source: branches/items/GDE/PHYML/lk.c

/*

PHYML :  a program that  computes maximum likelihood  phylogenies from
DNA or AA homologous sequences 

Copyright (C) Stephane Guindon. Oct 2003 onward

All parts of  the source except where indicated  are distributed under
the GNU public licence.  See http://www.opensource.org for details.

*/

#include "utilities.h"
#include "lk.h"
#include "optimiz.h"
#include "models.h"
#include "free.h"

/* int    LIM_SCALE; */
/* double LIM_SCALE_VAL; */
/* double MDBL_MAX; */
/* double MDBL_MIN; */

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

void Init_Tips_At_One_Site_Nucleotides(char state, double **p_lk)
{
  switch(state){
  case 'A' : (*p_lk)[0]=1.; (*p_lk)[1]=(*p_lk)[2]=(*p_lk)[3]=.0;
    break;
  case 'C' : (*p_lk)[1]=1.; (*p_lk)[0]=(*p_lk)[2]=(*p_lk)[3]=.0;
    break;
  case 'G' : (*p_lk)[2]=1.; (*p_lk)[1]=(*p_lk)[0]=(*p_lk)[3]=.0;
    break;
  case 'T' : (*p_lk)[3]=1.; (*p_lk)[1]=(*p_lk)[2]=(*p_lk)[0]=.0;
    break;
  case 'U' : (*p_lk)[3]=1.; (*p_lk)[1]=(*p_lk)[2]=(*p_lk)[0]=.0;
    break;
  case 'M' : (*p_lk)[0]=(*p_lk)[1]=1.; (*p_lk)[2]=(*p_lk)[3]=.0;
    break;
  case 'R' : (*p_lk)[0]=(*p_lk)[2]=1.; (*p_lk)[1]=(*p_lk)[3]=.0;
    break;
  case 'W' : (*p_lk)[0]=(*p_lk)[3]=1.; (*p_lk)[1]=(*p_lk)[2]=.0;
    break;
  case 'S' : (*p_lk)[1]=(*p_lk)[2]=1.; (*p_lk)[0]=(*p_lk)[3]=.0;
    break;
  case 'Y' : (*p_lk)[1]=(*p_lk)[3]=1.; (*p_lk)[0]=(*p_lk)[2]=.0;
    break;
  case 'K' : (*p_lk)[2]=(*p_lk)[3]=1.; (*p_lk)[0]=(*p_lk)[1]=.0;
    break;
  case 'B' : (*p_lk)[1]=(*p_lk)[2]=(*p_lk)[3]=1.; (*p_lk)[0]=.0;
    break;
  case 'D' : (*p_lk)[0]=(*p_lk)[2]=(*p_lk)[3]=1.; (*p_lk)[1]=.0;
    break;
  case 'H' : (*p_lk)[0]=(*p_lk)[1]=(*p_lk)[3]=1.; (*p_lk)[2]=.0;
    break;
  case 'V' : (*p_lk)[0]=(*p_lk)[1]=(*p_lk)[2]=1.; (*p_lk)[3]=.0;
    break;
  case 'N' : case 'X' : case '?' : case 'O' : case '-' : 
    (*p_lk)[0]=(*p_lk)[1]=(*p_lk)[2]=(*p_lk)[3]=1.;break;
  default : 
    {
      printf("\n. Unknown character state : %c\n",state);
      Exit("\n. Init failed (check the data type)\n"); 
      break;
    }
  }
}

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

void Init_Tips_At_One_Site_AA(char aa, double **p_lk)
{
  int i;

  For(i,20) (*p_lk)[i] = .0;

  switch(aa){
  case 'A' : (*p_lk)[0]= 1.; break;/* Alanine */
  case 'R' : (*p_lk)[1]= 1.; break;/* Arginine */
  case 'N' : (*p_lk)[2]= 1.; break;/* Asparagine */
  case 'D' : (*p_lk)[3]= 1.; break;/* Aspartic acid */
  case 'C' : (*p_lk)[4]= 1.; break;/* Cysteine */
  case 'Q' : (*p_lk)[5]= 1.; break;/* Glutamine */
  case 'E' : (*p_lk)[6]= 1.; break;/* Glutamic acid */ 
  case 'G' : (*p_lk)[7]= 1.; break;/* Glycine */
  case 'H' : (*p_lk)[8]= 1.; break;/* Histidine */ 
  case 'I' : (*p_lk)[9]= 1.; break;/* Isoleucine */
  case 'L' : (*p_lk)[10]=1.; break;/* Leucine */
  case 'K' : (*p_lk)[11]=1.; break;/* Lysine */
  case 'M' : (*p_lk)[12]=1.; break;/* Methionine */
  case 'F' : (*p_lk)[13]=1.; break;/* Phenylalanin */
  case 'P' : (*p_lk)[14]=1.; break;/* Proline */
  case 'S' : (*p_lk)[15]=1.; break;/* Serine */
  case 'T' : (*p_lk)[16]=1.; break;/* Threonine */
  case 'W' : (*p_lk)[17]=1.; break;/* Tryptophan */
  case 'Y' : (*p_lk)[18]=1.; break;/* Tyrosine */
  case 'V' : (*p_lk)[19]=1.; break;/* Valine */
    
  case 'B' : (*p_lk)[2]= 1.; break;/* Asparagine */
  case 'Z' : (*p_lk)[5]= 1.; break;/* Glutamine */

  case 'X' : case '?' : case '-' : For(i,20) (*p_lk)[i] = 1.; break;
  default : 
    {
      printf("\n. Unknown character state : %c\n",aa);
      Exit("\n. Init failed (check the data type)\n");  
      break;
    }
  }
}

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

void Get_All_Partial_Lk(arbre *tree, edge *b_fcus, node *a, node *d)
{
  int i,j;
  double p1_lk1,p2_lk2;
  double ***p_lk,***p_lk_v1,***p_lk_v2;
  int catg,site;
  double ***Pij1,***Pij2;
  
  if(d->tax) return;
  else
    {
      int dir1,dir2;
      
      dir1=dir2=-1;
      For(i,3) if(d->v[i] != a) (dir1<0)?(dir1=i):(dir2=i);

      if(b_fcus->l < BL_MIN) b_fcus->l = BL_MIN;

      p_lk = 
        (d == b_fcus->left)?
        (b_fcus->p_lk_left):
        (b_fcus->p_lk_rght);
      
      p_lk_v1 = 
        (d == d->b[dir1]->left)?
        (d->b[dir1]->p_lk_rght):
        (d->b[dir1]->p_lk_left);
      
      p_lk_v2 = 
        (d == d->b[dir2]->left)?
        (d->b[dir2]->p_lk_rght):
        (d->b[dir2]->p_lk_left);
      
      Pij1 = d->b[dir1]->Pij_rr;
      Pij2 = d->b[dir2]->Pij_rr;
      
      For(catg,tree->mod->n_catg)
        {         
          For(site,tree->n_pattern)
            {
              For(i,tree->mod->ns) /*sort sum terms ? No global effect*/
                {
                  p1_lk1 = p2_lk2 = .0;
                  For(j,tree->mod->ns)
                    {
                      p1_lk1 += (Pij1[catg][i][j] * p_lk_v1[site][catg][j]);
                      p2_lk2 += (Pij2[catg][i][j] * p_lk_v2[site][catg][j]);
                    }

                  p_lk[site][catg][i] = p1_lk1*p2_lk2;

                  
                  if(p_lk[site][catg][i] < MDBL_MIN) 
                    {
                      printf("\nWARNING : scaling is required at site %d\n",site);
                      /*          printf("Alpha = %f\n",tree->mod->alpha); */
                      /*          Exit(""); */
                    }
                }
            }
        }
   
    }
}

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

void Get_All_Partial_Lk_Scale(arbre *tree, edge *b_fcus, node *a, node *d)
{
  int i,j;
  double p1_lk1,p2_lk2;
  double ***p_lk,***p_lk_v1,***p_lk_v2;
  int catg,site;
  double ***Pij1,***Pij2;
  double max_p_lk;
/*   double min_p_lk; */
  double sum_scale_d1,sum_scale_d2;
  double try;
  
  p1_lk1 = p2_lk2 = .0;
  if(d->tax) return;
  else
    {
      int dir1,dir2;
      
      dir1=dir2=-1;
      For(i,3) if(d->v[i] != a) (dir1<0)?(dir1=i):(dir2=i);

      if(b_fcus->l < BL_MIN) b_fcus->l = BL_MIN;

      p_lk = 
        (d == b_fcus->left)?
        (b_fcus->p_lk_left):
        (b_fcus->p_lk_rght);
      
      p_lk_v1 = 
        (d == d->b[dir1]->left)?
        (d->b[dir1]->p_lk_rght):
        (d->b[dir1]->p_lk_left);
      
      p_lk_v2 = 
        (d == d->b[dir2]->left)?
        (d->b[dir2]->p_lk_rght):
        (d->b[dir2]->p_lk_left);
      
      Pij1 = d->b[dir1]->Pij_rr;
      Pij2 = d->b[dir2]->Pij_rr;

      

      For(site,tree->n_pattern)
        {         
          sum_scale_d1 = sum_scale_d2 = .0;

          (d == d->b[dir1]->left)?
            (sum_scale_d1 = d->b[dir1]->sum_scale_f_rght[site]):
            (sum_scale_d1 = d->b[dir1]->sum_scale_f_left[site]);
          
          (d == d->b[dir2]->left)?
            (sum_scale_d2 = d->b[dir2]->sum_scale_f_rght[site]):
            (sum_scale_d2 = d->b[dir2]->sum_scale_f_left[site]);

          (d == b_fcus->left)?
            (b_fcus->sum_scale_f_left[site] = sum_scale_d1 + sum_scale_d2):
            (b_fcus->sum_scale_f_rght[site] = sum_scale_d1 + sum_scale_d2);
        
/*        min_p_lk = MDBL_MAX; */
          max_p_lk = MDBL_MIN;
          For(catg,tree->mod->n_catg)
            {
              For(i,tree->mod->ns) /*sort sum terms ? No global effect*/
                {
                  p1_lk1 = p2_lk2 = .0;
                  For(j,tree->mod->ns)
                    {
                      p1_lk1 += (Pij1[catg][i][j] * p_lk_v1[site][catg][j]);
                      p2_lk2 += (Pij2[catg][i][j] * p_lk_v2[site][catg][j]);
                    }
                  
                  try = p1_lk1*p2_lk2;
                  
                  p_lk[site][catg][i]=try;

                  if((p_lk[site][catg][i] > max_p_lk)) max_p_lk = p_lk[site][catg][i];

/*                if((p_lk[site][catg][i] < min_p_lk)) min_p_lk = p_lk[site][catg][i]; */
                }
            }

          
          if(max_p_lk < LIM_SCALE_VAL)
            {
              For(catg,tree->mod->n_catg)
                {
                  For(i,tree->mod->ns)
                    {
                      p_lk[site][catg][i] /= max_p_lk;

                      if(p_lk[site][catg][i] > MDBL_MAX)
                        {
                          Exit("\n. Numerical underflow ! (send me an e-mail : s.guindon@auckland.ac.nz)\n");
/*                        p_lk[site][catg][i] = p_lk[site][catg-1][i] ; */
                        }
                    }
                }

              (d == b_fcus->left)?
                (b_fcus->sum_scale_f_left[site] += log(max_p_lk)):
                (b_fcus->sum_scale_f_rght[site] += log(max_p_lk));
            }

          if(max_p_lk > (1./LIM_SCALE_VAL))
            {
              For(catg,tree->mod->n_catg)
                {
                  For(i,tree->mod->ns)
                    {
                      p_lk[site][catg][i] /= max_p_lk;

                      if(p_lk[site][catg][i] < MDBL_MIN)
                        {
                          Exit("\n. Numerical overflow ! (send me an e-mail : s.guindon@auckland.ac.nz)\n");
/*                        p_lk[site][catg][i] = p_lk[site][catg-1][i] ; */
                        }
                    }
                }

              (d == b_fcus->left)?
                (b_fcus->sum_scale_f_left[site] += log(max_p_lk)):
                (b_fcus->sum_scale_f_rght[site] += log(max_p_lk));
            }
        }
    }
}


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

void Post_Order_Lk(node *pere, node *fils, arbre *tree)
{
  int i,dir1,dir2,dir3;

  dir1 = dir2 = dir3 = -1;

  if(fils->tax) return;
  else
    {
      For(i,3)
        {
          if(fils->v[i] != pere)
            {
              Post_Order_Lk(fils,fils->v[i],tree);
              if(dir1 < 0) dir1 = i;
              else dir2 = i;
            }
          else dir3 = i;
        }

      (tree->n_otu > LIM_SCALE)?
        (Get_All_Partial_Lk_Scale(tree,fils->b[dir3],pere,fils)):
        (Get_All_Partial_Lk(tree,fils->b[dir3],pere,fils));
    }
}

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

void Pre_Order_Lk(node *pere, node *fils, arbre *tree)
{
  int i,j,dir1,dir2;

  dir1 = dir2 = -1;
  
  if(fils->tax) return;
  else
    {
      For(i,3)
        {
          if(fils->v[i] != pere)
            {
              For(j,3)
                {
                  if(j != i)
                    {
                      if(dir1 < 0) dir1 = j;
                      else dir2 = j;
                    }
                }
              
              (tree->n_otu > LIM_SCALE)?
              (Get_All_Partial_Lk_Scale(tree,fils->b[i],fils->v[i],fils)):
              (Get_All_Partial_Lk(tree,fils->b[i],fils->v[i],fils));
              dir1 = dir2 = -1;
              Pre_Order_Lk(fils,fils->v[i],tree);
            }
        }
    }
}

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

void Lk(arbre *tree,allseq *alldata)
{
  int br,site,catg;
  double len;

  Set_Model_Parameters(tree);
  
  For(br,2*tree->n_otu-3) 
    {
      For(site,tree->n_pattern)
        {
          tree->t_edges[br]->sum_scale_f_rght[site] = .0;
          tree->t_edges[br]->sum_scale_f_left[site] = .0;
        }

      
      if(tree->t_edges[br]->l < BL_MIN) tree->t_edges[br]->l = BL_MIN;

      if(tree->t_edges[br]->l > BL_MAX) tree->t_edges[br]->l = BL_MAX;



      For(catg,tree->mod->n_catg)
        {
          len = tree->t_edges[br]->l*tree->mod->rr[catg];
          if(len < BL_MIN) len = BL_MIN;

          PMat(len,
               tree->mod,
               &tree->t_edges[br]->Pij_rr[catg]);
          
        }
    }

  Post_Order_Lk(tree->noeud[0],tree->noeud[0]->v[0],tree);
  if(tree->both_sides)
    Pre_Order_Lk(tree->noeud[0],
                  tree->noeud[0]->v[0],
                  tree);

  tree->tot_loglk = .0;    
  tree->curr_catg =  0;
  tree->curr_site =  0;

  For(site,tree->n_pattern)
    {
      tree->tot_loglk_sorted[site] = .0;
      tree->site_lk[site]          = .0;
      tree->curr_site              = site;
      Site_Lk(tree,alldata);
    }

  qksort(tree->tot_loglk_sorted, 0, tree->n_pattern-1);
/*   qsort(tree->tot_loglk_sorted,tree->n_pattern,sizeof(double),Sort_Double_Decrease); */

  tree->tot_loglk = .0;
  For(site, tree->n_pattern)
    {
      if(tree->tot_loglk_sorted[site] < .0) /* WARNING : change cautiously */
        tree->tot_loglk += tree->tot_loglk_sorted[site];
    }


  For(br,2*tree->n_otu-3)
    {
      if(tree->t_edges[br]->get_p_lk_left) tree->t_edges[br]->ud_p_lk_left = 1;
      if(tree->t_edges[br]->get_p_lk_rght) tree->t_edges[br]->ud_p_lk_rght = 1;
    }
}

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

void Site_Lk(arbre *tree, allseq *alldata)
{
  int j,k,l,m;
  double *site_dlk=NULL, *site_d2lk=NULL;
  double log_site_lk,site_lk,site_lk_previous,aux;
  int left;
  edge *eroot;
  int is_ambigu;
  int state_root, state_elsewhere, site = tree->curr_site;


  if(alldata->wght[site] < MDBL_MIN) 
    {
      tree->tot_loglk_sorted[tree->curr_site] = 1.; /* WARNING : change cautiously */ 
      return;
    }


  if(tree->mod->s_opt->opt_bl)
    {
      site_dlk = (double *)mCalloc(2*tree->n_otu-3,sizeof(double));
      site_d2lk = (double *)mCalloc(2*tree->n_otu-3,sizeof(double));
    }
  

  eroot = tree->noeud[0]->b[0];
  (eroot->rght->tax)?(left=1):(left=0);
  
/*   state = tree->data->invar[site]; */
  is_ambigu = alldata->ambigu[site];
  
  state_root = -1;
  state_root = Assign_State(alldata->c_seq[eroot->rght->num]->state + site,
                            tree->mod->datatype,
                            tree->mod->stepsize);

  state_elsewhere = -1;
  state_elsewhere = tree->data->invar[site];

  /**/
/*    is_ambigu = 1; */
  /**/
  

  if(tree->mod->s_opt->opt_bl)
    For(j,2*tree->n_otu-3) site_dlk[j] = site_d2lk[j] = 0.0;

  log_site_lk = site_lk = .0;      
  site_lk_previous = .0;

  For(j,tree->mod->n_catg)
    {
      if(is_ambigu)
        {
          For(k,tree->mod->ns) /*sort sum terms ? No global effect*/
            {
              For(l,tree->mod->ns)
                {
                  site_lk += 
                    tree->mod->r_proba[j] *
                    tree->mod->pi[k] *
                    eroot->p_lk_left[site][j][k] *
                    eroot->Pij_rr[j][k][l] *
                    eroot->p_lk_rght[site][j][l];
                }
            }
        }
      else
        {
          For(k,tree->mod->ns) /*sort sum terms ? No global effect*/
            {
              site_lk +=
                tree->mod->r_proba[j] *
                tree->mod->pi[k] * 
                eroot->p_lk_left[site][j][k] *
                eroot->Pij_rr[j][k][state_root];            
            }
        }

      tree->log_site_lk_cat[j][tree->curr_site] = (site_lk/tree->mod->r_proba[j] - site_lk_previous);
      site_lk_previous = site_lk/tree->mod->r_proba[j];
      
      if(tree->mod->s_opt->opt_bl)
        {
          For(k,2*tree->n_otu-3)
            {  
              tree->t_edges[k]->site_dlk_rr[j] = .0;
              tree->t_edges[k]->site_d2lk_rr[j] = .0;

              For(l,tree->mod->ns) /*sort sum terms ? No global effect*/
                {
                  For(m,tree->mod->ns)
                    {
                      tree->t_edges[k]->site_dlk_rr[j] += 
                        tree->mod->pi[l] * 
                        tree->t_edges[k]->p_lk_left[site][j][l]*
                        tree->t_edges[k]->p_lk_rght[site][j][m]*
                        tree->t_edges[k]->dPij_rr[j][l][m];
                      

                      tree->t_edges[k]->site_d2lk_rr[j] += 
                        tree->mod->pi[l] * 
                        tree->t_edges[k]->p_lk_left[site][j][l]*
                        tree->t_edges[k]->p_lk_rght[site][j][m]*
                        tree->t_edges[k]->d2Pij_rr[j][l][m];
                    }
                }

              site_dlk[k]  += tree->t_edges[k]->site_dlk_rr[j]*
                              tree->mod->r_proba[j];
              
              site_d2lk[k] += tree->t_edges[k]->site_d2lk_rr[j]*
                              tree->mod->r_proba[j];
            }
        }   
    }
  


  /* code 2.3 begin*/

  if (!tree->mod->invar)
    {
      log_site_lk += log(site_lk) 
        + eroot->sum_scale_f_left[site] + eroot->sum_scale_f_rght[site];
    }
  else
    {
      if ((double)tree->data->invar[site] > -0.5)
        {
          if (!(eroot->sum_scale_f_left[site] + eroot->sum_scale_f_rght[site]==0.0))
            site_lk *= exp(eroot->sum_scale_f_left[site] + eroot->sum_scale_f_rght[site]);
          
          log_site_lk = log(site_lk*(1.0-tree->mod->pinvar) + tree->mod->pinvar*tree->mod->pi[state_elsewhere]);
        }
      else
        {
          log_site_lk = log(site_lk*(1.0-tree->mod->pinvar))
            + eroot->sum_scale_f_left[site] + eroot->sum_scale_f_rght[site];
        }
    }

  For(j,tree->mod->n_catg)
    tree->log_site_lk_cat[j][tree->curr_site] = log(tree->log_site_lk_cat[j][tree->curr_site]) +
    + eroot->sum_scale_f_left[site] + eroot->sum_scale_f_rght[site];


  /* code 2.3 end*/
  
  if(log_site_lk < -MDBL_MAX)
    {
      printf("%d %E %f %f %f %f\n",
             site,
             log_site_lk,
             tree->mod->alpha,
             eroot->sum_scale_f_left[site],
             eroot->sum_scale_f_rght[site],
             tree->mod->pinvar);
      Exit("\nlog_site_lk < -MDBL_MAX\n");
    }


  tree->site_lk[site] = log_site_lk;
  
  
  if(tree->mod->s_opt->opt_bl)
    {
      For(k,2*tree->n_otu-3)
        {
          aux = exp(tree->t_edges[k]->sum_scale_f_rght[site]+
                    tree->t_edges[k]->sum_scale_f_left[site]);
          site_dlk[k]  *= aux;
          site_d2lk[k] *= aux;
          
          tree->t_edges[k]->site_dlk = site_dlk[k];
          tree->t_edges[k]->site_d2lk = site_d2lk[k];     
        }
    }
  
/*   tree->tot_loglk += alldata->wght[site]*log_site_lk; */
  tree->tot_loglk_sorted[site] = alldata->wght[site]*log_site_lk;


  if((tree->mod->s_opt->opt_bl) &&
     (fabs(site_lk = exp(log_site_lk)) > sqrt(MDBL_MIN)))
    {
      For(k,2*tree->n_otu-3)
        {
          aux = site_dlk[k] / site_lk;
          tree->tot_dloglk[k]  += alldata->wght[site] 
                               *  aux;
          tree->tot_d2loglk[k] += alldata->wght[site]
                               * (site_d2lk[k]/site_lk
                               -  aux*aux);
        }
    }

  if(tree->mod->s_opt->opt_bl)
    {
      Free(site_dlk);
      Free(site_d2lk);
    }
}

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

double Lk_At_Given_Edge(arbre *tree, edge *b_fcus)
{
  int site,catg,k,l,edge_num, ns = tree->mod->ns;
  double site_lk,log_site_lk,site_dlk,site_d2lk,aux;

  edge_num = b_fcus->num;
  tree->tot_loglk = log_site_lk = .0;
  tree->tot_dloglk[edge_num] = tree->tot_d2loglk[edge_num] = .0;
  tree->n_pattern = tree->data->crunch_len/tree->mod->stepsize;


  if(b_fcus->l < BL_MIN) b_fcus->l = BL_MIN;
  if(b_fcus->l > BL_MAX) b_fcus->l = BL_MAX;
  
  For(catg,tree->mod->n_catg)
    {
      aux = b_fcus->l*tree->mod->rr[catg];
      if(aux < BL_MIN) aux = BL_MIN;
      PMat(aux, tree->mod,&b_fcus->Pij_rr[catg]);
    }


  if((tree->mod->s_opt->opt_bl) && (tree->mod->datatype == NT))
    {
      For(catg,tree->mod->n_catg)
        {
          dPMat(tree->t_edges[edge_num]->l,
                tree->mod->rr[catg],
                tree->mod,
                &b_fcus->dPij_rr[catg]);
          d2PMat(tree->t_edges[edge_num]->l,
                 tree->mod->rr[catg],
                 tree->mod,
                 &b_fcus->d2Pij_rr[catg]);
        }
    }


  For(site,tree->data->crunch_len)
    {
      if(tree->data->wght[site])
        {
          log_site_lk = site_lk = .0;
          /* see equation (2) in phyml_tech_doc.pdf */
          For(catg,tree->mod->n_catg)
            {
              For(k,ns) /*sort sum terms ? No global effect*/
                {
                  For(l,ns)
                    {
                      site_lk += 
                        tree->mod->r_proba[catg] *
                        tree->mod->pi[k] * 
                        b_fcus->p_lk_left[site][catg][k] *
                        b_fcus->p_lk_rght[site][catg][l] *
                        b_fcus->Pij_rr[catg][k][l];
                    }
                }
            }

          /* code 2.3 begin*//* see equations in phyml_tech_doc.pdf */
          /* compute log_site_lk */
          if (!tree->mod->invar)
            {
              log_site_lk += log(site_lk) 
                + b_fcus->sum_scale_f_left[site] + b_fcus->sum_scale_f_rght[site];
            }
          else
            {
              if ((double)tree->data->invar[site] > -0.5)
                {
                  if (!(b_fcus->sum_scale_f_left[site] + b_fcus->sum_scale_f_rght[site]==0.0))
                    site_lk *= exp(b_fcus->sum_scale_f_left[site] + b_fcus->sum_scale_f_rght[site]);
                  
                  log_site_lk = log(site_lk*(1.0-tree->mod->pinvar) + tree->mod->pinvar*tree->mod->pi[tree->data->invar[site]]);
                }
              else
                {
                  log_site_lk = log(site_lk*(1.0-tree->mod->pinvar)) 
                    + b_fcus->sum_scale_f_left[site] + b_fcus->sum_scale_f_rght[site];
                }
            }
          /* code 2.3 end*/

          if(log_site_lk < -MDBL_MAX) Exit("\nlog_site_lk < -MDBL_MAX\n");

          tree->site_lk[site] = log_site_lk;

          /*tree->tot_loglk += *//* old code */
          tree->tot_loglk_sorted[site] = /* code 2.3 */
            tree->data->wght[site]*log_site_lk;
        }
      else tree->tot_loglk_sorted[site] = 1.; /* WARNING : change cautiously */
    }

  /* code 2.3 begin*/
  /* sort and add numbers from smallest to biggest */

  qksort(tree->tot_loglk_sorted, 0, tree->n_pattern-1);
/*   qsort(tree->tot_loglk_sorted,tree->n_pattern,sizeof(double),Sort_Double_Decrease); */

  tree->tot_loglk = .0;
  For(k, tree->data->crunch_len) 
    if(tree->tot_loglk_sorted[k] < .0) /* WARNING : change cautiously */
      tree->tot_loglk += tree->tot_loglk_sorted[k];
  /* code 2.3 end*/
  
  if((tree->mod->s_opt->opt_bl) && (tree->mod->datatype == NT))
    {
      For(site,tree->n_pattern)
        {
          if(tree->data->wght[site])
            {
              site_dlk = site_d2lk = .0;      
              b_fcus->site_dlk = b_fcus->site_d2lk = .0; 
              
              For(catg,tree->mod->n_catg)
                {
                  For(k,ns) /*sort sum terms ? No global effect*/
                    {
                      For(l,ns)
                        {
                          aux = tree->mod->r_proba[catg] *
                            tree->mod->pi[k] *
                            b_fcus->p_lk_left[site][catg][k];
                          
                          site_dlk +=
                            aux *
                            b_fcus->p_lk_rght[site][catg][l] *
                            b_fcus->dPij_rr[catg][k][l];
                          
                          site_d2lk +=
                            aux *
                            b_fcus->p_lk_rght[site][catg][l] *
                            b_fcus->d2Pij_rr[catg][k][l];
                        }
                    }
                }

              if(tree->n_otu > LIM_SCALE)
                {
                  aux = exp(b_fcus->sum_scale_f_rght[site]+
                            b_fcus->sum_scale_f_left[site]);
                  site_dlk  *= aux;
                  site_d2lk *= aux;
                }

              b_fcus->site_dlk = site_dlk;
              b_fcus->site_d2lk = site_d2lk;

              if(fabs(exp(log_site_lk)) > sqrt(MDBL_MIN))
                {
                  aux = site_dlk / tree->site_lk[site];
                  tree->tot_dloglk[edge_num]  += tree->data->wght[site] 
                                              * aux;
                  tree->tot_d2loglk[edge_num] += tree->data->wght[site] 
                                              * (site_d2lk/tree->site_lk[site] 
                                              - aux*aux);
                }
            }
        }
    }

  return tree->tot_loglk;
}
  
/*********************************************************/

void Update_P(arbre *tree, int t_edge_num)
{
  int i;
  double len;

  len = -1.0;
  For(i,tree->mod->n_catg)
    {
      tree->curr_catg = i;
      len = tree->t_edges[t_edge_num]->l*tree->mod->rr[i];
      if(len < BL_MIN) len = BL_MIN;
      tree->mod->update_eigen = 0;
      PMat(len,tree->mod,&tree->t_edges[t_edge_num]->Pij_rr[i]);
/*        Derivatives(tree->t_edges[t_edge_num],tree);    */
    }
}

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

double Return_Lk(arbre *tree)
{
  Lk(tree,tree->data);
  return tree->tot_loglk;
}

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

double Return_Abs_Lk(arbre *tree)
{
  Lk(tree,tree->data);
  return fabs(tree->tot_loglk);
}

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

matrix *ML_Dist(allseq *data, model *mod)
{
  int j,k,l;
  double init;
  int n_catg;
  double d_max;
  matrix *mat;
  allseq *twodata,*tmpdata;

  tmpdata = (allseq *)mCalloc(1,sizeof(allseq));
  tmpdata->n_otu=2;
  tmpdata->c_seq = (seq **)mCalloc(2,sizeof(seq *));
  tmpdata->b_frq = (double *)mCalloc(mod->ns,sizeof(double));
  tmpdata->ambigu = (int *)mCalloc(data->crunch_len,sizeof(int));

  tmpdata->crunch_len = tmpdata->init_len = data->crunch_len;


  mat = 
    (mod->datatype == NT) ?
    ((mod->whichmodel < 10)?(K2P_dist(data,2000)):(JC69_Dist(data,mod))):
    (JC69_Dist(data,mod));

  n_catg = -1;

 
  For(j,data->n_otu-1)
    {
      tmpdata->c_seq[0]=data->c_seq[j];
      tmpdata->c_seq[0]->name=data->c_seq[j]->name;
      tmpdata->wght = data->wght;

      for(k=j+1;k<data->n_otu;k++)
        {
          tmpdata->c_seq[1]=data->c_seq[k];
          tmpdata->c_seq[1]->name=data->c_seq[k]->name;

          twodata = Compact_CSeq(tmpdata,mod);
          For(l,mod->ns) twodata->b_frq[l]=data->b_frq[l];

          Check_Ambiguities(twodata,mod->datatype,1);

          Hide_Ambiguities(twodata);      

          init = mat->dist[j][k];
          if((init == DIST_MAX) || (init < .0)) init = 0.1;


          n_catg = mod->n_catg;
          mod->n_catg = 1;


/* BRENT */
          d_max = Optimize_Dist(mod,init,twodata);

/*        d_max = init; */

/* NEWTON-RAPHSON */
/*        if(d_max < .0) */
/*          { */
/*            d_max =  Optimize_One_Dist(twodata,0,1,init,mod); */
/*            d_max = init; */

/*          } */

          mod->n_catg = n_catg;


          if(d_max >= DIST_MAX) 
            {
              printf("\n. Large distance encountered between %s and %s sequences\n",
                     tmpdata->c_seq[1]->name,
                     tmpdata->c_seq[0]->name);
              d_max = DIST_MAX;
            }

          mat->dist[j][k] = d_max;
          mat->dist[k][j] = mat->dist[j][k];
          Free_Cseq(twodata);
        }
    }
 

  Free(tmpdata->ambigu);
  Free(tmpdata->b_frq);
  Free(tmpdata->c_seq);
  free(tmpdata);

  return mat;
}

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

double Lk_Given_Two_Seq(allseq *data, int numseq1, int numseq2, double dist, model *mod,
                        double *loglk, double *dloglk, double *d2loglk)
{
  seq *seq1,*seq2;
  double site_lk,site_dlk,site_d2lk,log_site_lk;
  int i,j,k,l;
  double **p_lk_l,**p_lk_r;
  double len;

  DiscreteGamma (mod->r_proba, mod->rr, mod->alpha,
                 mod->alpha,mod->n_catg,0);



  seq1 = data->c_seq[numseq1];
  seq2 = data->c_seq[numseq2];

  p_lk_l = (double **)mCalloc(data->c_seq[0]->len,sizeof(double *));
  p_lk_r = (double **)mCalloc(data->c_seq[0]->len,sizeof(double *));

  For(i,data->c_seq[0]->len)
    {
      p_lk_l[i] = (double *)mCalloc(mod->ns,sizeof(double));
      p_lk_r[i] = (double *)mCalloc(mod->ns,sizeof(double));
    }


  if(dist < BL_MIN) dist = BL_START;

  For(i,mod->n_catg) 
    {
      len = dist*mod->rr[i];
      if(len < BL_MIN) len = BL_MIN;
      PMat(len,mod,&(mod->Pij_rr[i]));        
    }


  if(mod->datatype == NT)
    {
      For(i,mod->n_catg) 
        {
          dPMat(dist,mod->rr[i],mod,&(mod->dPij_rr[i]));      
          d2PMat(dist,mod->rr[i],mod,&(mod->d2Pij_rr[i]));      
        }

      For(i,data->c_seq[0]->len)
        {
          Init_Tips_At_One_Site_Nucleotides(seq1->state[i],
                                            &p_lk_l[i]);
          Init_Tips_At_One_Site_Nucleotides(seq2->state[i],
                                            &p_lk_r[i]);
        }
    }
  else
    {
      For(i,data->c_seq[0]->len)
        {
          Init_Tips_At_One_Site_AA(seq1->state[i],
                                   &p_lk_l[i]);
          Init_Tips_At_One_Site_AA(seq2->state[i],
                                   &p_lk_r[i]);
        }
    }
    

  site_lk = site_dlk = site_d2lk = .0;
  *loglk = *dloglk = *d2loglk = 0;

  For(i,data->c_seq[0]->len)
    {
      if(data->wght[i])
        {
          site_lk = log_site_lk = .0;
          if(!data->ambigu[i])
            {
              For(k,mod->ns) {if(p_lk_l[i][k] > .0001) break;}
              For(l,mod->ns) {if(p_lk_r[i][l] > .0001) break;}
              For(j,mod->n_catg)
                {
                  site_lk +=
                    mod->r_proba[j] *
                    mod->pi[k] *
                    p_lk_l[i][k] *
                    mod->Pij_rr[j][k][l] *
                    p_lk_r[i][l];
                }
            }
          else
            {
              For(j,mod->n_catg)
                {
                  For(k,mod->ns) /*sort sum terms ? No global effect*/
                    {
                      For(l,mod->ns)
                        {
                          site_lk += 
                            mod->r_proba[j] *
                            mod->pi[k] * 
                            p_lk_l[i][k] *
                            mod->Pij_rr[j][k][l] *
                            p_lk_r[i][l]; 
                        }
                    }
                }
            }

/*        printf("'%c' '%c' -> %f\n",seq1->state[i],seq2->state[i],site_lk); */

          if(site_lk <= .0) 
            {
              printf("'%c' '%c'\n",seq1->state[i],seq2->state[i]);
              Exit("\n. Err: site lk <= 0\n");
            }

          log_site_lk += log(site_lk);

          *loglk   += data->wght[i] * log_site_lk;/* sort sum terms ? No global effect*/
        }
    }

  For(i,data->c_seq[0]->len)
    {
      Free(p_lk_l[i]);
      Free(p_lk_r[i]);
    }
  Free(p_lk_l); Free(p_lk_r);
  return *loglk;
}

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

double ***Get_Partial_Lk_Struct(arbre *tree, int len, int n_catg)
{
  double ***p_lk;
  int j,k;

  p_lk = (double ***)mCalloc(len,sizeof(double **)); 
  For(j,len)
    {
      p_lk[j] = (double **)mCalloc((int)n_catg,sizeof(double *));
      For(k,n_catg) p_lk[j][k] = (double *)mCalloc(tree->mod->ns,sizeof(double ));
    }
  return p_lk;
}

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

void Unconstraint_Lk(arbre *tree)
{
  int i;

  tree->unconstraint_lk = .0;

  For(i,tree->data->crunch_len)
    {
      tree->unconstraint_lk += 
        tree->data->wght[i]*log(tree->data->wght[i]);
    }
  tree->unconstraint_lk -= 
    tree->data->init_len*log(tree->data->init_len);
}

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

void Update_P_Lk(arbre *tree, edge *b_fcus, node *n)
{
/*  
           |
           |<- b_cus
           |
           n
          / \
         /   \
        /     \
*/

  int k,l;
  int site, catg;
  double ***p_lk, ***p_lk_v1, ***p_lk_v2;
  double **Pij1, **Pij2;
  double *n_scale_f, *d1_scale_f, *d2_scale_f;
  double p1_lk1,p2_lk2;
  double max_p_lk;
  edge *b1, *b2;

  
  b1 = b2  = NULL;
  p_lk = p_lk_v1 = p_lk_v2 = NULL;
  max_p_lk = MDBL_MIN;


  if(n == b_fcus->left)
    {
/*       if(b_fcus->ud_p_lk_left) { printf("This p_lk is up to date\n"); return;} */
      p_lk = b_fcus->p_lk_left;
      
      p_lk_v1 = 
      (n == n->b[b_fcus->l_v1]->left)?
      (n->b[b_fcus->l_v1]->p_lk_rght):
      (n->b[b_fcus->l_v1]->p_lk_left);

      p_lk_v2 = 
      (n == n->b[b_fcus->l_v2]->left)?
      (n->b[b_fcus->l_v2]->p_lk_rght):
      (n->b[b_fcus->l_v2]->p_lk_left);


      n_scale_f = b_fcus->sum_scale_f_left;

      d1_scale_f = 
      (n == n->b[b_fcus->l_v1]->left)?
      (n->b[b_fcus->l_v1]->sum_scale_f_rght):
      (n->b[b_fcus->l_v1]->sum_scale_f_left);

      d2_scale_f = 
      (n == n->b[b_fcus->l_v2]->left)?
      (n->b[b_fcus->l_v2]->sum_scale_f_rght):
      (n->b[b_fcus->l_v2]->sum_scale_f_left);
    
      b_fcus->get_p_lk_left = 1;
      b_fcus->ud_p_lk_left  = 1;
    }

  else
    {
      p_lk = b_fcus->p_lk_rght;
      
      p_lk_v1 = 
      (n == n->b[b_fcus->r_v1]->left)?
      (n->b[b_fcus->r_v1]->p_lk_rght):
      (n->b[b_fcus->r_v1]->p_lk_left);

      p_lk_v2 = 
      (n == n->b[b_fcus->r_v2]->left)?
      (n->b[b_fcus->r_v2]->p_lk_rght):
      (n->b[b_fcus->r_v2]->p_lk_left);

      n_scale_f = b_fcus->sum_scale_f_rght;

      d1_scale_f = 
      (n == n->b[b_fcus->r_v1]->left)?
      (n->b[b_fcus->r_v1]->sum_scale_f_rght):
      (n->b[b_fcus->r_v1]->sum_scale_f_left);

      d2_scale_f = 
      (n == n->b[b_fcus->r_v2]->left)?
      (n->b[b_fcus->r_v2]->sum_scale_f_rght):
      (n->b[b_fcus->r_v2]->sum_scale_f_left);

      b_fcus->get_p_lk_rght = 1;
      b_fcus->ud_p_lk_rght  = 1;
    }

  if(b_fcus->l < BL_MIN) b_fcus->l = BL_MIN;
  
 

  if(n == b_fcus->left) 
    {
      b1 = n->b[b_fcus->l_v1];
      b2 = n->b[b_fcus->l_v2];
    }
  else
    {
      b1 = n->b[b_fcus->r_v1];
      b2 = n->b[b_fcus->r_v2];
    }


  if(tree->n_otu <= LIM_SCALE)
    {
      /* NO SCALE */

      For(site,tree->n_pattern)
        {
          if(tree->data->wght[site])
            {
              For(catg,tree->mod->n_catg)
                {
                  
                  Pij1 = b1->Pij_rr[catg];
                  Pij2 = b2->Pij_rr[catg];
                  
                  
                  For(k,tree->mod->ns) /*sort sum terms ? No global effect*/
                    {
                      p1_lk1 = p2_lk2 = .0;
                      
                      For(l,tree->mod->ns)
                        {
                          p1_lk1 += Pij1[k][l] * p_lk_v1[site][catg][l];
                          p2_lk2 += Pij2[k][l] * p_lk_v2[site][catg][l];
                        }
                      p_lk[site][catg][k] = p1_lk1 * p2_lk2;
                    }
                }
            }
        }
    }
  else
    {
      /* SCALE */

      For(site,tree->n_pattern)
        {
          if(tree->data->wght[site])
            {
              For(catg,tree->mod->n_catg)
                {
                  
                  Pij1 = b1->Pij_rr[catg];
                  Pij2 = b2->Pij_rr[catg];
                  
                  if(!catg) 
                    {
                      n_scale_f[site] = d1_scale_f[site] + d2_scale_f[site];
                      max_p_lk = -MDBL_MAX;
                    }
                  
                  For(k,tree->mod->ns) /*sort sum terms ? No global effect*/
                    {
                      p_lk[site][catg][k] = .0;
                      p1_lk1 = p2_lk2     = .0;
                                      
                      For(l,tree->mod->ns)
                        {
                          p1_lk1 += Pij1[k][l] * p_lk_v1[site][catg][l];
                          p2_lk2 += Pij2[k][l] * p_lk_v2[site][catg][l];
                        }

                      p_lk[site][catg][k] = p1_lk1 * p2_lk2;
                      

                      if((p_lk[site][catg][k] > max_p_lk)) max_p_lk = p_lk[site][catg][k];
                      
                    }
                }
                 
              if(max_p_lk < LIM_SCALE_VAL)
                {
                  For(catg,tree->mod->n_catg)
                    {
                      For(k,tree->mod->ns) 
                        {
                          p_lk[site][catg][k] /= max_p_lk;
                          
                          if(p_lk[site][catg][k] > MDBL_MAX)
                            {
                              Exit("\n. Numerical overflow ! (send me an e-mail : s.guindon@auckland.ac.nz)\n");
                            }                     
                        }
                    }
                  n_scale_f[site] += log(max_p_lk);
                }
              
              if(max_p_lk > (1./LIM_SCALE_VAL))
                {
                  For(catg,tree->mod->n_catg)
                    {
                      For(k,tree->mod->ns) 
                        {
                          p_lk[site][catg][k] /= max_p_lk;
                          if(p_lk[site][catg][k] < MDBL_MIN)
                            {
                              printf("\n. Numerical underflow ! (send me an e-mail : s.guindon@auckland.ac.nz)\n");
                            }                     
                        }
                    }
                  n_scale_f[site] += log(max_p_lk);
                }
            }
        }
    }
}

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

void Make_Tree_4_Lk(arbre *tree, allseq *alldata, int n_site)
{
  int i;

  if(!tree->tot_loglk_sorted) tree->tot_loglk_sorted = (double *)mCalloc(tree->n_pattern, sizeof(double));
  if(!tree->tot_dloglk)       tree->tot_dloglk       = (double *)mCalloc(2*tree->n_otu-3,sizeof(double));
  if(!tree->tot_d2loglk)      tree->tot_d2loglk      = (double *)mCalloc(2*tree->n_otu-3,sizeof(double));
  if(!tree->site_lk)          tree->site_lk          = (double *)mCalloc(alldata->crunch_len,sizeof(double));
  if(!tree->log_site_lk_cat)      
    {
      tree->log_site_lk_cat      = (double **)mCalloc(tree->mod->n_catg,sizeof(double *));
      For(i,tree->mod->n_catg)
        tree->log_site_lk_cat[i] = (double *)mCalloc(alldata->crunch_len,sizeof(double));
    }

  tree->root = tree->noeud[0];
 
  For(i,2*tree->n_otu-3)
    {
      Make_Edge_Lk(tree->t_edges[i]->left,
                   tree->t_edges[i]->rght,
                   tree);
    }

  For(i,2*tree->n_otu-2)
    Make_Node_Lk(tree->noeud[i]);

  Alloc_All_P_Lk(tree);
/*   Make_P_Lk_Struct(tree);   */

  Init_P_Lk_Tips(tree);
}

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

void Init_P_Lk_Tips(arbre *tree)
{
  int curr_site,i,j,k;
  

  Fors(curr_site,tree->data->crunch_len,tree->mod->stepsize)
    {
      For(i,tree->n_otu)
        {
          if (tree->mod->datatype == NT)
            {
                Init_Tips_At_One_Site_Nucleotides(tree->data->c_seq[i]->state[curr_site],
                                                  &tree->noeud[i]->b[0]->p_lk_rght[curr_site][0]);
                
            }
          else
            Init_Tips_At_One_Site_AA(tree->data->c_seq[i]->state[curr_site],
                                     &tree->noeud[i]->b[0]->p_lk_rght[curr_site][0]);
          


          if((tree->noeud[i]->b[0]->p_lk_rght) && (tree->noeud[i]->b[0]->get_p_lk_rght))
            {
              for(j=1;j<tree->mod->n_catg;j++)
                {
                  For(k,tree->mod->ns)
                    {
                      tree->noeud[i]->b[0]->p_lk_rght[curr_site][j][k]=
                      tree->noeud[i]->b[0]->p_lk_rght[curr_site][0][k];
                    }
                }
            }
          else
            {
              for(j=1;j<tree->mod->n_catg;j++)
                For(k,tree->mod->ns)
                  tree->noeud[i]->b[0]->p_lk_rght[curr_site][j][k]=
                  tree->noeud[i]->b[0]->p_lk_rght[curr_site][0][k];
            }
        }
    }
}

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