    }
    gp_flag = gp[j];
    j++;
  }
  return gp_flag;
}

int Fix_M(Step *_step, XMatrix *_Y, MMatrix *_M, int S[], M_Rank *_MR, 
        FVList *_FVl){

  int f_flag=1, i=0, j, m, IP;

  while(f_flag && (i!=_M[_step->f].codim)){
    if(i == S[_FVl->vl[_step->f].v[_step->v]])
      IP = 1;
    else
      IP = 0;
    for(j = 0; j < _MR->m[_step->f]; j++)
      IP += -_Y[_step->f].X[j][_step->v] * _M[_step->f].M[j][i];
    m = (IP / _Y[_step->f].X[_MR->m[_step->f]][_step->v]);
    if((IP - m * _Y[_step->f].X[_MR->m[_step->f]][_step->v]) != 0)
      f_flag=0;
    else
      _M[_step->f].M[_MR->m[_step->f]][i] = m;
    i++;
  }
  return f_flag;
}

int Check_Consistence(Step *_step, XMatrix *_Y, MMatrix *_M, int S[], 
                  M_Rank *_MR, FVList *_FVl){

  int c_flag=1, i=0, j, IP;

  while(c_flag && (i!=_M[_step->f].codim)){
    IP = 0;
    for(j = 0; j < _MR->m[_step->f]; j++)
      IP += _Y[_step->f].X[j][_step->v] * _M[_step->f].M[j][i];
    if(i == S[_FVl->vl[_step->f].v[_step->v]]){
      if(IP != 1)
                        c_flag = 0;
    }
    else{
      if(IP != 0)
                        c_flag = 0;
    }
    i++;
  }
  return c_flag;
}

int New_V(V_Flag *_VF, int *_i){

  int new_flag = 0;

  if (!_VF->s[*_i]){
    _VF->s[*_i] = 1;
    new_flag = 1;
  }
  return new_flag;
}

int Next_Step(FVList *_FVl, Step *_step){

  int step_flag = 1;

   if(_step->v == _FVl->vl[_step->f].nv-1){
      _step->f += 1;
      _step->v = 0;
  }
  else
    _step->v += 1;
  if(_step->f == _FVl->nf)
    step_flag = 0;
  return step_flag;
}

void New_VFlag(V_Flag *_VF,  /* int *_Nv, */  int *_n){

  _VF->s[*_n] = 1;
}

void Old_VFlag(V_Flag *_VF,  /* int *_Nv, */  int *_n){

  _VF->s[*_n] = 0;
}

void Raise_M_Rank(M_Rank *_MR, int *_facet){

  _MR->m[*_facet] += 1;
}

void Lower_M_Rank(M_Rank *_MR, int *_facet){

  _MR->m[*_facet] -= 1;
}

void Zero_M_Rank(M_Rank *_MR, int *_facet){
  _MR->m[*_facet] = 0;
}

void Initial_Conditions(MMatrix *_M, XMatrix *_Y, M_Rank *_MR, Step *_step, 
                  FVList *_FVl, V_Flag *_VF,  int S[], int *_codim, 
                  int *_dim, PartList *_PTL){

  int i;
  for(i = 0; i < _FVl->nf; i++){
    _M[i].codim = *_codim; 
    _M[i].d = *_dim;
    _MR->m[i] = 0;
  } 
  _step->f = 0; _step->v = 0; 
  for(i = 0; i < _FVl->Nv; i++)
    _VF->s[i] = 0;
  _VF->s[_FVl->vl[0].v[0]] = 1;
  _MR->m[0] = 1;
  assert((_Y[0].X[0][0] == 1) || (_Y[0].X[0][0] == -1));
  for(i = 0; i < *_codim; i++)
    _M[0].M[0][i] = 0;
  _M[0].M[0][0] = _Y[0].X[0][0];
  S[_FVl->vl[0].v[0]] = 0;
  _PTL->n = 0;
  _PTL->nv = _FVl->Nv;
  _PTL->codim = *_codim;
}

void INCI_To_VList( INCI *_X, VList *_Vl, int *_N){
  /* INCI X -> {3, 5, 7, ...} ... List of Vertices in 
     VertexNumList of corresponding face */

  int i, n=0;
  INCI Y = *_X;

  for (i = 0; i < *_N; i++) {
            if (INCI_M2(Y)){
          _Vl->v[n] = *_N-i-1;
          n++;
            }
            Y = INCI_D2(Y);
  }
  _Vl->nv = n;
}

void INCI_To_FVList(FaceInfo *_I, PolyPointList *_P, FVList *_FVl){
  /* FaceInfo I ->  {3, 5, 7, ...}, {1, 4, 8, ...}, ...  
     Lists of Vertices in VertexNumList of all facets  */

  int i;

  for (i = 0; i < _I->nf[_P->n - 1]; i++) 
    INCI_To_VList( &_I->v[_P->n - 1][i], &_FVl->vl[i], &_I->nf[0]);
  _FVl->nf = _I->nf[_P->n - 1];
  _FVl->Nv = _I->nf[0];
}

void Sort_FVList(FVList *_FVl, FVList *_FVl_new, int f[]){
  /* gives f[]  = LIST OF SORTED FACETS IN _FVl:
     f[0]: facet with max # of Vertices
     f[k != 0]: facet with max # of Vertices in f[0],...,f[k-1]
     _FVl->vl[k] -> _FVl->vl[f[k]] = 
     {v in f[0],...,f[k-1]}U{v not in f[0],...,f[k-1]} =: FVl_new->vl[k] */

  int i, j, k, l, n, Vequal, vequal, newfacet, newvertex,  
      v[VERT_Nmax], w[VERT_Nmax], nv, nw;

  f[0] = 0;
  for (i = 1; i < _FVl->nf; i++)  /* first facet */
    if (_FVl->vl[i].nv > _FVl->vl[f[0]].nv)
      f[0] = i;    
  for(i = 0; i < _FVl->vl[f[0]].nv; i++)
    v[i] = _FVl->vl[f[0]].v[i];
  nv = _FVl->vl[f[0]].nv;
  for (n = 1; n < _FVl->nf; n++){  /* next facet */ 
    Vequal = 0;
    for (i = 0; i < _FVl->nf; i++){
      newfacet = 1;
      k = 0;
      while((k < n) && newfacet){
            if (f[k] == i)
        newfacet = 0;
      k++;
      }
      if(newfacet){
            vequal = 0;
      for(j = 0; j < _FVl->vl[i].nv; j++){
        newvertex = 1;
        k = 0;
        while((k < nv) && newvertex){
          if (v[k] == _FVl->vl[i].v[j])
            newvertex = 0;
          k++;
        }
        if(!newvertex)
          vequal++;
      }
            if(vequal >= Vequal){
        Vequal = vequal;
        f[n] = i;
            }
      }
    }
    nw = 0;
    for(j = 0; j < _FVl->vl[f[n]].nv; j++){
      newvertex = 1;
      k = 0;
      while((k < nv) && newvertex){
      if (v[k] == _FVl->vl[f[n]].v[j])
        newvertex = 0;
      k++;
      }
      if(newvertex){
      v[nv] = _FVl->vl[f[n]].v[j];
      nv++;
      }
      else{
      w[nw] = _FVl->vl[f[n]].v[j];
      nw++;
      }
    }
    for(l = 0; l < nw; l++) 
      _FVl->vl[f[n]].v[l] = w[l];
    for(l = 0; l < _FVl->vl[f[n]].nv - nw; l++)
      _FVl->vl[f[n]].v[nw+l] = v[nv-l-1];  
  }
  for(i = 0; i < _FVl->nf; i++){
    for(j = 0; j <_FVl->vl[f[i]].nv; j++)
      _FVl_new->vl[i].v[j] = _FVl->vl[f[i]].v[j];
    _FVl_new->vl[i].nv = _FVl->vl[f[i]].nv;
  }
  _FVl_new->nf = _FVl->nf;
  _FVl_new->Nv = _FVl->Nv;
}

void Make_Matrix(XMatrix * _X, XMatrix * _Y, VList *_Vl, 
             PolyPointList *_P,  VertexNumList *_V){
  /* Vl -> Matrix X */ 

  int d, j;

  for (d=0; d < _P->n; d++)
    for (j=0; j < _Vl->nv; j++){ 
      _X->X[d][j] = _P->x[_V->v[_Vl->v[j]]][d];
      _Y->X[d][j] = _P->x[_V->v[_Vl->v[j]]][d];
    }
  _X->d = _P->n; _X->nv = _Vl->nv;
  _Y->d = _P->n; _Y->nv = _Vl->nv;
}

void Copy_PTL(PartList *_IN_PTL, PartList *_OUT_PTL){

  int i, j;
  for(i = 0; i < _IN_PTL->n; i++)
    for(j = 0; j < _IN_PTL->nv; j++)
      _OUT_PTL->S[i][j] = _IN_PTL->S[i][j];
  _OUT_PTL->n = _IN_PTL->n; _OUT_PTL->nv = _IN_PTL->nv; 
  _OUT_PTL->codim = _IN_PTL->codim; 
}

void Select_Sv(int S[], V_Flag *_VF, MMatrix *_M, GMatrix *_G, XMatrix *_X, 
             XMatrix *_Y, M_Rank * _MR, FVList *_FVl, Step step, 
             PartList *_PTL, NEF_Flags* _F){
 
  int i;
  if(Next_Step(_FVl, &step)){
    if(step.v == 0)
      Zero_M_Rank(_MR, &step.f);
    if(!New_V(_VF, &_FVl->vl[step.f].v[step.v])){
      if (_F->Test){
      char c;
      fprintf(outFILE, "\nold vertex f:%d v:%d\n",step.f,step.v);
      scanf("%c",&c);
      }
      if((_MR->m[step.f] == _M[step.f].d) || 
       (_Y[step.f].X[_MR->m[step.f]][step.v] == 0)){
      if(Check_Consistence(&step, _Y, _M, S, _MR, _FVl)){
        if (_F->Test)
          fprintf(outFILE, "f:%d v:%d consistent\n",step.f,step.v);
                Select_Sv(S, _VF, _M, _G, _X, _Y, _MR, _FVl, step, _PTL, _F);
      }
      }
      else{
      if(Fix_M(&step, _Y, _M, S, _MR, _FVl)){
        if (_F->Test)
          fprintf(outFILE, "f:%d v:%d fixed\n",step.f,step.v);
        Raise_M_Rank(_MR, &step.f); 
        Select_Sv(S, _VF, _M, _G, _X, _Y, _MR, _FVl, step, _PTL, _F);
        }
      }
    }
    else{
      if (_F->Test){
      fprintf(outFILE, "\nnew vertex f:%d v:%d",step.f,step.v);
      }
      New_VFlag(_VF,  /* &_FVl->Nv,*/  &_FVl->vl[step.f].v[step.v]);
      for(i = 0; i < _M[step.f].codim; i++){
      S[_FVl->vl[step.f].v[step.v]] = i;
      if (_F->Test)
        fprintf(outFILE, "to partition: %d\n",i);
            if((_MR->m[step.f] == _M[step.f].d) || 
         (_Y[step.f].X[_MR->m[step.f]][step.v] == 0)){
              if(Check_Consistence(&step, _Y, _M, S, _MR, _FVl)){
          if (_F->Test)     
            fprintf(outFILE, "f:%d v:%d consistent\n",step.f,step.v);
                Select_Sv(S, _VF, _M, _G, _X, _Y, _MR, _FVl, step, _PTL, _F);
              }
      }
      else{
        if(Fix_M(&step, _Y, _M, S, _MR, _FVl)){
          if (_F->Test)
            fprintf(outFILE, "f:%d v:%d fixed\n",step.f,step.v);
          Raise_M_Rank(_MR, &step.f);
          Select_Sv(S, _VF, _M, _G, _X, _Y, _MR, _FVl, step, _PTL, _F);
          Lower_M_Rank(_MR, &step.f);
        }
      }     
      }
      Old_VFlag(_VF, /* &_FVl->Nv, */ &_FVl->vl[step.f].v[step.v]);
    }
  }
  else{
    if(_F->Test){
      fprintf(outFILE, "\n********************************************\n");
      for(i = 0; i < _FVl->Nv; i++)
      fprintf(outFILE, " %d ", S[i]);
      fprintf(outFILE, "\n");
      fprintf(outFILE, "**********************************************\n");
      fflush(0);
    }
    if (Codim_Check(S, &_M[step.f-1].codim, &_FVl->Nv))
      if (Convex_Check(_M, _G, _X, S, _FVl, _F)){
      assert(_PTL->n < Nef_Max);
      for(i = 0; i < _FVl->Nv; i++)
        _PTL->S[_PTL->n][i] = S[i];
      _PTL->n += 1;
      }
  }
}

void part_nef(PolyPointList *_P, VertexNumList *_V, EqList *_E, 
            PartList *_OUT_PTL, int *_codim, NEF_Flags* _F){

  FaceInfo I;
  FVList FVl_temp, FVl;
  XMatrix *_X, *_Y;
  MMatrix *_M;
  GMatrix *_G;
  Step step;
  V_Flag VF;
  M_Rank MR;
  int i, f[FACE_Nmax], S[VERT_Nmax] = {0}; 

  PartList *_PTL = (PartList *) malloc(sizeof(PartList));
  assert(_PTL != NULL);

  Make_Incidence(_P, _V, _E, &I);

  FVl.vl = (VList *) calloc(I.nf[_P->n - 1], sizeof(VList));
  assert(FVl.vl != NULL);

  if (_F->Sort){
    FVl_temp.vl = (VList *) calloc(I.nf[_P->n - 1], sizeof(VList));
    assert(FVl_temp.vl != NULL);
    INCI_To_FVList(&I, _P, &FVl_temp);   
    Sort_FVList(&FVl_temp, &FVl, f);
    free(FVl_temp.vl);
  }
  else
    INCI_To_FVList(&I, _P, &FVl);
  if (_F->Test){
    Print_VL(_P, _V, "Vertices of P:");
    Print_FVl(&FVl, "Facets/Vertices:");
  }
  _X = (XMatrix *) calloc(FVl.nf, sizeof(XMatrix)); 
  assert(_X != NULL);
  _Y = (XMatrix *) calloc(FVl.nf, sizeof(XMatrix)); 
  assert(_Y != NULL); 
  _M = (MMatrix *) calloc(FVl.nf, sizeof(MMatrix)); 
  assert(_M != NULL);
  _G = (GMatrix *) calloc(FVl.nf, sizeof(GMatrix)); 
  assert(_G != NULL); 

  for(i = 0; i < FVl.nf; i++){
    Make_Matrix(&_X[i], &_Y[i], &FVl.vl[i], _P, _V);  
    GLZ_Make_Trian_NF(_Y[i].X, &_P->n, &FVl.vl[i].nv, _G[i].G);
  }  
  Initial_Conditions(_M, _Y, &MR, &step, &FVl, &VF, S, _codim, &_P->n, _PTL);
  Select_Sv(S, &VF, _M, _G, _X, _Y, &MR, &FVl, step, _PTL, _F);
  free(_X); free(_Y); free(_M); free(_G); free(FVl.vl);
  if(_F->Sym){
    SYM *_VP = (SYM *) malloc(sizeof(SYM));
    assert(_VP != NULL);
    
    Poly_Sym(_P, _V, _E, &_VP->ns, _VP->Vp);
    Remove_Sym(_VP, _PTL, _OUT_PTL);
    free(_VP);
  }
  else
    Copy_PTL(_PTL, _OUT_PTL);
  /*Dir_Product(_OUT_PTL, _V, _P);*/
  if(*_codim > 1)
    REC_Dir_Product(_OUT_PTL, _V, _P);
  free(_PTL);
}

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