packages feed

ViennaRNA-bindings-0.233.1.1: C/ViennaRNA/2Dpfold.c

/*
      minimum free energy
      RNA secondary structure with
      basepair distance d_1 to reference structure 1 and distance d_2 to reference structure 2

*/

#ifdef HAVE_CONFIG_H
#include "config.h"
#endif

#include <stdio.h>
#include <stdlib.h>
#include <math.h>
#include <ctype.h>
#include <string.h>
#include <float.h>    /* #defines FLT_MAX ... */
#include "ViennaRNA/utils.h"
#include "ViennaRNA/fold_vars.h"
#include "ViennaRNA/params.h"
#include "ViennaRNA/energy_par.h"
#include "ViennaRNA/loop_energies.h"
#include "ViennaRNA/2Dpfold.h"

/*
#################################
# GLOBAL VARIABLES              #
#################################
*/

/*
#################################
# PRIVATE VARIABLES             #
#################################
*/

/*
#################################
# PRIVATE FUNCTION DECLARATIONS #
#################################
*/
PRIVATE void  crosslink(TwoDpfold_vars *vars);

PRIVATE         void  pf2D_linear(vrna_fold_compound_t *vc);
PRIVATE         void  pf2D_circ(vrna_fold_compound_t *vc);
PRIVATE         char  *pbacktrack_circ( vrna_fold_compound_t *vc,
                                        int d1,
                                        int d2);

PRIVATE         void  backtrack(vrna_fold_compound_t *vc,
                                char *pstruc,
                                int d1,
                                int d2,
                                unsigned int i,
                                unsigned int j);
PRIVATE         void  backtrack_qm( vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2,
                                    unsigned int i,
                                    unsigned int j);
PRIVATE         void  backtrack_qm1(vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2,
                                    unsigned int i,
                                    unsigned int j);
PRIVATE         void  backtrack_qm2(vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2,
                                    unsigned int k);
PRIVATE         void  backtrack_qcH(vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2);
PRIVATE         void  backtrack_qcI(vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2);
PRIVATE         void  backtrack_qcM(vrna_fold_compound_t *vc,
                                    char *pstruc,
                                    int d1,
                                    int d2);

PRIVATE         void  adjustArrayBoundaries(
                        FLT_OR_DBL ***array,
                        int *k_min, int *k_max,
                        int **l_min, int **l_max,
                        int k_min_real, int k_max_real,
                        int *l_min_real, int *l_max_real);

INLINE  PRIVATE void  preparePosteriorBoundaries(
                        int size, int shift,
                        int *min_k, int *max_k,
                        int **min_l, int **max_l);
INLINE  PRIVATE void  updatePosteriorBoundaries(
                        int d1, int d2,
                        int *min_k, int *max_k,
                        int **min_l, int **max_l);
INLINE  PRIVATE void  prepareBoundaries(
                        int min_k_pre, int max_k_pre,
                        int min_l_pre, int max_l_pre,
                        int bpdist,
                        int *min_k, int *max_k,
                        int **min_l, int **max_l);
INLINE  PRIVATE void  prepareArray(
                        FLT_OR_DBL ***array,
                        int min_k, int max_k,
                        int *min_l, int *max_l);

/*
#################################
# BEGIN OF FUNCTION DEFINITIONS #
#################################
*/

PUBLIC vrna_sol_TwoD_pf_t *
vrna_pf_TwoD( vrna_fold_compound_t *vc,
                int distance1,
                int distance2){

  unsigned int  maxD1 = 0, maxD2 = 0, counter = 0;
  int           cnt1, cnt2, k_min, k_max, l_min, l_max, ndx;
  FLT_OR_DBL    q = 0.;

  vrna_sol_TwoD_pf_t  *output;
  vrna_md_t           *md;
  vrna_mx_pf_t        *matrices;

  maxD1     = vc->maxD1;
  maxD2     = vc->maxD2;
  matrices  = vc->exp_matrices;
  md        = &(vc->exp_params->model_details);

  if(distance1 >= 0){
    if((unsigned int)distance1 > maxD1)
      vrna_message_warning("vrna_pf_TwoD@2Dpfold.c: limiting maximum basepair distance 1 to %u\n",
                                  maxD1);
    else
      maxD1 = (unsigned int)distance1;
  }

  if(distance2 >= 0){
    if((unsigned int)distance2 > maxD2)
      vrna_message_warning("vrna_pf_TwoD@2Dpfold.c: limiting maximum basepair distance 2 to %u\n",
                                  maxD2);
    else
      maxD2 = (unsigned int)distance2;
  }

  vc->maxD1 = maxD1;
  vc->maxD2 = maxD2;

  output = (vrna_sol_TwoD_pf_t *)vrna_alloc((((maxD1+1)*(maxD2+2))/2 + 2) * sizeof(vrna_sol_TwoD_pf_t));

  pf2D_linear(vc);
  if(md->circ) pf2D_circ(vc);

  ndx   = vc->iindx[1] - vc->length;
  k_min = (md->circ) ? matrices->k_min_Q_c: matrices->k_min_Q[ndx];
  k_max = (md->circ) ? matrices->k_max_Q_c: matrices->k_max_Q[ndx];

  for(cnt1 =  k_min;
      cnt1 <= k_max;
      cnt1++){
    l_min = (md->circ) ? matrices->l_min_Q_c[cnt1] : matrices->l_min_Q[ndx][cnt1];
    l_max = (md->circ) ? matrices->l_max_Q_c[cnt1] : matrices->l_max_Q[ndx][cnt1];
    for(cnt2 =  l_min;
        cnt2 <= l_max;
        cnt2 += 2){
      q = (md->circ) ? matrices->Q_c[cnt1][cnt2/2] : matrices->Q[ndx][cnt1][cnt2/2];
      if(q == 0.) continue;
      output[counter].k = cnt1;
      output[counter].l = cnt2;
      output[counter].q = q;
      counter++;
    }
  }

  /* store entry for remaining partition if it exists */
  q = (md->circ) ? matrices->Q_c_rem : matrices->Q_rem[ndx];
  if(q != 0.){
    output[counter].k = -1;
    output[counter].l = -1;
    output[counter].q = q;
    counter++;
  }

  /* insert end-marker entry */
  output[counter].k = output[counter].l = INF;
  counter++;

  /* resize to actual dataset amount */
  output = (vrna_sol_TwoD_pf_t *)vrna_realloc(output, sizeof(vrna_sol_TwoD_pf_t) * counter);
  return output;
}

#if 0
PUBLIC FLT_OR_DBL **TwoDpfold(TwoDpfold_vars *vars, int distance1, int distance2){
  unsigned int  i;
  unsigned int  maxD1 = 0;
  unsigned int  maxD2 = 0;
  unsigned int  mm;
  int           cnt1, cnt2;

  FLT_OR_DBL **output;

  initialize_TwoDpfold_vars(vars);

  vars->S   = encode_sequence(vars->sequence, 0);
  vars->S1  = encode_sequence(vars->sequence, 1);
  make_ptypes2(vars);

  for(i=1; i<=(unsigned int)vars->reference_pt1[0]; i++)
    if(i < (unsigned int)vars->reference_pt1[i]) maxD1++;
  for(i=1; i<=(unsigned int)vars->reference_pt2[0]; i++)
    if(i < (unsigned int)vars->reference_pt2[i]) maxD2++;
  mm    = maximumMatching(vars->sequence);
  maxD1 += mm;
  maxD2 += mm;

  if(distance1 >= 0){
    if((unsigned int)distance1 > maxD1)
      fprintf(stderr, "limiting maximum basepair distance 1 to %u\n", maxD1);
    maxD1 = (unsigned int)distance1;
  }

  if(distance2 >= 0){
    if((unsigned int)distance2 > maxD2)
      fprintf(stderr, "limiting maximum basepair distance 2 to %u\n", maxD2);
    maxD2 = (unsigned int)distance2;
  }
  vars->maxD1 = maxD1;
  vars->maxD2 = maxD2;


  output = (FLT_OR_DBL **) vrna_alloc(sizeof(FLT_OR_DBL*) * (maxD1+1));
  pf2D_linear(vars);
  int ndx = vars->my_iindx[1] - vars->seq_length;
  for(cnt1 = vars->k_min_values[ndx]; cnt1 <= MIN2(vars->k_max_values[ndx], vars->maxD1); cnt1++){
    output[cnt1] = (FLT_OR_DBL *)vrna_alloc((vars->maxD2+1)*sizeof(FLT_OR_DBL));
    for(cnt2 = vars->l_min_values[ndx][cnt1]; cnt2 <= MIN2(vars->l_max_values[ndx][cnt1], vars->maxD2); cnt2+=2){
      output[cnt1][cnt2] = vars->Q[ndx][cnt1][cnt2/2];
    }
  }
  return output;
}

PUBLIC FLT_OR_DBL **TwoDpfold_circ(TwoDpfold_vars *vars, int distance1, int distance2){
  unsigned int i;
  unsigned int maxD1 = 0;
  unsigned int maxD2 = 0;
  unsigned int mm;
  int           cnt1, cnt2;
  FLT_OR_DBL **output;

  initialize_TwoDpfold_vars(vars);

  vars->S   = encode_sequence(vars->sequence, 0);
  vars->S1  = encode_sequence(vars->sequence, 1);
  make_ptypes2(vars);

  for(i=1; i<=(unsigned int)vars->reference_pt1[0]; i++)
    if(i < (unsigned int)vars->reference_pt1[i]) maxD1++;
  for(i=1; i<=(unsigned int)vars->reference_pt2[0]; i++)
    if(i < (unsigned int)vars->reference_pt2[i]) maxD2++;
  mm = maximumMatching(vars->sequence);
  maxD1 += mm;
  maxD2 += mm;

  if(distance1 >= 0){
    if((unsigned int)distance1 > maxD1)
      fprintf(stderr, "limiting maximum basepair distance 1 to %u\n", maxD1);
    maxD1 = (unsigned int)distance1;
  }

  if(distance2 >= 0){
    if((unsigned int)distance2 > maxD2)
      fprintf(stderr, "limiting maximum basepair distance 2 to %u\n", maxD2);
    maxD2 = (unsigned int)distance2;
  }
  vars->maxD1 = maxD1;
  vars->maxD2 = maxD2;

  output = (FLT_OR_DBL **) vrna_alloc(sizeof(FLT_OR_DBL*) * (maxD1+1));
  pf2D_linear(vars);
  pf2D_circ(vars);

  for(cnt1 = vars->k_min_values_qc; cnt1 <= MIN2(vars->k_max_values_qc, vars->maxD1); cnt1++){
    output[cnt1] = (FLT_OR_DBL *)vrna_alloc((vars->maxD2+1)*sizeof(FLT_OR_DBL));
    for(cnt2 = vars->l_min_values_qc[cnt1]; cnt2 <= MIN2(vars->l_max_values_qc[cnt1], vars->maxD2); cnt2+=2){
      output[cnt1][cnt2] = vars->Q_c[cnt1][cnt2/2];
    }
  }
  return output;
}

#endif

PRIVATE void
pf2D_linear(vrna_fold_compound_t *vc){

  char          *sequence, *ptype;
  short         *S1, *reference_pt1, *reference_pt2;
  unsigned int  *referenceBPs1, *referenceBPs2,
                d, i, j, ij, seq_length, maxD1,
                maxD2, *mm1, *mm2, *bpdist;
  int           *my_iindx, *jindx, circ, cnt1, cnt2, cnt3, cnt4, *rtype;
  double        max_real;
  FLT_OR_DBL    *scale, Qmax;
  vrna_exp_param_t  *pf_params;
  vrna_mx_pf_t      *matrices;
  vrna_md_t         *md;

  max_real = (sizeof(FLT_OR_DBL) == sizeof(float)) ? FLT_MAX : DBL_MAX;

  pf_params     = vc->exp_params;
  md            = &(pf_params->model_details);
  matrices      = vc->exp_matrices;
  sequence      = vc->sequence;
  seq_length    = vc->length;
  maxD1         = vc->maxD1;
  maxD2         = vc->maxD2;
  S1            = vc->sequence_encoding;
  ptype         = vc->ptype;
  rtype         = &(md->rtype[0]);
  scale         = matrices->scale;
  reference_pt1 = vc->reference_pt1;
  reference_pt2 = vc->reference_pt2;
  my_iindx      = vc->iindx;
  jindx         = vc->jindx;
  referenceBPs1 = vc->referenceBPs1;
  referenceBPs2 = vc->referenceBPs2;
  dangles       = md->dangles;
  circ          = md->circ;
  mm1           = vc->mm1;
  mm2           = vc->mm2;
  bpdist        = vc->bpdist;
  Qmax          = 0.;

  /*array initialization ; qb,qm,q
    qb,qm,q (i,j) are stored as ((n+1-i)*(n-i) div 2 + n+1-j */

  for (j = 1; j<=seq_length; j++)
    for (i=(j>TURN?(j-TURN):1); i<=j; i++){
      ij                        = my_iindx[i]-j;
      matrices->k_min_Q[ij]    = 0;
      matrices->k_max_Q[ij]    = 0;
      matrices->l_min_Q[ij]    = (int *)vrna_alloc(sizeof(int));
      matrices->l_max_Q[ij]    = (int *)vrna_alloc(sizeof(int));
      matrices->l_min_Q[ij][0] = 0;
      matrices->l_max_Q[ij][0] = 0;
      matrices->Q[ij]               = (FLT_OR_DBL **) vrna_alloc(sizeof(FLT_OR_DBL *));
      matrices->Q[ij][0]            = (FLT_OR_DBL *)  vrna_alloc(sizeof(FLT_OR_DBL));
      matrices->Q[ij][0][0]         = 1.0 * scale[j-i+1];
    }


  for (d = TURN+2; d <= seq_length; d++) { /* i,j in [1..seq_length] */
#ifdef _OPENMP
  #pragma omp parallel for private(i, j, ij, cnt1, cnt2, cnt3, cnt4)
#endif
    for (j = d; j <= seq_length; j++) {
      unsigned int k,l, kl, u, ii, dij;
      int no_close, type, type_2, tt, da, db, base_da, base_db;
      FLT_OR_DBL  temp2, aux_en;

      i     = j-d+1;
      ij    = my_iindx[i]-j;
      dij   = j - i - 1;
      type  = ptype[jindx[j] + i];


      no_close = (((type==3)||(type==4))&&no_closingGU);

      if (type) {   /* we have a pair */

        int k_min_Q_B, k_max_Q_B, l_min_Q_B, l_max_Q_B;
        int k_min_post_b, k_max_post_b, *l_min_post_b, *l_max_post_b;
        int update_b = 0;

        if(!matrices->Q_B[ij]){
          update_b = 1;
          k_min_Q_B = l_min_Q_B = 0;
          k_max_Q_B = mm1[ij] + referenceBPs1[ij];
          l_max_Q_B = mm2[ij] + referenceBPs2[ij];

          prepareBoundaries(k_min_Q_B,
                            k_max_Q_B,
                            l_min_Q_B,
                            l_max_Q_B,
                            bpdist[ij],
                            &matrices->k_min_Q_B[ij],
                            &matrices->k_max_Q_B[ij],
                            &matrices->l_min_Q_B[ij],
                            &matrices->l_max_Q_B[ij]
                            );
          preparePosteriorBoundaries( matrices->k_max_Q_B[ij] - matrices->k_min_Q_B[ij] + 1,
                                      matrices->k_min_Q_B[ij],
                                      &k_min_post_b,
                                      &k_max_post_b,
                                      &l_min_post_b,
                                      &l_max_post_b
                                  );

          prepareArray( &matrices->Q_B[ij],
                        matrices->k_min_Q_B[ij],
                        matrices->k_max_Q_B[ij],
                        matrices->l_min_Q_B[ij],
                        matrices->l_max_Q_B[ij]
                    );
        }


        /* hairpin ----------------------------------------------*/

        /* get distance to reference if closing the hairpin
        *  d1a = dbp(T1_{i,j}, {i,j})
        */
        base_da = ((unsigned int)reference_pt1[i] != j) ? 1 : -1;
        base_db = ((unsigned int)reference_pt2[i] != j) ? 1 : -1;

        da = base_da + referenceBPs1[ij];
        db = base_db + referenceBPs2[ij];

        if(!no_close)
          if((da >= 0) && (db >= 0)){
            if(((unsigned int)da<=maxD1) && ((unsigned int)db <= maxD2)){
              matrices->Q_B[ij][da][db/2] = exp_E_Hairpin(dij, type, S1[i+1], S1[j-1], sequence+i-1, pf_params) * scale[dij+2];
              if(update_b){
                updatePosteriorBoundaries( da,
                                           db,
                                           &k_min_post_b,
                                           &k_max_post_b,
                                           &l_min_post_b,
                                           &l_max_post_b
                                         );
              }
            }
            else{
              matrices->Q_B_rem[ij] = exp_E_Hairpin(dij, type, S1[i+1], S1[j-1], sequence+i-1, pf_params) * scale[dij+2];
            }
          }
        /*--------------------------------------------------------
          check for elementary structures involving more than one
          closing pair.
        --------------------------------------------------------*/
        for (k = i+1; k <= MIN2(j-2-TURN,i+MAXLOOP+1) ; k++) {
          unsigned int minl, ln_pre;
          minl = k + TURN + 1;
          ln_pre = dij + k;
          if(ln_pre > minl + MAXLOOP) minl = ln_pre - MAXLOOP - 1;
          for (l = minl; l < j; l++) {
            kl = my_iindx[k] - l;
            type_2 = ptype[jindx[l] + k];

            if (type_2==0) continue;
            type_2 = rtype[type_2];
            aux_en = exp_E_IntLoop(k-i-1, j-l-1, type, type_2, S1[i+1], S1[j-1], S1[k-1], S1[l+1], pf_params) * scale[k-i+j-l];

            /* get distance to reference if closing the interior loop
            *  d2 = dbp(S_{i,j}, S_{k,l} + {i,j})
            */
            da = base_da + referenceBPs1[ij] - referenceBPs1[kl];
            db = base_db + referenceBPs2[ij] - referenceBPs2[kl];

            if(matrices->Q_B_rem[kl]){
              matrices->Q_B_rem[ij] += matrices->Q_B_rem[kl] * aux_en;
            }
            if(!matrices->Q_B[kl]) continue;
            for(cnt1 = matrices->k_min_Q_B[kl];
                cnt1 <= matrices->k_max_Q_B[kl];
                cnt1++)
              for(cnt2 = matrices->l_min_Q_B[kl][cnt1];
                  cnt2 <= matrices->l_max_Q_B[kl][cnt1];
                  cnt2 += 2){
                if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
                  matrices->Q_B[ij][cnt1 + da][(cnt2 + db)/2] += matrices->Q_B[kl][cnt1][cnt2/2] * aux_en;
                  if(update_b){
                    updatePosteriorBoundaries( da + cnt1,
                                               db + cnt2,
                                               &k_min_post_b,
                                               &k_max_post_b,
                                               &l_min_post_b,
                                               &l_max_post_b
                                             );
                  }
                }
                else{
                  matrices->Q_B_rem[ij] += matrices->Q_B[kl][cnt1][cnt2/2] * aux_en;
                }
              }

          } /* end l-loop */
        } /* end k-loop */

        /* multi-loop contribution ------------------------*/
        if(!no_close){
          for(u=i+TURN+2; u<j-TURN-2;u++){
            tt = rtype[type];
            temp2 = pf_params->expMLclosing * exp_E_MLstem(tt, S1[j-1], S1[i+1], pf_params) * scale[2];

            if(matrices->Q_M_rem[my_iindx[i+1]-u]){
              if(matrices->Q_M1[jindx[j-1]+u+1])
                for(cnt1 = matrices->k_min_Q_M1[jindx[j-1]+u+1];
                    cnt1 <= matrices->k_max_Q_M1[jindx[j-1]+u+1];
                    cnt1++)
                  for(cnt2 = matrices->l_min_Q_M1[jindx[j-1]+u+1][cnt1];
                      cnt2 <= matrices->l_max_Q_M1[jindx[j-1]+u+1][cnt1];
                      cnt2 += 2)
                    matrices->Q_B_rem[ij] += matrices->Q_M_rem[my_iindx[i+1]-u] * matrices->Q_M1[jindx[j-1]+u+1][cnt1][cnt2/2] * temp2;

              if(matrices->Q_M1_rem[jindx[j-1]+u+1])
                matrices->Q_B_rem[ij] += matrices->Q_M_rem[my_iindx[i+1]-u] * matrices->Q_M1_rem[jindx[j-1]+u+1] * temp2;
            }
            if(matrices->Q_M1_rem[jindx[j-1]+u+1]){
              if(matrices->Q_M[my_iindx[i+1]-u])
                for(cnt1 = matrices->k_min_Q_M[my_iindx[i+1]-u];
                    cnt1 <= matrices->k_max_Q_M[my_iindx[i+1]-u];
                    cnt1++)
                  for(cnt2 = matrices->l_min_Q_M[my_iindx[i+1]-u][cnt1];
                      cnt2 <= matrices->l_max_Q_M[my_iindx[i+1]-u][cnt1];
                      cnt2 += 2)
                    matrices->Q_B_rem[ij] += matrices->Q_M[my_iindx[i+1]-u][cnt1][cnt2/2] * matrices->Q_M1_rem[jindx[j-1]+u+1] * temp2;
            }

            /* get distance to reference if closing the multiloop
            *  dist3 = dbp(S_{i,j}, {i,j} + S_{i+1,u} + S_{u+1,j-1})
            */
            da = base_da + referenceBPs1[ij] - referenceBPs1[my_iindx[i+1]-u] - referenceBPs1[my_iindx[u+1]-j+1];
            db = base_db + referenceBPs2[ij] - referenceBPs2[my_iindx[i+1]-u] - referenceBPs2[my_iindx[u+1]-j+1];

            if(!matrices->Q_M[my_iindx[i+1]-u]) continue;
            if(!matrices->Q_M1[jindx[j-1]+u+1]) continue;
            for(cnt1 = matrices->k_min_Q_M[my_iindx[i+1]-u];
                cnt1 <= matrices->k_max_Q_M[my_iindx[i+1]-u];
                cnt1++)
              for(cnt2 = matrices->l_min_Q_M[my_iindx[i+1]-u][cnt1];
                  cnt2 <= matrices->l_max_Q_M[my_iindx[i+1]-u][cnt1];
                  cnt2 += 2){
                for(cnt3 = matrices->k_min_Q_M1[jindx[j-1]+u+1];
                    cnt3 <= matrices->k_max_Q_M1[jindx[j-1]+u+1];
                    cnt3++)
                  for(cnt4 = matrices->l_min_Q_M1[jindx[j-1]+u+1][cnt3];
                      cnt4 <= matrices->l_max_Q_M1[jindx[j-1]+u+1][cnt3];
                      cnt4 += 2){
                    if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                      matrices->Q_B[ij][cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] +=  matrices->Q_M[my_iindx[i+1]-u][cnt1][cnt2/2]
                                                                              * matrices->Q_M1[jindx[j-1]+u+1][cnt3][cnt4/2]
                                                                              * temp2;
                      if(update_b){
                        updatePosteriorBoundaries( cnt1 + cnt3 + da,
                                                   cnt2 + cnt4 + db,
                                                   &k_min_post_b,
                                                   &k_max_post_b,
                                                   &l_min_post_b,
                                                   &l_max_post_b
                                                 );
                      }
                    }
                    else{
                      matrices->Q_B_rem[ij] +=  matrices->Q_M[my_iindx[i+1]-u][cnt1][cnt2/2]
                                    * matrices->Q_M1[jindx[j-1]+u+1][cnt3][cnt4/2]
                                    * temp2;
                    }
                  }

              }

          }
        }

        if(update_b){
          adjustArrayBoundaries(&matrices->Q_B[ij],
                                &matrices->k_min_Q_B[ij],
                                &matrices->k_max_Q_B[ij],
                                &matrices->l_min_Q_B[ij],
                                &matrices->l_max_Q_B[ij],
                                k_min_post_b,
                                k_max_post_b,
                                l_min_post_b,
                                l_max_post_b
                                );
        }
      } /* end >> if (pair) << */

      /* free ends ? -----------------------------------------*/

      int k_min_Q_M, k_max_Q_M, l_min_Q_M, l_max_Q_M;
      int k_min_post_m, k_max_post_m, *l_min_post_m, *l_max_post_m;
      int update_m = 0;
      int k_min_Q_M1, k_max_Q_M1, l_min_Q_M1, l_max_Q_M1;
      int k_min_post_m1, k_max_post_m1, *l_min_post_m1, *l_max_post_m1;
      int update_m1 = 0;

      if(!matrices->Q_M[ij]){
        update_m = 1;
        k_min_Q_M = l_min_Q_M = 0;
        k_max_Q_M = mm1[ij] + referenceBPs1[ij];
        l_max_Q_M = mm2[ij] + referenceBPs2[ij];

        prepareBoundaries(k_min_Q_M,
                          k_max_Q_M,
                          l_min_Q_M,
                          l_max_Q_M,
                          bpdist[ij],
                          &matrices->k_min_Q_M[ij],
                          &matrices->k_max_Q_M[ij],
                          &matrices->l_min_Q_M[ij],
                          &matrices->l_max_Q_M[ij]
                          );
        preparePosteriorBoundaries( matrices->k_max_Q_M[ij] - matrices->k_min_Q_M[ij] + 1,
                                    matrices->k_min_Q_M[ij],
                                    &k_min_post_m,
                                    &k_max_post_m,
                                    &l_min_post_m,
                                    &l_max_post_m
                                );

        prepareArray( &matrices->Q_M[ij],
                      matrices->k_min_Q_M[ij],
                      matrices->k_max_Q_M[ij],
                      matrices->l_min_Q_M[ij],
                      matrices->l_max_Q_M[ij]
                  );
      }
      if(!matrices->Q_M1[jindx[j]+i]){
        update_m1 = 1;
        k_min_Q_M1 = l_min_Q_M1 = 0;
        k_max_Q_M1 = mm1[ij] + referenceBPs1[ij];
        l_max_Q_M1 = mm2[ij] + referenceBPs2[ij];

        prepareBoundaries(k_min_Q_M1,
                          k_max_Q_M1,
                          l_min_Q_M1,
                          l_max_Q_M1,
                          bpdist[ij],
                          &matrices->k_min_Q_M1[jindx[j]+i],
                          &matrices->k_max_Q_M1[jindx[j]+i],
                          &matrices->l_min_Q_M1[jindx[j]+i],
                          &matrices->l_max_Q_M1[jindx[j]+i]
                          );
        preparePosteriorBoundaries( matrices->k_max_Q_M1[jindx[j]+i] - matrices->k_min_Q_M1[jindx[j]+i] + 1,
                                    matrices->k_min_Q_M1[jindx[j]+i],
                                    &k_min_post_m1,
                                    &k_max_post_m1,
                                    &l_min_post_m1,
                                    &l_max_post_m1
                                );

        prepareArray( &matrices->Q_M1[jindx[j]+i],
                      matrices->k_min_Q_M1[jindx[j]+i],
                      matrices->k_max_Q_M1[jindx[j]+i],
                      matrices->l_min_Q_M1[jindx[j]+i],
                      matrices->l_max_Q_M1[jindx[j]+i]
                  );
      }


      /* j is unpaired */
      da = referenceBPs1[ij] - referenceBPs1[ij+1];
      db = referenceBPs2[ij] - referenceBPs2[ij+1];

      if(matrices->Q_M_rem[ij+1])
        matrices->Q_M_rem[ij] += matrices->Q_M_rem[ij+1] * pf_params->expMLbase * scale[1];

      if(matrices->Q_M[ij+1])
        for(cnt1 = matrices->k_min_Q_M[ij+1];
            cnt1 <= matrices->k_max_Q_M[ij+1];
            cnt1++){
          for(cnt2 = matrices->l_min_Q_M[ij+1][cnt1];
              cnt2 <= matrices->l_max_Q_M[ij+1][cnt1];
              cnt2 += 2){
            if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
              matrices->Q_M[ij][cnt1 + da][(cnt2 + db)/2] += matrices->Q_M[ij+1][cnt1][cnt2/2] * pf_params->expMLbase * scale[1];
              if(update_m){
                updatePosteriorBoundaries(cnt1 + da,
                                          cnt2 + db,
                                          &k_min_post_m,
                                          &k_max_post_m,
                                          &l_min_post_m,
                                          &l_max_post_m
                                          );
              }
            }
            else{
              matrices->Q_M_rem[ij] += matrices->Q_M[ij+1][cnt1][cnt2/2] * pf_params->expMLbase * scale[1];
            }
          }
        }

      if(matrices->Q_M1_rem[jindx[j-1]+i])
        matrices->Q_M1_rem[jindx[j]+i] += matrices->Q_M1_rem[jindx[j-1]+i] * pf_params->expMLbase * scale[1];

      if(matrices->Q_M1[jindx[j-1]+i])
        for(cnt1 = matrices->k_min_Q_M1[jindx[j-1]+i];
            cnt1 <= matrices->k_max_Q_M1[jindx[j-1]+i];
            cnt1++)
          for(cnt2 = matrices->l_min_Q_M1[jindx[j-1]+i][cnt1];
              cnt2 <= matrices->l_max_Q_M1[jindx[j-1]+i][cnt1];
              cnt2 += 2){
            if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
              matrices->Q_M1[jindx[j]+i][cnt1 + da][(cnt2 + db)/2] += matrices->Q_M1[jindx[j-1]+i][cnt1][cnt2/2] * pf_params->expMLbase * scale[1];
              if(update_m1){
                updatePosteriorBoundaries(cnt1 + da,
                                          cnt2 + db,
                                          &k_min_post_m1,
                                          &k_max_post_m1,
                                          &l_min_post_m1,
                                          &l_max_post_m1
                                          );
              }
            }
            else{
              matrices->Q_M1_rem[jindx[j]+i] += matrices->Q_M1[jindx[j-1]+i][cnt1][cnt2/2] * pf_params->expMLbase * scale[1];
            }
          }


      /* j pairs with i */
      if((!no_close) && type){
        FLT_OR_DBL aux_en = exp_E_MLstem(type, (i>1) || circ ? S1[i-1] : -1, (j<seq_length) || circ ? S1[j+1] : -1, pf_params);

        if(matrices->Q_B_rem[ij]){
          matrices->Q_M_rem[ij]           += matrices->Q_B_rem[ij] * aux_en;
          matrices->Q_M1_rem[jindx[j]+i]  += matrices->Q_B_rem[ij] * aux_en;
        }

        if(matrices->Q_B[ij]){
          for(cnt1 = matrices->k_min_Q_B[ij];
              cnt1 <= matrices->k_max_Q_B[ij];
              cnt1++)
            for(cnt2 = matrices->l_min_Q_B[ij][cnt1];
                cnt2 <= matrices->l_max_Q_B[ij][cnt1];
                cnt2 += 2){
              matrices->Q_M[ij][cnt1][cnt2/2] += matrices->Q_B[ij][cnt1][cnt2/2] * aux_en;
              if(update_m){
                updatePosteriorBoundaries(cnt1,
                                          cnt2,
                                          &k_min_post_m,
                                          &k_max_post_m,
                                          &l_min_post_m,
                                          &l_max_post_m
                                          );
              }
              matrices->Q_M1[jindx[j]+i][cnt1][cnt2/2] += matrices->Q_B[ij][cnt1][cnt2/2] * aux_en;
              if(update_m1){
                updatePosteriorBoundaries(cnt1,
                                          cnt2,
                                          &k_min_post_m1,
                                          &k_max_post_m1,
                                          &l_min_post_m1,
                                          &l_max_post_m1
                                          );
              }
            }
        }
      }

      /* j pairs with k: i<k<j */
      ii = my_iindx[i];
      for (k=i+1; k<=j; k++){
        tt = ptype[jindx[j] + k];
        temp2 = exp_E_MLstem(tt, S1[k-1], (j<seq_length) || circ ? S1[j+1] : -1, pf_params);

        if(matrices->Q_B_rem[my_iindx[k]-j]){
          matrices->Q_M_rem[ij] += matrices->Q_B_rem[my_iindx[k]-j] * pow(pf_params->expMLbase, (double)(k-i)) * scale[k-i] * temp2;
          if(matrices->Q_M[ii-k+1])
            for(cnt1 = matrices->k_min_Q_M[ii-k+1];
                cnt1 <= matrices->k_max_Q_M[ii-k+1];
                cnt1++)
              for(cnt2 = matrices->l_min_Q_M[ii-k+1][cnt1];
                  cnt2 <= matrices->l_max_Q_M[ii-k+1][cnt1];
                  cnt2 += 2)
                matrices->Q_M_rem[ij] += matrices->Q_M[ii-k+1][cnt1][cnt2/2] * matrices->Q_B_rem[my_iindx[k]-j] * temp2;

          if(matrices->Q_M_rem[ii-k+1])
            matrices->Q_M_rem[ij] += matrices->Q_M_rem[ii-k+1] * matrices->Q_B_rem[my_iindx[k]-j] * temp2;
        }
        if(matrices->Q_M_rem[ii-k+1]){
          if(matrices->Q_B[my_iindx[k]-j])
            for(cnt1 = matrices->k_min_Q_B[my_iindx[k]-j];
                cnt1 <= matrices->k_max_Q_B[my_iindx[k]-j];
                cnt1++)
              for(cnt2 = matrices->l_min_Q_B[my_iindx[k]-j][cnt1];
                  cnt2 <= matrices->l_max_Q_B[my_iindx[k]-j][cnt1];
                  cnt2 += 2)
                matrices->Q_M_rem[ij] += matrices->Q_M_rem[my_iindx[k]-j] * matrices->Q_B[my_iindx[k]-j][cnt1][cnt2/2] * temp2;
        }

        /* add contributions of QM(i,k-1)*QB(k,j)*e^b and
        *  e^((k-i) * c) * QB(k,j) * e^b
        *  therefor we need d1a = dbp(T1_{i,j}, T1_{i,k-1} + T1_{k,j}),
        *  d1b = dbp(T2_{i,j}, T2_{i,k-1} + T2_{k,j})
        *  d1c = dbp(T1_{i,j}, T1_{k,j})circ = 0;
        *  d1d = dbp(T2_{i,j}, T2_{k,j})
        */
        da = referenceBPs1[ij] - referenceBPs1[my_iindx[k]-j];
        db = referenceBPs2[ij] - referenceBPs2[my_iindx[k]-j];

        if(!matrices->Q_B[my_iindx[k]-j]) continue;
        for(cnt1 = matrices->k_min_Q_B[my_iindx[k]-j];
            cnt1 <= matrices->k_max_Q_B[my_iindx[k]-j];
            cnt1++)
          for(cnt2 = matrices->l_min_Q_B[my_iindx[k]-j][cnt1];
              cnt2 <= matrices->l_max_Q_B[my_iindx[k]-j][cnt1];
              cnt2 += 2){
            if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
                matrices->Q_M[ij][cnt1 + da][(cnt2 + db)/2] += matrices->Q_B[my_iindx[k]-j][cnt1][cnt2/2] * pow(pf_params->expMLbase, (double)(k-i)) * scale[k-i] * temp2;
              if(update_m){
                updatePosteriorBoundaries(cnt1 + da,
                                          cnt2 + db,
                                          &k_min_post_m,
                                          &k_max_post_m,
                                          &l_min_post_m,
                                          &l_max_post_m
                                          );
              }
            }
            else{
              matrices->Q_M_rem[ij] += matrices->Q_B[my_iindx[k]-j][cnt1][cnt2/2] * pow(pf_params->expMLbase, (double)(k-i)) * scale[k-i] * temp2;
            }
          }

        if(!matrices->Q_M[ii-k+1]) continue;
        da -= referenceBPs1[ii-k+1];
        db -= referenceBPs2[ii-k+1];

        for(cnt1 = matrices->k_min_Q_M[ii-k+1];
            cnt1 <= matrices->k_max_Q_M[ii-k+1];
            cnt1++)
          for(cnt2 = matrices->l_min_Q_M[ii-k+1][cnt1];
              cnt2 <= matrices->l_max_Q_M[ii-k+1][cnt1];
              cnt2 += 2)
            for(cnt3 = matrices->k_min_Q_B[my_iindx[k]-j];
                cnt3 <= matrices->k_max_Q_B[my_iindx[k]-j];
                cnt3++)
              for(cnt4 = matrices->l_min_Q_B[my_iindx[k]-j][cnt3];
                  cnt4 <= matrices->l_max_Q_B[my_iindx[k]-j][cnt3];
                  cnt4 += 2){
                if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                  matrices->Q_M[ij][cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] += matrices->Q_M[ii-k+1][cnt1][cnt2/2] * matrices->Q_B[my_iindx[k]-j][cnt3][cnt4/2] * temp2;
                  if(update_m){
                    updatePosteriorBoundaries(cnt1 + cnt3 + da,
                                              cnt2 + cnt4 + db,
                                              &k_min_post_m,
                                              &k_max_post_m,
                                              &l_min_post_m,
                                              &l_max_post_m
                                              );
                  }
                }
                else{
                  matrices->Q_M_rem[ij] += matrices->Q_M[ii-k+1][cnt1][cnt2/2] * matrices->Q_B[my_iindx[k]-j][cnt3][cnt4/2] * temp2;
                }
              }
      }

      if(update_m){
        adjustArrayBoundaries(&matrices->Q_M[ij],
                              &matrices->k_min_Q_M[ij],
                              &matrices->k_max_Q_M[ij],
                              &matrices->l_min_Q_M[ij],
                              &matrices->l_max_Q_M[ij],
                              k_min_post_m,
                              k_max_post_m,
                              l_min_post_m,
                              l_max_post_m
                              );
      }
      if(update_m1){
        adjustArrayBoundaries(&matrices->Q_M1[jindx[j]+i],
                              &matrices->k_min_Q_M1[jindx[j]+i],
                              &matrices->k_max_Q_M1[jindx[j]+i],
                              &matrices->l_min_Q_M1[jindx[j]+i],
                              &matrices->l_max_Q_M1[jindx[j]+i],
                              k_min_post_m1,
                              k_max_post_m1,
                              l_min_post_m1,
                              l_max_post_m1
                              );
      }

      /* compute contributions for Q(i,j) */
      int k_min, k_max, l_min, l_max;
      int k_min_post, k_max_post, *l_min_post, *l_max_post;
      int update_q = 0;
      if(!matrices->Q[ij]){
        update_q = 1;
        k_min = l_min = 0;
        k_max = mm1[ij] + referenceBPs1[ij];
        l_max = mm2[ij] + referenceBPs2[ij];

        prepareBoundaries(k_min,
                          k_max,
                          l_min,
                          l_max,
                          bpdist[ij],
                          &matrices->k_min_Q[ij],
                          &matrices->k_max_Q[ij],
                          &matrices->l_min_Q[ij],
                          &matrices->l_max_Q[ij]
                          );
        preparePosteriorBoundaries( matrices->k_max_Q[ij] - matrices->k_min_Q[ij] + 1,
                                    matrices->k_min_Q[ij],
                                    &k_min_post,
                                    &k_max_post,
                                    &l_min_post,
                                    &l_max_post
                                );

        prepareArray( &matrices->Q[ij],
                      matrices->k_min_Q[ij],
                      matrices->k_max_Q[ij],
                      matrices->l_min_Q[ij],
                      matrices->l_max_Q[ij]
                  );
      }

      if (type){
        aux_en = exp_E_ExtLoop(type, (i>1) || circ ? S1[i-1] : -1, (j < seq_length) || circ ? S1[j+1] : -1, pf_params);

        if(matrices->Q_B_rem[ij])
          matrices->Q_rem[ij] += matrices->Q_B_rem[ij] * aux_en;

        if(matrices->Q_B[ij])
          for(cnt1 = matrices->k_min_Q_B[ij];
              cnt1 <= matrices->k_max_Q_B[ij];
              cnt1++)
            for(cnt2 = matrices->l_min_Q_B[ij][cnt1];
                cnt2 <= matrices->l_max_Q_B[ij][cnt1];
                cnt2 += 2){
              matrices->Q[ij][cnt1][cnt2/2] += matrices->Q_B[ij][cnt1][cnt2/2] * aux_en;
              if(update_q){
                updatePosteriorBoundaries(cnt1,
                                          cnt2,
                                          &k_min_post,
                                          &k_max_post,
                                          &l_min_post,
                                          &l_max_post
                                          );
              }
            }
      }

      /* j is unpaired */
      if(matrices->Q_rem[ij+1])
        matrices->Q_rem[ij] += matrices->Q_rem[ij+1] * scale[1];

      /* da = dbp(T1_{i,j}, T1_{i,j-1})
      *  db = dbp(T2_{i,j}, T2_{i,j-1})
      */
      da = referenceBPs1[ij] - referenceBPs1[ij+1];
      db = referenceBPs2[ij] - referenceBPs2[ij+1];
      if(matrices->Q[ij+1])
        for(cnt1 = matrices->k_min_Q[ij+1];
            cnt1 <= matrices->k_max_Q[ij+1];
            cnt1++)
          for(cnt2 = matrices->l_min_Q[ij+1][cnt1];
              cnt2 <= matrices->l_max_Q[ij+1][cnt1];
              cnt2 += 2){
            if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
              matrices->Q[ij][cnt1 + da][(cnt2 + db)/2] += matrices->Q[ij+1][cnt1][cnt2/2] * scale[1];
              if(update_q){
                updatePosteriorBoundaries(cnt1 + da,
                                          cnt2 + db,
                                          &k_min_post,
                                          &k_max_post,
                                          &l_min_post,
                                          &l_max_post
                                          );
              }
            }
            else{
              matrices->Q_rem[ij] += matrices->Q[ij+1][cnt1][cnt2/2] * scale[1];
            }
          }

      for(k=j-TURN-1; k>i; k--){
        tt = ptype[jindx[j] + k];
        temp2 = exp_E_ExtLoop(tt, S1[k-1], (j<seq_length) || circ ? S1[j+1] : -1, pf_params);

        if(matrices->Q_rem[my_iindx[i]-k+1]){
          if(matrices->Q_B[my_iindx[k]-j])
            for(cnt1 = matrices->k_min_Q_B[my_iindx[k]-j];
                cnt1 <=  matrices->k_max_Q_B[my_iindx[k]-j];
                cnt1++)
              for(cnt2 = matrices->l_min_Q_B[my_iindx[k]-j][cnt1];
                  cnt2 <= matrices->l_max_Q_B[my_iindx[k]-j][cnt1];
                  cnt2 += 2)
                matrices->Q_rem[ij] += matrices->Q_rem[my_iindx[i]-k+1] * matrices->Q_B[my_iindx[k]-j][cnt1][cnt2/2] * temp2;
          if(matrices->Q_B_rem[my_iindx[k]-j])
            matrices->Q_rem[ij] += matrices->Q_rem[my_iindx[i]-k+1] * matrices->Q_B_rem[my_iindx[k]-j] * temp2;
        }
        if(matrices->Q_B_rem[my_iindx[k]-j]){
          if(matrices->Q[my_iindx[i]-k+1])
            for(cnt1 = matrices->k_min_Q[my_iindx[i]-k+1];
                cnt1 <= matrices->k_max_Q[my_iindx[i]-k+1];
                cnt1++)
              for(cnt2 = matrices->l_min_Q[my_iindx[i]-k+1][cnt1];
                  cnt2 <= matrices->l_max_Q[my_iindx[i]-k+1][cnt1];
                  cnt2 += 2)
                matrices->Q_rem[ij] += matrices->Q[my_iindx[i]-k+1][cnt1][cnt2/2] * matrices->Q_B_rem[my_iindx[k]-j] * temp2;
        }

        /* da = dbp{T1_{i,j}, T1_{k,j}
        *  db = dbp{T2_{i,j}, T2_{k,j}}
        */
        da = referenceBPs1[ij] - referenceBPs1[my_iindx[k] - j] - referenceBPs1[my_iindx[i]-k+1];
        db = referenceBPs2[ij] - referenceBPs2[my_iindx[k] - j] - referenceBPs2[my_iindx[i]-k+1];


        if(!matrices->Q[my_iindx[i]-k+1]) continue;
        if(!matrices->Q_B[my_iindx[k]-j]) continue;
        for(cnt1 = matrices->k_min_Q[my_iindx[i]-k+1];
            cnt1 <= matrices->k_max_Q[my_iindx[i]-k+1];
            cnt1++)
          for(cnt2 = matrices->l_min_Q[my_iindx[i]-k+1][cnt1];
              cnt2 <= matrices->l_max_Q[my_iindx[i]-k+1][cnt1];
              cnt2 += 2)
            for(cnt3 = matrices->k_min_Q_B[my_iindx[k]-j];
                cnt3 <= matrices->k_max_Q_B[my_iindx[k]-j];
                cnt3++)
              for(cnt4 = matrices->l_min_Q_B[my_iindx[k]-j][cnt3];
                  cnt4 <= matrices->l_max_Q_B[my_iindx[k]-j][cnt3];
                  cnt4 += 2){
                if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                    matrices->Q[ij][cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] += matrices->Q[my_iindx[i]-k+1][cnt1][cnt2/2] * matrices->Q_B[my_iindx[k]-j][cnt3][cnt4/2] * temp2;
                  if(update_q){
                    updatePosteriorBoundaries(cnt1 + cnt3 + da,
                                              cnt2 + cnt4 + db,
                                              &k_min_post,
                                              &k_max_post,
                                              &l_min_post,
                                              &l_max_post
                                              );
                  }
                }
                else{
                  matrices->Q_rem[ij] += matrices->Q[my_iindx[i]-k+1][cnt1][cnt2/2] * matrices->Q_B[my_iindx[k]-j][cnt3][cnt4/2] * temp2;
                }
              }
      }

      if(update_q){
        adjustArrayBoundaries(&matrices->Q[ij],
                              &matrices->k_min_Q[ij],
                              &matrices->k_max_Q[ij],
                              &matrices->l_min_Q[ij],
                              &matrices->l_max_Q[ij],
                              k_min_post,
                              k_max_post,
                              l_min_post,
                              l_max_post
                              );
      }
#if 1
      for(cnt1 = matrices->k_min_Q[ij];
          cnt1 <= matrices->k_max_Q[ij];
          cnt1++){
        for(cnt2 = matrices->l_min_Q[ij][cnt1];
            cnt2 <= matrices->l_max_Q[ij][cnt1];
            cnt2 += 2){
          if(matrices->Q[ij][cnt1][cnt2/2] > Qmax) {
            Qmax = matrices->Q[ij][cnt1][cnt2/2];
            if (Qmax > max_real/10.)
              vrna_message_warning("Q close to overflow: %u %u %g\n", i,j,matrices->Q[ij][cnt1][cnt2/2]);
          }
          if(matrices->Q[ij][cnt1][cnt2/2] >= max_real) {
            vrna_message_error("overflow in pf_fold while calculating q[%u,%u]\n"
                                      "use larger pf_scale", i,j);
          }
        }

      }
#endif

    } /* end of j-loop */
  }
}

/* calculate partition function for circular case */
/* NOTE: this is the postprocessing step ONLY     */
/* You have to call pf2D_linear first to calculate  */
/* complete circular case!!!                      */
PRIVATE void
pf2D_circ(vrna_fold_compound_t *vc){

  unsigned int  d, p, q, pq, k, l, kl, u, da, db, seq_length, maxD1, maxD2, base_d1, base_d2, *mm1, *mm2, *bpdist;
  int         *my_iindx, *jindx, type, cnt1, cnt2, cnt3, cnt4, *rtype;
  short       *S1;
  unsigned int  *referenceBPs1, *referenceBPs2;
  char        *sequence, *ptype;
  FLT_OR_DBL  *scale;
  vrna_exp_param_t  *pf_params;     /* holds all [unscaled] pf parameters */
  vrna_md_t         *md;
  vrna_mx_pf_t     *matrices;

  pf_params       = vc->exp_params;
  md              = &(pf_params->model_details);
  matrices        = vc->exp_matrices;
  sequence        = vc->sequence;
  seq_length      = vc->length;
  maxD1           = vc->maxD1;
  maxD2           = vc->maxD2;
  S1              = vc->sequence_encoding;
  ptype           = vc->ptype;
  rtype           = &(md->rtype[0]);
  scale           = matrices->scale;
  my_iindx        = vc->iindx;
  jindx           = vc->jindx;
  referenceBPs1   = vc->referenceBPs1;
  referenceBPs2   = vc->referenceBPs2;
  dangles         = md->dangles;
  mm1             = vc->mm1;
  mm2             = vc->mm2;
  bpdist          = vc->bpdist;

  FLT_OR_DBL      ***Q_B, ***Q_M, ***Q_M1;
  FLT_OR_DBL      *Q_B_rem, *Q_M_rem, *Q_M1_rem;
  int             **l_min_Q_B, **l_max_Q_B, **l_min_Q_M, **l_max_Q_M, **l_min_Q_M1, **l_max_Q_M1;
  int             *k_min_Q_B, *k_max_Q_B,*k_min_Q_M, *k_max_Q_M,*k_min_Q_M1, *k_max_Q_M1;

  Q_B             = matrices->Q_B;
  l_min_Q_B  = matrices->l_min_Q_B;
  l_max_Q_B  = matrices->l_max_Q_B;
  k_min_Q_B  = matrices->k_min_Q_B;
  k_max_Q_B  = matrices->k_max_Q_B;

  Q_M             = matrices->Q_M;
  l_min_Q_M  = matrices->l_min_Q_M;
  l_max_Q_M  = matrices->l_max_Q_M;
  k_min_Q_M  = matrices->k_min_Q_M;
  k_max_Q_M  = matrices->k_max_Q_M;

  Q_M1            = matrices->Q_M1;
  l_min_Q_M1 = matrices->l_min_Q_M1;
  l_max_Q_M1 = matrices->l_max_Q_M1;
  k_min_Q_M1 = matrices->k_min_Q_M1;
  k_max_Q_M1 = matrices->k_max_Q_M1;


  Q_B_rem        = matrices->Q_B_rem;
  Q_M_rem        = matrices->Q_M_rem;
  Q_M1_rem       = matrices->Q_M1_rem;

  matrices->Q_c_rem   = 0.;
  matrices->Q_cH_rem  = 0.;
  matrices->Q_cI_rem  = 0.;
  matrices->Q_cM_rem  = 0.;


  /* construct qm2 matrix from qm1 entries  */
#ifdef _OPENMP
  #pragma omp parallel for private(d, k, l, da, db, cnt1, cnt2, cnt3, cnt4)
#endif
  for(k=1; k<seq_length-TURN-1; k++){
    int k_min_Q_M2, k_max_Q_M2, l_min_Q_M2, l_max_Q_M2;
    int k_min_post_m2, k_max_post_m2, *l_min_post_m2, *l_max_post_m2;
    int update_m2 = 0;
    if(!matrices->Q_M2[k]){
      update_m2 = 1;
      k_min_Q_M2 = l_min_Q_M2 = 0;
      k_max_Q_M2 = mm1[my_iindx[k]-seq_length] + referenceBPs1[my_iindx[k] - seq_length];
      l_max_Q_M2 = mm2[my_iindx[k]-seq_length] + referenceBPs2[my_iindx[k] - seq_length];

      prepareBoundaries(k_min_Q_M2,
                        k_max_Q_M2,
                        l_min_Q_M2,
                        l_max_Q_M2,
                        bpdist[my_iindx[k]-seq_length],
                        &matrices->k_min_Q_M2[k],
                        &matrices->k_max_Q_M2[k],
                        &matrices->l_min_Q_M2[k],
                        &matrices->l_max_Q_M2[k]
                        );
      preparePosteriorBoundaries( matrices->k_max_Q_M2[k] - matrices->k_min_Q_M2[k] + 1,
                                  matrices->k_min_Q_M2[k],
                                  &k_min_post_m2,
                                  &k_max_post_m2,
                                  &l_min_post_m2,
                                  &l_max_post_m2
                              );

      prepareArray( &matrices->Q_M2[k],
                    matrices->k_min_Q_M2[k],
                    matrices->k_max_Q_M2[k],
                    matrices->l_min_Q_M2[k],
                    matrices->l_max_Q_M2[k]
                );
    }

    /* construct Q_M2 */
    for (l=k+TURN+1; l<seq_length-TURN-1; l++){
      if(Q_M1_rem[jindx[l]+k]){
        if(Q_M1[jindx[seq_length]+l+1]){
          for(cnt1 = k_min_Q_M1[jindx[seq_length]+l+1];
              cnt1 <= k_max_Q_M1[jindx[seq_length]+l+1];
              cnt1++)
            for(cnt2 = l_min_Q_M1[jindx[seq_length]+l+1][cnt1];
                cnt2 <= l_max_Q_M1[jindx[seq_length]+l+1][cnt1];
                cnt2 += 2)
              matrices->Q_M2_rem[k] += Q_M1_rem[jindx[l]+k] * Q_M1[jindx[seq_length]+l+1][cnt1][cnt2/2];
        }
        if(Q_M1_rem[jindx[seq_length]+l+1])
          matrices->Q_M2_rem[k] += Q_M1_rem[jindx[l]+k] * Q_M1_rem[jindx[seq_length]+l+1];      
      }
      if(Q_M1_rem[jindx[seq_length]+l+1]){
        if(Q_M1[jindx[l]+k])
          for(cnt1 = k_min_Q_M1[jindx[l]+k];
              cnt1 <= k_max_Q_M1[jindx[l]+k];
              cnt1++)
            for(cnt2 = l_min_Q_M1[jindx[l]+k][cnt1];
                cnt2 <= l_max_Q_M1[jindx[l]+k][cnt1];
                cnt2 += 2)
              matrices->Q_M2_rem[k] += Q_M1[jindx[l]+k][cnt1][cnt2/2]*Q_M1_rem[jindx[seq_length]+l+1];
      
      }

      if(matrices->Q_M1[jindx[l]+k] && matrices->Q_M1[jindx[seq_length] + l + 1]){
        da = referenceBPs1[my_iindx[k]-seq_length] - referenceBPs1[my_iindx[k]-l] - referenceBPs1[my_iindx[l+1]-seq_length];
        db = referenceBPs2[my_iindx[k]-seq_length] - referenceBPs2[my_iindx[k]-l] - referenceBPs2[my_iindx[l+1]-seq_length];
        for(cnt1 = k_min_Q_M1[jindx[l]+k]; cnt1 <= k_max_Q_M1[jindx[l]+k]; cnt1++)
          for(cnt2 = l_min_Q_M1[jindx[l]+k][cnt1]; cnt2 <= l_max_Q_M1[jindx[l]+k][cnt1]; cnt2+=2){
            for(cnt3 = k_min_Q_M1[jindx[seq_length] + l + 1]; cnt3 <= k_max_Q_M1[jindx[seq_length] + l + 1]; cnt3++)
              for(cnt4 = l_min_Q_M1[jindx[seq_length] + l + 1][cnt3]; cnt4 <= l_max_Q_M1[jindx[seq_length] + l + 1][cnt3]; cnt4+=2){
                if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                  matrices->Q_M2[k][cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] += Q_M1[jindx[l]+k][cnt1][cnt2/2] * Q_M1[jindx[seq_length] + l + 1][cnt3][cnt4/2];
                  if(update_m2){
                      updatePosteriorBoundaries(cnt1 + cnt3 + da,
                                                cnt2 + cnt4 + db,
                                                &k_min_post_m2,
                                                &k_max_post_m2,
                                                &l_min_post_m2,
                                                &l_max_post_m2
                                                );
                  }
                }
                else{
                  matrices->Q_M2_rem[k] += Q_M1[jindx[l]+k][cnt1][cnt2/2] * Q_M1[jindx[seq_length] + l + 1][cnt3][cnt4/2];
                }
              }
          }
      }
    }
    if(update_m2){
      adjustArrayBoundaries(&matrices->Q_M2[k],
                            &matrices->k_min_Q_M2[k],
                            &matrices->k_max_Q_M2[k],
                            &matrices->l_min_Q_M2[k],
                            &matrices->l_max_Q_M2[k],
                            k_min_post_m2,
                            k_max_post_m2,
                            l_min_post_m2,
                            l_max_post_m2
                            );
    }
  }

  base_d1 = referenceBPs1[my_iindx[1]-seq_length];
  base_d2 = referenceBPs2[my_iindx[1]-seq_length];

  int min_k, max_k, max_l, min_l;
  int min_k_real, max_k_real, min_k_real_qcH, max_k_real_qcH, min_k_real_qcI, max_k_real_qcI, min_k_real_qcM, max_k_real_qcM;
  int *min_l_real, *max_l_real, *min_l_real_qcH, *max_l_real_qcH, *min_l_real_qcI, *max_l_real_qcI,*min_l_real_qcM, *max_l_real_qcM;
  int update_c, update_cH, update_cI, update_cM;

  update_c = update_cH = update_cI = update_cM = 0;

  min_k = min_l = 0;

  max_k = mm1[my_iindx[1] - seq_length] + referenceBPs1[my_iindx[1] - seq_length];
  max_l = mm2[my_iindx[1] - seq_length] + referenceBPs2[my_iindx[1] - seq_length];

#ifdef _OPENMP
  #pragma omp sections
  {

  #pragma omp section
  {
#endif
  if(!matrices->Q_c){
    update_c = 1;
    prepareBoundaries(min_k,
                      max_k,
                      min_l,
                      max_l,
                      bpdist[my_iindx[1] - seq_length],
                      &matrices->k_min_Q_c,
                      &matrices->k_max_Q_c,
                      &matrices->l_min_Q_c,
                      &matrices->l_max_Q_c
                      );
    prepareArray( &matrices->Q_c,
                  matrices->k_min_Q_c,
                  matrices->k_max_Q_c,
                  matrices->l_min_Q_c,
                  matrices->l_max_Q_c
                );
    preparePosteriorBoundaries( max_k - min_k + 1,
                                min_k,
                                &min_k_real,
                                &max_k_real,
                                &min_l_real,
                                &max_l_real
                              );
  }
#ifdef _OPENMP
  }
  #pragma omp section
  {
#endif
  if(!matrices->Q_cH){
    update_cH = 1;
    prepareBoundaries(min_k,
                      max_k,
                      min_l,
                      max_l,
                      bpdist[my_iindx[1] - seq_length],
                      &matrices->k_min_Q_cH,
                      &matrices->k_max_Q_cH,
                      &matrices->l_min_Q_cH,
                      &matrices->l_max_Q_cH
                      );
    prepareArray( &matrices->Q_cH,
                  matrices->k_min_Q_cH,
                  matrices->k_max_Q_cH,
                  matrices->l_min_Q_cH,
                  matrices->l_max_Q_cH
                );
    preparePosteriorBoundaries( max_k - min_k + 1,
                                min_k,
                                &min_k_real_qcH,
                                &max_k_real_qcH,
                                &min_l_real_qcH,
                                &max_l_real_qcH
                              );
  }
#ifdef _OPENMP
  }
  #pragma omp section
  {
#endif
  if(!matrices->Q_cI){
    update_cI = 1;
    prepareBoundaries(min_k,
                      max_k,
                      min_l,
                      max_l,
                      bpdist[my_iindx[1] - seq_length],
                      &matrices->k_min_Q_cI,
                      &matrices->k_max_Q_cI,
                      &matrices->l_min_Q_cI,
                      &matrices->l_max_Q_cI
                      );
    prepareArray( &matrices->Q_cI,
                  matrices->k_min_Q_cI,
                  matrices->k_max_Q_cI,
                  matrices->l_min_Q_cI,
                  matrices->l_max_Q_cI
                );
    preparePosteriorBoundaries( max_k - min_k + 1,
                                min_k,
                                &min_k_real_qcI,
                                &max_k_real_qcI,
                                &min_l_real_qcI,
                                &max_l_real_qcI
                              );
  }
#ifdef _OPENMP
  }
  #pragma omp section
  {
#endif
  if(!matrices->Q_cM){
    update_cM = 1;
    prepareBoundaries(min_k,
                      max_k,
                      min_l,
                      max_l,
                      bpdist[my_iindx[1] - seq_length],
                      &matrices->k_min_Q_cM,
                      &matrices->k_max_Q_cM,
                      &matrices->l_min_Q_cM,
                      &matrices->l_max_Q_cM
                      );
    prepareArray( &matrices->Q_cM,
                  matrices->k_min_Q_cM,
                  matrices->k_max_Q_cM,
                  matrices->l_min_Q_cM,
                  matrices->l_max_Q_cM
                );
    preparePosteriorBoundaries( max_k - min_k + 1,
                                min_k,
                                &min_k_real_qcM,
                                &max_k_real_qcM,
                                &min_l_real_qcM,
                                &max_l_real_qcM
                              );
  }
#ifdef _OPENMP
  }
  }
#endif




  for (d = TURN+2; d <= seq_length; d++) /* i,j in [1..length] */
#ifdef _OPENMP
    #pragma omp parallel for private(p, q, pq, k, l, kl, u, da, db, type, cnt1, cnt2, cnt3, cnt4)
#endif
    for (q = d; q <= seq_length; q++) {
      FLT_OR_DBL qot;
      char loopseq[10];
      p = q - d + 1;
      pq = my_iindx[p]-q;

      /* 1. get exterior hairpin contribution  */
      u = seq_length-q + p-1;
      if (u<TURN) continue;
      type = ptype[jindx[q] + p];
      if (!type) continue;
      if(((type==3)||(type==4))&&no_closingGU) continue;

       /* cause we want to calc the exterior loops, we need the reversed pair type from now on  */
      type=rtype[type];

      if (u<7){
        strcpy(loopseq , sequence+q-1);
        strncat(loopseq, sequence, p);
      }
      /* get distance to reference if closing the hairpin
      *  da = dbp(T1_[1,n}, T1_{p,q})
      *  db = dbp(T2_{1,n}, T2_{p,q})
      */
      da = base_d1 - referenceBPs1[pq];
      db = base_d2 - referenceBPs2[pq];
      qot = exp_E_Hairpin(u, type, S1[q+1], S1[p-1],  loopseq, pf_params) * scale[u];
      
      if(Q_B_rem[pq])
        matrices->Q_cH_rem += Q_B_rem[pq] * qot;
      
      if(Q_B[pq]){
        for(cnt1 = k_min_Q_B[pq];
            cnt1 <= k_max_Q_B[pq];
            cnt1++)
          for(cnt2 = l_min_Q_B[pq][cnt1];
              cnt2 <= l_max_Q_B[pq][cnt1];
              cnt2 += 2){
            if(((cnt1 + da) <= maxD1) && ((cnt2 + db) <= maxD2)){
              matrices->Q_cH[cnt1 + da][(cnt2 + db)/2] += Q_B[pq][cnt1][cnt2/2] * qot;
              if(update_cH){
                updatePosteriorBoundaries(cnt1 + da,
                                      cnt2 + db,
                                      &min_k_real_qcH,
                                      &max_k_real_qcH,
                                      &min_l_real_qcH,
                                      &max_l_real_qcH
                                      );
              }
            }
            else{
              matrices->Q_cH_rem += Q_B[pq][cnt1][cnt2/2] * qot;
            }
          }
      }

      /* 2. exterior interior loops, i "define" the (k,l) pair as "outer pair"  */
      /* so "outer type" is rtype[type[k,l]] and inner type is type[p,q]        */
      if(Q_B_rem[pq])
        for(k=q+1; k < seq_length; k++){
          unsigned int ln1, lstart, ln_pre;
          ln1 = k - q - 1;
          if(ln1+p-1>MAXLOOP) break;
          lstart = k + TURN + 1;
          ln_pre = ln1 + p + seq_length;
          if(ln_pre > lstart + MAXLOOP) lstart = ln_pre - MAXLOOP - 1;
          for(l=lstart;l <= seq_length; l++){
            unsigned int ln2;
            int type2;
            kl = my_iindx[k]-l;
            ln2 = (p - 1) + (seq_length - l);

            if((ln1+ln2) > MAXLOOP) continue;

            type2 = ptype[jindx[l] + k];
            if(!type2) continue;

            qot = exp_E_IntLoop(ln2, ln1, rtype[type2], type, S1[l+1], S1[k-1], S1[p-1], S1[q+1], pf_params) * scale[ln1+ln2];

            if(Q_B_rem[kl])
              matrices->Q_cI_rem += Q_B_rem[pq] * Q_B_rem[kl] * qot;

            if(Q_B[kl])
              for(cnt1 = k_min_Q_B[kl];
                  cnt1 <= k_max_Q_B[kl];
                  cnt1++)
                for(cnt2 = l_min_Q_B[kl][cnt1];
                    cnt2 <= l_max_Q_B[kl][cnt1];
                    cnt2 += 2)
                  matrices->Q_cI_rem += Q_B_rem[pq] * Q_B[kl][cnt1][cnt2/2] * qot;
          }
        }

      if(Q_B[pq])
        for(k=q+1; k < seq_length; k++){
          unsigned int ln1, lstart, ln_pre;
          ln1 = k - q - 1;
          if(ln1+p-1>MAXLOOP) break;
          lstart = k + TURN + 1;
          ln_pre = ln1 + p + seq_length;
          if(ln_pre > lstart + MAXLOOP) lstart = ln_pre - MAXLOOP - 1;
          for(l=lstart;l <= seq_length; l++){
            unsigned int ln2;
            int type2;
            kl = my_iindx[k]-l;
            ln2 = (p - 1) + (seq_length - l);

            if((ln1+ln2) > MAXLOOP) continue;

            type2 = ptype[jindx[l] + k];
            if(!type2) continue;

            qot = exp_E_IntLoop(ln2, ln1, rtype[type2], type, S1[l+1], S1[k-1], S1[p-1], S1[q+1], pf_params) * scale[ln1+ln2];

            if(Q_B_rem[kl]){
              for(cnt1 = k_min_Q_B[pq];
                  cnt1 <= k_max_Q_B[pq];
                  cnt1++)
                for(cnt2 = l_min_Q_B[pq][cnt1];
                    cnt2 <= l_max_Q_B[pq][cnt1];
                    cnt2 += 2)
                  matrices->Q_cI_rem += Q_B[pq][cnt1][cnt2/2] * Q_B_rem[kl] * qot;
            }

            if(!Q_B[kl]) continue;

            /* get distance to reference if closing the interior loop
            *  d2a = dbp(T1_[1,n}, T1_{p,q} + T1_{k,l})
            *  d2b = dbp(T2_[1,n}, T2_{p,q} + T2_{k,l})
            */
            da = base_d1 - referenceBPs1[pq] - referenceBPs1[kl];
            db = base_d2 - referenceBPs2[pq] - referenceBPs2[kl];

            for(cnt1 = k_min_Q_B[pq]; cnt1 <= k_max_Q_B[pq]; cnt1++)
              for(cnt2 = l_min_Q_B[pq][cnt1]; cnt2 <= l_max_Q_B[pq][cnt1]; cnt2+=2)
                for(cnt3 = k_min_Q_B[kl]; cnt3 <= k_max_Q_B[kl]; cnt3++)
                  for(cnt4 = l_min_Q_B[kl][cnt3]; cnt4 <= l_max_Q_B[kl][cnt3]; cnt4+=2){
                    if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                      matrices->Q_cI[cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] += Q_B[pq][cnt1][cnt2/2] * Q_B[kl][cnt3][cnt4/2] * qot;
                      if(update_cI){
                        updatePosteriorBoundaries(cnt1 + cnt3 + da,
                                                cnt2 + cnt4 + db,
                                                &min_k_real_qcI,
                                                &max_k_real_qcI,
                                                &min_l_real_qcI,
                                                &max_l_real_qcI
                                                );
                      }
                    }
                    else{
                      matrices->Q_cI_rem += Q_B[pq][cnt1][cnt2/2] * Q_B[kl][cnt3][cnt4/2] * qot;
                    }
                  }
          }
        }
    }

  if(update_cH){
    adjustArrayBoundaries(&matrices->Q_cH,
                          &matrices->k_min_Q_cH,
                          &matrices->k_max_Q_cH,
                          &matrices->l_min_Q_cH,
                          &matrices->l_max_Q_cH,
                          min_k_real_qcH,
                          max_k_real_qcH,
                          min_l_real_qcH,
                          max_l_real_qcH
                        );
  }
  if(update_cI){
    adjustArrayBoundaries(&matrices->Q_cI,
                          &matrices->k_min_Q_cI,
                          &matrices->k_max_Q_cI,
                          &matrices->l_min_Q_cI,
                          &matrices->l_max_Q_cI,
                          min_k_real_qcI,
                          max_k_real_qcI,
                          min_l_real_qcI,
                          max_l_real_qcI
                        );
  }

  /* 3. Multiloops  */
  if(seq_length > 2*TURN-3)
#ifdef _OPENMP
  #pragma omp parallel for private(k, da, db, cnt1, cnt2, cnt3, cnt4)
#endif
    for(k=TURN+2; k<seq_length-2*TURN-3; k++){
      if(Q_M_rem[my_iindx[1]-k]){
        if(matrices->Q_M2[k+1])
          for(cnt1 = matrices->k_min_Q_M2[k+1];
              cnt1 <= matrices->k_max_Q_M2[k+1];
              cnt1++)
            for(cnt2 = matrices->l_min_Q_M2[k+1][cnt1];
                cnt2 <= matrices->l_max_Q_M2[k+1][cnt1];
                cnt2 += 2)
              matrices->Q_cM_rem += Q_M_rem[my_iindx[1]-k] * matrices->Q_M2[k+1][cnt1][cnt2/2] * pf_params->expMLclosing;
        if(matrices->Q_M2_rem[k+1])
          matrices->Q_cM_rem += Q_M_rem[my_iindx[1]-k] * matrices->Q_M2_rem[k+1] * pf_params->expMLclosing;
      }
      if(matrices->Q_M2_rem[k+1]){
        if(Q_M[my_iindx[1]-k])
          for(cnt1 = k_min_Q_M[my_iindx[1]-k];
              cnt1 <= k_max_Q_M[my_iindx[1]-k];
              cnt1++)
            for(cnt2 = l_min_Q_M[my_iindx[1]-k][cnt1];
                cnt2 <= l_max_Q_M[my_iindx[1]-k][cnt1];
                cnt2 += 2)
              matrices->Q_cM_rem += Q_M[my_iindx[1]-k][cnt1][cnt2/2] * matrices->Q_M2_rem[k+1] * pf_params->expMLclosing;
      }

      /* get distancies to references
      * d3a = dbp(T1_[1,n}, T1_{1,k} + T1_{k+1, n})
      * d3b = dbp(T2_[1,n}, T2_{1,k} + T2_{k+1, n})
      */
      da = base_d1 - referenceBPs1[my_iindx[1]-k] - referenceBPs1[my_iindx[k+1]-seq_length];
      db = base_d2 - referenceBPs2[my_iindx[1]-k] - referenceBPs2[my_iindx[k+1]-seq_length];
      if(Q_M[my_iindx[1]-k] && matrices->Q_M2[k+1])
        for(cnt1 = k_min_Q_M[my_iindx[1]-k]; cnt1 <= k_max_Q_M[my_iindx[1]-k]; cnt1++)
          for(cnt2 = l_min_Q_M[my_iindx[1]-k][cnt1]; cnt2 <= l_max_Q_M[my_iindx[1]-k][cnt1]; cnt2+=2)
            for(cnt3 = matrices->k_min_Q_M2[k+1]; cnt3 <= matrices->k_max_Q_M2[k+1]; cnt3++)
              for(cnt4 = matrices->l_min_Q_M2[k+1][cnt3]; cnt4 <= matrices->l_max_Q_M2[k+1][cnt3]; cnt4+=2){
                if(((cnt1 + cnt3 + da) <= maxD1) && ((cnt2 + cnt4 + db) <= maxD2)){
                  matrices->Q_cM[cnt1 + cnt3 + da][(cnt2 + cnt4 + db)/2] += Q_M[my_iindx[1]-k][cnt1][cnt2/2] * matrices->Q_M2[k+1][cnt3][cnt4/2] * pf_params->expMLclosing;
                  if(update_cM){
                    updatePosteriorBoundaries(cnt1 + cnt3 + da,
                                            cnt2 + cnt4 + db,
                                            &min_k_real_qcM,
                                            &max_k_real_qcM,
                                            &min_l_real_qcM,
                                            &max_l_real_qcM
                                            );
                  }
                }
                else{
                  matrices->Q_cM_rem += Q_M[my_iindx[1]-k][cnt1][cnt2/2] * matrices->Q_M2[k+1][cnt3][cnt4/2] * pf_params->expMLclosing;
                }
              }
    }
  if(update_cM){
    adjustArrayBoundaries(&matrices->Q_cM,
                          &matrices->k_min_Q_cM,
                          &matrices->k_max_Q_cM,
                          &matrices->l_min_Q_cM,
                          &matrices->l_max_Q_cM,
                          min_k_real_qcM,
                          max_k_real_qcM,
                          min_l_real_qcM,
                          max_l_real_qcM
                        );
  }

  for(cnt1 = matrices->k_min_Q_cH;
      cnt1 <= matrices->k_max_Q_cH;
      cnt1++)
    for(cnt2 = matrices->l_min_Q_cH[cnt1];
        cnt2 <= matrices->l_max_Q_cH[cnt1];
        cnt2 += 2){
      matrices->Q_c[cnt1][cnt2/2] += matrices->Q_cH[cnt1][cnt2/2];
      if(update_c){
        updatePosteriorBoundaries(cnt1,
                                  cnt2,
                                  &min_k_real,
                                  &max_k_real,
                                  &min_l_real,
                                  &max_l_real
                                  );
      }
    }
  for(cnt1 = matrices->k_min_Q_cI;
      cnt1 <= matrices->k_max_Q_cI;
      cnt1++)
    for(cnt2 = matrices->l_min_Q_cI[cnt1];
        cnt2 <= matrices->l_max_Q_cI[cnt1];
        cnt2 += 2){
      matrices->Q_c[cnt1][cnt2/2] += matrices->Q_cI[cnt1][cnt2/2];
      if(update_c){
        updatePosteriorBoundaries(cnt1,
                                  cnt2,
                                  &min_k_real,
                                  &max_k_real,
                                  &min_l_real,
                                  &max_l_real
                                  );
      }
    }
  for(cnt1 = matrices->k_min_Q_cM;
      cnt1 <= matrices->k_max_Q_cM;
      cnt1++)
    for(cnt2 = matrices->l_min_Q_cM[cnt1];
        cnt2 <= matrices->l_max_Q_cM[cnt1];
        cnt2 += 2){
      matrices->Q_c[cnt1][cnt2/2] += matrices->Q_cM[cnt1][cnt2/2];
      if(update_c){
        updatePosteriorBoundaries(cnt1,
                                  cnt2,
                                  &min_k_real,
                                  &max_k_real,
                                  &min_l_real,
                                  &max_l_real
                                  );
      }
    }

  matrices->Q_c_rem   = matrices->Q_cH_rem + matrices->Q_cI_rem + matrices->Q_cM_rem;

  /* add the case were structure is unfolded chain */
  if((referenceBPs1[my_iindx[1]-seq_length] <= maxD1) && (referenceBPs2[my_iindx[1]-seq_length] <= maxD2)){
    matrices->Q_c[referenceBPs1[my_iindx[1]-seq_length]][referenceBPs2[my_iindx[1]-seq_length]/2] += 1.0 * scale[seq_length];
    if(update_c){
      updatePosteriorBoundaries(referenceBPs1[my_iindx[1]-seq_length],
                              referenceBPs2[my_iindx[1]-seq_length],
                              &min_k_real,
                              &max_k_real,
                              &min_l_real,
                              &max_l_real
                              );
    }
  }
  else{
    matrices->Q_c_rem += 1.0 * scale[seq_length];
  }

  adjustArrayBoundaries(&matrices->Q_c,
                        &matrices->k_min_Q_c,
                        &matrices->k_max_Q_c,
                        &matrices->l_min_Q_c,
                        &matrices->l_max_Q_c,
                        min_k_real,
                        max_k_real,
                        min_l_real,
                        max_l_real
                      );
}

/*
* ###################################################
* stochastic backtracking
* ###################################################
*/

PUBLIC char *
vrna_pbacktrack_TwoD( vrna_fold_compound_t *vc,
                      int d1,
                      int d2){

  return vrna_pbacktrack5_TwoD(vc, d1, d2, vc->length);
}

PUBLIC char *
vrna_pbacktrack5_TwoD(vrna_fold_compound_t *vc,
                      int d1,
                      int d2,
                      unsigned int length){

  char            *pstruc, *ptype;
  short           *S1;
  unsigned int    i, j, n, start, maxD1, maxD2, da, db,
                  *referenceBPs1, *referenceBPs2;
  int             *my_iindx, *jindx, ij, cnt1, cnt2, cnt3, cnt4, type,
                  **l_min_Q, **l_max_Q,
                  **l_min_Q_B, **l_max_Q_B,
                  *k_min_Q, *k_max_Q,
                  *k_min_Q_B, *k_max_Q_B;
  FLT_OR_DBL      r, qt, *scale, ***Q, ***Q_B, *Q_rem, *Q_B_rem;
  vrna_exp_param_t  *pf_params;
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  n               = vc->length;
  pf_params       = vc->exp_params;
  md              = &(pf_params->model_details);
  matrices        = vc->exp_matrices;
  maxD1           = vc->maxD1;
  maxD2           = vc->maxD2;
  my_iindx        = vc->iindx;
  jindx           = vc->jindx;
  scale           = matrices->scale;
  ptype           = vc->ptype;
  S1              = vc->sequence_encoding;
  referenceBPs1   = vc->referenceBPs1;
  referenceBPs2   = vc->referenceBPs2;

  Q               = matrices->Q;
  l_min_Q    = matrices->l_min_Q;
  l_max_Q    = matrices->l_max_Q;
  k_min_Q    = matrices->k_min_Q;
  k_max_Q    = matrices->k_max_Q;

  Q_B             = matrices->Q_B;
  l_min_Q_B  = matrices->l_min_Q_B;
  l_max_Q_B  = matrices->l_max_Q_B;
  k_min_Q_B  = matrices->k_min_Q_B;
  k_max_Q_B  = matrices->k_max_Q_B;

  Q_rem           = matrices->Q_rem;
  Q_B_rem         = matrices->Q_B_rem;

  if(md->circ){
    if(n != length)
      vrna_message_error("vrna_pbacktrack_TwoD@2Dfold.c: cotranscriptional backtracking for circular RNAs not supported!");
    return pbacktrack_circ(vc, d1, d2);
  }

  if(length > n)
    vrna_message_error("vrna_pbacktrack_TwoD@2Dpfold.c: requested transcript length exceeds sequence length!");

#if 0
  if(d1 > maxD1)
    vrna_message_error("pbacktrack@2Dpfold.c: distance to 1st reference structure to high!");
  if(d2 > maxD2)
    vrna_message_error("pbacktrack@2Dpfold.c: distance to 2nd reference structure to high!");
#endif

  /* check whether the chosen neighborhood exists at all */
  int dumb = 1;
  ij = my_iindx[1]-length;
  if((d1 == -1) && (Q_rem[ij] != 0.)) dumb = 0;
  else{
    if((k_min_Q[ij] <= d1) && (k_max_Q[ij] >= d1)){
      int l_min = l_min_Q[ij][d1];
      if((d2 % 2) == (l_min%2))
        if((l_min <= d2) && (l_max_Q[ij][d1] >= d2))
          dumb = 0;
    }
  }
  if(dumb){
    vrna_message_error("neighborhood %d:%d is not in scope of calculated partition function!\n"
                              "pbacktrack@2Dpfold.c: exiting...",
                              d1, d2);
  }

  pstruc = vrna_alloc((length+1)*sizeof(char));

  for (i=0; i<length; i++) pstruc[i] = '.';
  pstruc[i] = '\0';

  start = 1;
  while (start<length) {
    int sn = my_iindx[start] - length;
    /* find i position of first pair */
    FLT_OR_DBL qln_i = 0, qln_i1 = 0;

    if(d1 == -1){
      qln_i = Q_rem[sn];

      /* open chain ? */
      if(   (maxD1 > referenceBPs1[sn])
        &&  (maxD2 > referenceBPs2[sn])){
        r = vrna_urn() * qln_i;
        if(scale[length-start+1] > r)
          return pstruc;
      }

      /* lets see if we find a base pair with i involved */
      for (i=start; i<length; i++) {
        r = vrna_urn() * qln_i;

        qln_i1 = Q_rem[my_iindx[i+1] - length];

        da = referenceBPs1[sn] - referenceBPs1[my_iindx[i+1] - length];
        db = referenceBPs2[sn] - referenceBPs2[my_iindx[i+1] - length];

        for(cnt1 = k_min_Q[my_iindx[i+1] - length];
            cnt1 <= k_max_Q[my_iindx[i+1] - length];
            cnt1++)
          for(cnt2 = l_min_Q[my_iindx[i+1] - length][cnt1];
              cnt2 <= l_max_Q[my_iindx[i+1] - length][cnt1];
              cnt2 += 2)
            if(((cnt1 + da) > maxD1) || ((cnt2 + db) > maxD2)){
              qln_i1 += Q[my_iindx[i+1] - length][cnt1][cnt2/2];
            }

        if(r > qln_i1*scale[1]) break;

        qln_i = qln_i1;
      }
      if (i>=length) break; /* no more pairs */

      /* i is paired, find pairing partner j */
      r = vrna_urn() * (qln_i - qln_i1*scale[1]);
      for (qt=0, j=i+TURN+1; j<length; j++) {
        ij = my_iindx[i]-j;
        type = ptype[jindx[j] + i];
        if (type) {
          cnt1 = cnt2 = cnt3 = cnt4 = -1;
          double qkl = exp_E_ExtLoop(type, (i>1) ? S1[i-1] : -1, S1[j+1], pf_params);

          if(Q_B_rem[ij] != 0.){
            if(Q_rem[my_iindx[j+1]-length] != 0.){
              qt += qkl * Q_B_rem[ij] * Q_rem[my_iindx[j+1]-length];
              if(qt >= r)
                goto pbacktrack_ext_loop_early_escape_rem;
            }
            if(Q[my_iindx[j+1]-length])
              for(cnt3 = k_min_Q[my_iindx[j+1]-length];
                  cnt3 <= k_max_Q[my_iindx[j+1]-length];
                  cnt3++)
                for(cnt4 = l_min_Q[my_iindx[j+1]-length][cnt3];
                    cnt4 <= l_max_Q[my_iindx[j+1]-length][cnt3];
                    cnt4 += 2){
                  qt += qkl * Q_B_rem[ij] * Q[my_iindx[j+1]-length][cnt3][cnt4/2];
                  if(qt >= r)
                    goto pbacktrack_ext_loop_early_escape_rem;
                }
          }
          if(Q_rem[my_iindx[j+1]-length] != 0.){
            cnt3 = cnt4 = -1;
            if(Q_B[ij]){
              for(cnt1 = k_min_Q_B[ij];
                  cnt1 <= k_max_Q_B[ij];
                  cnt1++)
                for(cnt2 = l_min_Q_B[ij][cnt1];
                    cnt2 <= l_max_Q_B[ij][cnt1];
                    cnt2 += 2){
                  qt += qkl * Q_B[ij][cnt1][cnt2/2] * Q_rem[my_iindx[j+1]-length];
                  if(qt >= r)
                    goto pbacktrack_ext_loop_early_escape_rem;
                }
            }
          }
          /* if we still search for pairing partner j, we go on here... */
          if(Q_B[ij] && Q[my_iindx[j+1]-length]){
            da = referenceBPs1[sn] - referenceBPs1[ij] - referenceBPs1[my_iindx[j+1]-length];
            db = referenceBPs2[sn] - referenceBPs2[ij] - referenceBPs2[my_iindx[j+1]-length];
            for(cnt1 = k_min_Q_B[ij];
                cnt1 <= k_max_Q_B[ij];
                cnt1++)
              for(cnt2 = l_min_Q_B[ij][cnt1];
                  cnt2 <= l_max_Q_B[ij][cnt1];
                  cnt2 += 2)
                for(cnt3 = k_min_Q[my_iindx[j+1]-length];
                    cnt3 <= k_max_Q[my_iindx[j+1]-length];
                    cnt3++)
                  for(cnt4 = l_min_Q[my_iindx[j+1]-length][cnt3];
                      cnt4 <= l_max_Q[my_iindx[j+1]-length][cnt3];
                      cnt4 += 2)
                    if(((cnt1 + cnt3 + da) > maxD1) || ((cnt2 + cnt4 + db) > maxD2)){
                      qt += qkl * Q_B[ij][cnt1][cnt2/2] * Q[my_iindx[j+1]-length][cnt3][cnt4/2];
                      if(qt >= r)
                        goto pbacktrack_ext_loop_early_escape_rem;
                    }
          }
        } /* end if(type) */
      } /* end for(j) */
      cnt1 = cnt2 = cnt3 = cnt4 = -1;
      /* dont forget the case where i pairs with n */
      j = length;
      ij = my_iindx[i]-j;
      type = ptype[jindx[j] + i];
      if (type) {
        double qkl = exp_E_ExtLoop(type, (i>1) ? S1[i-1] : -1, (j<n) ? S1[j+1] : -1, pf_params);
        if(Q_B_rem[ij] != 0.){
          qt += qkl * Q_B_rem[ij];
          if(qt >= r)
            goto pbacktrack_ext_loop_early_escape_rem;
        }
        /* if we still search for pairing partner j, we go on here... */
        if(Q_B[ij]){
          da = referenceBPs1[sn] - referenceBPs1[ij];
          db = referenceBPs2[sn] - referenceBPs2[ij];
          for(cnt1 = k_min_Q_B[ij];
              cnt1 <= k_max_Q_B[ij];
              cnt1++)
            for(cnt2 = l_min_Q_B[ij][cnt1];
                cnt2 <= l_max_Q_B[ij][cnt1];
                cnt2 += 2)
              if(((cnt1 + da) > maxD1) || ((cnt2 + db) > maxD2)){
                qt += qkl * Q_B[ij][cnt1][cnt2/2];
                if(qt >= r)
                  goto pbacktrack_ext_loop_early_escape_rem;
              }
        }
      } /* end if(type) */
      j++;

pbacktrack_ext_loop_early_escape_rem:

      if (j==length+1){
        vrna_message_error("pbacktrack@2Dpfold.c: backtracking failed in ext loop (rem)");
      }

      /* finally start backtracking the first exterior stem */
      backtrack(vc, pstruc, cnt1, cnt2, i,j);
      if(j==length) break;
      start = j+1;
      d1 = cnt3;
      d2 = cnt4;

    } /* end if d1 ==-1 */
    else{
      qln_i = Q[sn][d1][d2/2];

      /* open chain ? */
      if(   (d1 == referenceBPs1[sn])
        &&  (d2 == referenceBPs2[sn])){
        r = vrna_urn() * qln_i;
        if(scale[length-start+1] > r)
          return pstruc;
      }

      for (i=start; i<length; i++) {
        r = vrna_urn() * qln_i;
        da = referenceBPs1[sn] - referenceBPs1[my_iindx[i+1] - length];
        db = referenceBPs2[sn] - referenceBPs2[my_iindx[i+1] - length];
        qln_i1 = 0;
        if(d1 >= da && d2 >= db)
          if(
              (d1-da >= k_min_Q[my_iindx[i+1] - length])
           && (d1 - da <= k_max_Q[my_iindx[i+1] - length]))
            if(
                  (d2 - db >= l_min_Q[my_iindx[i+1] - length][d1 - da])
              &&  (d2 - db <= l_max_Q[my_iindx[i+1] - length][d1 - da]))
              qln_i1 += Q[my_iindx[i+1] - length][d1-da][(d2-db)/2];
        if (r > qln_i1*scale[1])  break; /* i is paired */
        qln_i = qln_i1;
      }

      if (i>=length) break; /* no more pairs */

      /* now find the pairing partner j */
      r = vrna_urn() * (qln_i - qln_i1*scale[1]);

      for (qt=0, j=i+1; j<length; j++) {
        int type;
        ij = my_iindx[i]-j;
        type = ptype[jindx[j] + i];
        if (type) {
          double qkl = 1.0;
          qkl *= exp_E_ExtLoop(type, (i>1) ? S1[i-1] : -1, S1[j+1], pf_params);

          da = referenceBPs1[sn] - referenceBPs1[ij] - referenceBPs1[my_iindx[j+1]-length];
          db = referenceBPs2[sn] - referenceBPs2[ij] - referenceBPs2[my_iindx[j+1]-length];

          if(   (d1 >= da)
            &&  (d2 >= db)
            &&  Q_B[ij]
            &&  Q[my_iindx[j+1]-length])
            for(cnt1 = k_min_Q_B[ij];
                cnt1 <= MIN2(k_max_Q_B[ij], d1-da);
                cnt1++)
              for(cnt2 = l_min_Q_B[ij][cnt1];
                  cnt2 <= MIN2(l_max_Q_B[ij][cnt1], d2-db);
                  cnt2+=2)
                if(   (d1-da-cnt1 >= k_min_Q[my_iindx[j+1]-length])
                  &&  (d1-da-cnt1 <= k_max_Q[my_iindx[j+1]-length]))
                  if(   (d2 - db - cnt2 >= l_min_Q[my_iindx[j+1]-length][d1-da-cnt1]) 
                    &&  (d2 - db - cnt2 <= l_max_Q[my_iindx[j+1]-length][d1-da-cnt1])){
                    qt += qkl * Q_B[ij][cnt1][cnt2/2] * Q[my_iindx[j+1]-length][d1-da-cnt1][(d2-db-cnt2)/2];
                    if(qt >= r)
                      goto pbacktrack_ext_loop_early_escape;
                  }
        }
      }
      /* now dont forget the case j==n */
      j = length;
      ij = my_iindx[i]-j;
      int type = ptype[jindx[j] + i];
      if (type) {
        double qkl = 1.0;

        qkl *= exp_E_ExtLoop(type, (i>1) ? S1[i-1] : -1, (j<n) ? S1[j+1] : -1, pf_params);

        da = referenceBPs1[sn] - referenceBPs1[ij];
        db = referenceBPs2[sn] - referenceBPs2[ij];
        if(d1 >= da && d2 >= db){
          cnt1 = d1 - da;
          cnt2 = d2 - db;
          if((cnt1 >= k_min_Q_B[ij]) && (cnt1 <= k_max_Q_B[ij]))
            if((cnt2 >= l_min_Q_B[ij][cnt1]) && (cnt2 <= l_max_Q_B[ij][cnt1])){
              qt += qkl * Q_B[ij][cnt1][cnt2/2];
              if(qt >= r)
                goto pbacktrack_ext_loop_early_escape; /* j is paired */
            }
        }
      }
      j++;

pbacktrack_ext_loop_early_escape:

      if (j==length+1){
        vrna_message_error("pbacktrack@2Dpfold.c: backtracking failed in ext loop");
      }

      backtrack(vc, pstruc, cnt1, cnt2, i,j);

      if(j==length) break;
      start = j+1;
      d1 -= cnt1 + da;
      d2 -= cnt2 + db;
    } /* end if d1!=-1 */
  }
  return pstruc;
}


PRIVATE char *
pbacktrack_circ(vrna_fold_compound_t *vc,
                int d1,
                int d2){

  char            *pstruc;
  unsigned int    i, n, maxD1, maxD2,
                  *referenceBPs1, *referenceBPs2;
  int             *my_iindx,
                  k_min_Q_c, k_max_Q_c,
                  k_min_Q_cH, k_max_Q_cH,
                  k_min_Q_cI, k_max_Q_cI,
                  k_min_Q_cM, k_max_Q_cM,
                  *l_min_Q_c, *l_max_Q_c,
                  *l_min_Q_cH, *l_max_Q_cH,
                  *l_min_Q_cI, *l_max_Q_cI,
                  *l_min_Q_cM, *l_max_Q_cM;
  FLT_OR_DBL      r, *scale, qot,
                  **Q_c, **Q_cH, **Q_cI, **Q_cM,
                  Q_c_rem, Q_cH_rem, Q_cI_rem, Q_cM_rem;
  vrna_mx_pf_t      *matrices;
  vrna_md_t         *md;
  vrna_exp_param_t  *pf_params;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  n                 = vc->length;
  maxD1             = vc->maxD1;
  maxD2             = vc->maxD2;
  my_iindx          = vc->iindx;
  scale             = matrices->scale;
  referenceBPs1     = vc->referenceBPs1;
  referenceBPs2     = vc->referenceBPs2;

  Q_c               = matrices->Q_c;
  l_min_Q_c   = matrices->l_min_Q_c;
  l_max_Q_c   = matrices->l_max_Q_c;
  k_min_Q_c   = matrices->k_min_Q_c;
  k_max_Q_c   = matrices->k_max_Q_c;

  Q_cH              = matrices->Q_cH;
  l_min_Q_cH  = matrices->l_min_Q_cH;
  l_max_Q_cH  = matrices->l_max_Q_cH;
  k_min_Q_cH  = matrices->k_min_Q_cH;
  k_max_Q_cH  = matrices->k_max_Q_cH;

  Q_cI              = matrices->Q_cI;
  l_min_Q_cI  = matrices->l_min_Q_cI;
  l_max_Q_cI  = matrices->l_max_Q_cI;
  k_min_Q_cI  = matrices->k_min_Q_cI;
  k_max_Q_cI  = matrices->k_max_Q_cI;

  Q_cM              = matrices->Q_cM;
  l_min_Q_cM  = matrices->l_min_Q_cM;
  l_max_Q_cM  = matrices->l_max_Q_cM;
  k_min_Q_cM  = matrices->k_min_Q_cM;
  k_max_Q_cM  = matrices->k_max_Q_cM;

  Q_c_rem           = matrices->Q_c_rem;
  Q_cH_rem          = matrices->Q_cH_rem;
  Q_cI_rem          = matrices->Q_cI_rem;
  Q_cM_rem          = matrices->Q_cM_rem;

  /* check whether the chosen neighborhood exists at all */
  int dumb = 1;
  if((d1 == -1) && (Q_c_rem != 0.)) dumb = 0;
  else{
    if((k_min_Q_c <= d1) && (k_max_Q_c >= d1)){
      int l_min = l_min_Q_c[d1];
      if((d2 % 2) == (l_min%2))
        if((l_min <= d2) && (l_max_Q_c[d1] >= d2))
          dumb = 0;
    }
  }
  if(dumb){
    vrna_message_error("neighborhood %d:%d is not in scope of calculated partition function!\n"
                              "pbacktrack_circ@2Dpfold.c: exiting cheerless...",
                              d1, d2);
  }

  pstruc = vrna_alloc((n+1)*sizeof(char));

  for (i=0; i<n; i++) pstruc[i] = '.';
  pstruc[i] = '\0';

  /* now we come to the actual backtracking process */

  qot = 0.;
  /* backtrack in rest-partition */
  if(d1 == -1){
    r = vrna_urn() * Q_c_rem;
    /* open chain ? */
    if((referenceBPs1[my_iindx[1]-n] > maxD1) || (referenceBPs2[my_iindx[1]-n] > maxD2)){
      qot = 1.0 * scale[n];
      if(qot >= r)
        goto pbacktrack_circ_escape;
    }
    qot += Q_cH_rem;
    if(qot >= r){
      backtrack_qcH(vc, pstruc, d1, d2);
      goto pbacktrack_circ_escape;
    }
    qot += Q_cI_rem;
    if(qot >= r){
      backtrack_qcI(vc, pstruc, d1, d2);
      goto pbacktrack_circ_escape;
    }
    qot += Q_cM_rem;
    if(qot >= r){
      backtrack_qcM(vc, pstruc, d1, d2);
      goto pbacktrack_circ_escape;
    }
    vrna_message_error("pbacktrack_circ@2Dpfold.c: backtracking failed in exterior loop! Exiting cheerless...");
  }
  /* normal backtracking */
  else{
    r = vrna_urn() * Q_c[d1][d2/2];

    /* open chain ? */
    if((referenceBPs1[my_iindx[1]-n] == d1) && (referenceBPs2[my_iindx[1]-n] == d2)){
      qot += 1.0 * scale[n];
      if(qot >= r)
        goto pbacktrack_circ_escape;
    }

    /* exterior hairpin loop ? */
    if((k_min_Q_cH <= d1) && (k_max_Q_cH >= d1)){
      int l_min = l_min_Q_cH[d1];
      if((d2 % 2) == (l_min%2))
        if((l_min <= d2) && (l_max_Q_cH[d1] >= d2)){
          qot += Q_cH[d1][d2/2];
          if(qot >= r){
            backtrack_qcH(vc, pstruc, d1, d2);
            goto pbacktrack_circ_escape;
          }
        }
    }

    /* exterior interior loop ? */
    if((k_min_Q_cI <= d1) && (k_max_Q_cI >= d1)){
      int l_min = l_min_Q_cI[d1];
      if((d2 % 2) == (l_min%2))
        if((l_min <= d2) && (l_max_Q_cI[d1] >= d2)){
          qot += Q_cI[d1][d2/2];
          if(qot >= r){
            backtrack_qcI(vc, pstruc, d1, d2);
            goto pbacktrack_circ_escape;
          }
        }
    }

    /* exterior multibranch loop ? */
    if((k_min_Q_cM <= d1) && (k_max_Q_cM >= d1)){
      int l_min = l_min_Q_cM[d1];
      if((d2 % 2) == (l_min%2))
        if((l_min <= d2) && (l_max_Q_cM[d1] >= d2)){
          qot += Q_cM[d1][d2/2];
          if(qot >= r){
            backtrack_qcM(vc, pstruc, d1, d2);
            goto pbacktrack_circ_escape;
          }
        }
    }
  }

pbacktrack_circ_escape:
  return pstruc;
}



PRIVATE void
backtrack_qcH(vrna_fold_compound_t *vc,
              char *pstruc,
              int d1,
              int d2){

  char            *ptype, *sequence;
  short           *S1;
  unsigned int    i, j, n, maxD1, maxD2,
                  base_d1, base_d2, da, db,
                  *referenceBPs1, *referenceBPs2;
  int             u, *my_iindx, *jindx, ij, cnt1, cnt2,type,
                  **l_min_Q_B, **l_max_Q_B,
                  *k_min_Q_B, *k_max_Q_B, *rtype;
  FLT_OR_DBL      r, qt, *scale, qot,
                  ***Q_B, **Q_cH, *Q_B_rem,
                  Q_cH_rem;

  vrna_exp_param_t  *pf_params;
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  sequence          = vc->sequence;
  n                 = vc->length;
  my_iindx          = vc->iindx;
  jindx             = vc->jindx;
  scale             = matrices->scale;
  ptype             = vc->ptype;
  rtype           = &(md->rtype[0]);
  S1                = vc->sequence_encoding;
  referenceBPs1     = vc->referenceBPs1;
  referenceBPs2     = vc->referenceBPs2;
  maxD1             = vc->maxD1;
  maxD2             = vc->maxD2;

  Q_B_rem           = matrices->Q_B_rem;
  Q_B               = matrices->Q_B;
  l_min_Q_B    = matrices->l_min_Q_B;
  l_max_Q_B    = matrices->l_max_Q_B;
  k_min_Q_B    = matrices->k_min_Q_B;
  k_max_Q_B    = matrices->k_max_Q_B;

  Q_cH_rem          = matrices->Q_cH_rem;
  Q_cH              = matrices->Q_cH;

  qot = qt = 0.;

  base_d1 = referenceBPs1[my_iindx[1]-n];
  base_d2 = referenceBPs2[my_iindx[1]-n];

  if(d1 == -1){
    r = vrna_urn() * Q_cH_rem;
    for(i=1;i<n;i++)
      for(j=i+TURN+1;j<=n;j++){
        char loopseq[10];
        ij = my_iindx[i]-j;
        u = n-j + i-1;
        if (u<TURN) continue;
        type = ptype[jindx[j] + i];
        if (!type) continue;
        if(((type==3)||(type==4))&&no_closingGU) continue;
        type=rtype[type];
        if (u<7){
          strcpy(loopseq , sequence+j-1);
          strncat(loopseq, sequence, i);
        }
        qt  = exp_E_Hairpin(u, type,
                            S1[j+1], S1[i-1],
                            loopseq, pf_params)
              * scale[u];

        if(Q_B_rem[ij]){
          qot += Q_B_rem[ij] * qt;
          if(qot >= r){
            backtrack(vc, pstruc, d1, d2, i, j);
            return;
          }
        }

        da = base_d1 - referenceBPs1[ij];
        db = base_d2 - referenceBPs2[ij];

        if(Q_B[ij]){
          for(cnt1 = k_min_Q_B[ij];
              cnt1 <= k_max_Q_B[ij];
              cnt1++)
            for(cnt2 = l_min_Q_B[ij][cnt1];
                cnt2 <= l_max_Q_B[ij][cnt1];
                cnt2 += 2){
              if(     ((cnt1 + da) > maxD1)
                  ||  ((cnt2 + db) > maxD2)){
                qot += Q_B[ij][cnt1][cnt2/2] * qt;
                if(qot >= r){
                  backtrack(vc, pstruc, cnt1, cnt2, i, j);
                  return;
                }
              }
            }
        }
    }
  }
  else{
    r = vrna_urn() * Q_cH[d1][d2/2];
    for(i=1;i<n;i++)
      for(j=i+TURN+1;j<=n;j++){
        char loopseq[10];
        ij = my_iindx[i]-j;
        if(!Q_B[ij]) continue;
        u = n-j + i-1;
        if (u<TURN) continue;
        type = ptype[jindx[j] + i];
        if (!type) continue;
        if(((type==3)||(type==4))&&no_closingGU) continue;
        type=rtype[type];
        if (u<7){
          strcpy(loopseq , sequence+j-1);
          strncat(loopseq, sequence, i);
        }
        qt  = exp_E_Hairpin(u, type,
                            S1[j+1], S1[i-1],
                            loopseq, pf_params)
              * scale[u];
        da  = base_d1 - referenceBPs1[ij];
        db  = base_d2 - referenceBPs2[ij];

        for(cnt1 = k_min_Q_B[ij];
            cnt1 <= k_max_Q_B[ij];
            cnt1++)
          for(cnt2 = l_min_Q_B[ij][cnt1];
              cnt2 <= l_max_Q_B[ij][cnt1];
              cnt2 += 2){
            if( ((cnt1 + da) == d1)
                && ((cnt2 + db) == d2)){
              qot += Q_B[ij][cnt1][cnt2/2] * qt;
              if(qot >= r){
                backtrack(vc, pstruc, cnt1, cnt2, i, j);
                return;
              }
            }
          }
      }
  }
  vrna_message_error("backtrack_qcH@2Dpfold.c: failed to find closing pair!");
}

PRIVATE void  backtrack_qcI(vrna_fold_compound_t *vc,
                            char *pstruc,
                            int d1, int d2){

  char            *ptype;
  short           *S1;
  unsigned int    i, j, ij, p, q, pq, n, maxD1, maxD2,
                  base_d1, base_d2, da, db,
                  *referenceBPs1, *referenceBPs2;
  int             *my_iindx, *jindx, cnt1, cnt2, cnt3, cnt4, type,
                  **l_min_Q_B, **l_max_Q_B,
                  *k_min_Q_B, *k_max_Q_B, *rtype;
  FLT_OR_DBL      r, qt, *scale, qot,
                  ***Q_B, *Q_B_rem,
                  **Q_cI, Q_cI_rem;
  vrna_exp_param_t       *pf_params;
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  n                 = vc->length;
  my_iindx          = vc->iindx;
  jindx             = vc->jindx;
  scale             = matrices->scale;
  ptype             = vc->ptype;
  rtype           = &(md->rtype[0]);
  S1                = vc->sequence_encoding;
  referenceBPs1     = vc->referenceBPs1;
  referenceBPs2     = vc->referenceBPs2;
  maxD1             = vc->maxD1;
  maxD2             = vc->maxD2;

  Q_B               = matrices->Q_B;
  l_min_Q_B    = matrices->l_min_Q_B;
  l_max_Q_B    = matrices->l_max_Q_B;
  k_min_Q_B    = matrices->k_min_Q_B;
  k_max_Q_B    = matrices->k_max_Q_B;

  Q_cI              = matrices->Q_cI;
  Q_B_rem           = matrices->Q_B_rem;
  Q_cI_rem          = matrices->Q_cI_rem;

  qot = qt = 0.;

  base_d1 = referenceBPs1[my_iindx[1]-n];
  base_d2 = referenceBPs2[my_iindx[1]-n];

  if(d1 == -1){
    r = vrna_urn() * Q_cI_rem;
    for(i=1;i<n;i++)
      for(j=i+TURN+1;j<=n;j++){
        ij = my_iindx[i]-j;
        type = rtype[(unsigned int)ptype[jindx[j] + i]];
        if(!type) continue;

        if(Q_B_rem[ij])
          for(p=j+1; p < n; p++){
            unsigned int ln1, qstart, ln_pre;
            ln1 = p - j - 1;
            if(ln1+i-1>MAXLOOP) break;
            qstart = p + TURN + 1;
            ln_pre = ln1 + i + n;
            if(ln_pre > qstart + MAXLOOP)
              qstart = ln_pre - MAXLOOP - 1;
            for(q=qstart;q <= n; q++){
              unsigned int ln2;
              int type2;
              pq = my_iindx[p]-q;
              ln2 = (i - 1) + (n - q);
              if((ln1+ln2) > MAXLOOP) continue;
              type2 = ptype[jindx[q] + p];
              if(!type2) continue;
              qt  = exp_E_IntLoop(ln2, ln1,
                                  rtype[type2], type,
                                  S1[q+1], S1[p-1],
                                  S1[i-1], S1[j+1],
                                  pf_params)
                    * scale[ln1 + ln2];
              if(Q_B_rem[pq]){
                qot +=  Q_B_rem[ij] * Q_B_rem[pq] * qt;
                if(qot > r){
                  backtrack(vc, pstruc, d1, d2, i, j);
                  backtrack(vc, pstruc, d1, d2, p, q);
                  return;
                }
              }
              if(Q_B[pq])
                for(cnt1 = k_min_Q_B[pq];
                    cnt1 <= k_max_Q_B[pq];
                    cnt1++)
                  for(cnt2 = l_min_Q_B[pq][cnt1];
                      cnt2 <= l_max_Q_B[pq][cnt1];
                      cnt2 += 2){
                    qot +=  Q_B_rem[ij] * Q_B[pq][cnt1][cnt2/2] * qt;
                    if(qot > r){
                      backtrack(vc, pstruc, d1, d2, i, j);
                      backtrack(vc, pstruc, cnt1, cnt2, p, q);
                      return;
                    }
                  }
            }
          }

        if(Q_B[ij]){
          for(p=j+1; p < n; p++){
            unsigned int ln1, qstart, ln_pre;
            ln1 = p - j - 1;
            if(ln1+i-1>MAXLOOP) break;
            qstart = p + TURN + 1;
            ln_pre = ln1 + i + n;
            if(ln_pre > qstart + MAXLOOP)
              qstart = ln_pre - MAXLOOP - 1;
            for(q=qstart;q <= n; q++){
              unsigned int ln2;
              int type2;
              pq = my_iindx[p]-q;
              ln2 = (i - 1) + (n - q);
              if((ln1+ln2) > MAXLOOP) continue;
              type2 = ptype[jindx[q] + p];
              if(!type2) continue;
              qt  = exp_E_IntLoop(ln2, ln1,
                                  rtype[type2], type,
                                  S1[q+1], S1[p-1],
                                  S1[i-1], S1[j+1],
                                  pf_params)
                    * scale[ln1 + ln2];
              if(Q_B_rem[pq])
                for(cnt1 = k_min_Q_B[ij];
                    cnt1 <= k_max_Q_B[ij];
                    cnt1++)
                  for(cnt2 = l_min_Q_B[ij][cnt1];
                      cnt2 <= l_max_Q_B[ij][cnt1];
                      cnt2 += 2){
                    qot +=  Q_B[ij][cnt1][cnt2/2] * Q_B_rem[pq] * qt;
                    if(qot > r){
                      backtrack(vc, pstruc, cnt1, cnt2, i, j);
                      backtrack(vc, pstruc, d1, d2, p, q);
                      return;
                    }
                  }
              if(Q_B[pq]){
                da  = base_d1
                      - referenceBPs1[ij]
                      - referenceBPs1[pq];
                db  = base_d2
                      - referenceBPs2[ij]
                      - referenceBPs2[pq];
                for(cnt1 = k_min_Q_B[ij];
                    cnt1 <= k_max_Q_B[ij];
                    cnt1++)
                  for(cnt2 = l_min_Q_B[ij][cnt1];
                      cnt2 <= l_max_Q_B[ij][cnt1];
                      cnt2 += 2)
                    for(cnt3 = k_min_Q_B[pq];
                        cnt3 <= k_max_Q_B[pq];
                        cnt3++)
                      for(cnt4 = l_min_Q_B[pq][cnt3];
                          cnt4 <= l_max_Q_B[pq][cnt3];
                          cnt4 += 2){
                        if(     ((cnt1 + cnt3 + da) > maxD1)
                            ||  ((cnt2 + cnt4 + db) > maxD2)){
                          qot +=  Q_B[ij][cnt1][cnt2/2]
                                  * Q_B[pq][cnt3][cnt4/2]
                                  * qt;
                          if(qot > r){
                            backtrack(vc, pstruc, cnt1, cnt2, i, j);
                            backtrack(vc, pstruc, cnt3, cnt4, p, q);
                            return;
                          }
                        }
                      }
              }
            }
          }
        }

      }
  }
  else{
    r = vrna_urn() * Q_cI[d1][d2/2];
    for(i=1;i<n;i++)
      for(j=i+TURN+1;j<=n;j++){
        ij = my_iindx[i]-j;
        type = rtype[(unsigned int)ptype[jindx[j] + i]];
        if(!type) continue;
        if(!Q_B[ij]) continue;
        for(p=j+1; p < n; p++){
          unsigned int ln1, qstart, ln_pre;
          ln1 = p - j - 1;
          if(ln1+i-1>MAXLOOP) break;
          qstart = p + TURN + 1;
          ln_pre = ln1 + i + n;
          if(ln_pre > qstart + MAXLOOP)
            qstart = ln_pre - MAXLOOP - 1;
          for(q=qstart;q <= n; q++){
            unsigned int ln2;
            int type2;
            pq    = my_iindx[p]-q;
            if(!Q_B[pq]) continue;
            ln2   = (i - 1) + (n - q);
            if((ln1+ln2) > MAXLOOP) continue;
            type2 = ptype[jindx[q] + p];
            if(!type2) continue;
            qt  = exp_E_IntLoop( ln2, ln1,
                                rtype[type2], type,
                                S1[q+1], S1[p-1],
                                S1[i-1], S1[j+1],
                                pf_params)
                  * scale[ln1 + ln2];
            da  = base_d1
                  - referenceBPs1[ij]
                  - referenceBPs1[pq];
            db  = base_d2
                  - referenceBPs2[ij]
                  - referenceBPs2[pq];
            for(cnt1 = k_min_Q_B[ij];
                cnt1 <= k_max_Q_B[ij];
                cnt1++)
              for(cnt2 = l_min_Q_B[ij][cnt1];
                  cnt2 <= l_max_Q_B[ij][cnt1];
                  cnt2 += 2)
                for(cnt3 = k_min_Q_B[pq];
                    cnt3 <= k_max_Q_B[pq];
                    cnt3++)
                  for(cnt4 = l_min_Q_B[pq][cnt3];
                      cnt4 <= l_max_Q_B[pq][cnt3];
                      cnt4 += 2){
                    if(     ((cnt1 + cnt3 + da) == d1)
                        &&  ((cnt2 + cnt4 + db) == d2)){
                      qot +=  Q_B[ij][cnt1][cnt2/2]
                              * Q_B[pq][cnt3][cnt4/2]
                              * qt;
                      if(qot > r){
                        backtrack(vc, pstruc, cnt1, cnt2, i, j);
                        backtrack(vc, pstruc, cnt3, cnt4, p, q);
                        return;
                      }
                    }
                  }
          }
        }
      }
  }
}

PRIVATE void  backtrack_qcM(vrna_fold_compound_t *vc,
                            char *pstruc,
                            int d1, int d2){

  unsigned int  k, n, maxD1, maxD2, base_d1, base_d2,
                da, db, *referenceBPs1, *referenceBPs2;
  int           *my_iindx, cnt1, cnt2, cnt3, cnt4,
                **l_min_Q_M, **l_max_Q_M,
                **l_min_Q_M2, **l_max_Q_M2,
                *k_min_Q_M, *k_max_Q_M,
                *k_min_Q_M2, *k_max_Q_M2;
  FLT_OR_DBL    r, qt, qot,
                ***Q_M, ***Q_M2, **Q_cM,
                *Q_M_rem, *Q_M2_rem, Q_cM_rem;
  vrna_exp_param_t  *pf_params;
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  n                 = vc->length;
  my_iindx          = vc->iindx;
  referenceBPs1     = vc->referenceBPs1;
  referenceBPs2     = vc->referenceBPs2;
  maxD1             = vc->maxD1;
  maxD2             = vc->maxD2;

  Q_cM              = matrices->Q_cM;

  Q_M               = matrices->Q_M;
  l_min_Q_M    = matrices->l_min_Q_M;
  l_max_Q_M    = matrices->l_max_Q_M;
  k_min_Q_M    = matrices->k_min_Q_M;
  k_max_Q_M    = matrices->k_max_Q_M;

  Q_M2              = matrices->Q_M2;
  l_min_Q_M2   = matrices->l_min_Q_M2;
  l_max_Q_M2   = matrices->l_max_Q_M2;
  k_min_Q_M2   = matrices->k_min_Q_M2;
  k_max_Q_M2   = matrices->k_max_Q_M2;

  Q_cM_rem          = matrices->Q_cM_rem;
  Q_M_rem           = matrices->Q_M_rem;
  Q_M2_rem          = matrices->Q_M2_rem;

  base_d1 = referenceBPs1[my_iindx[1]-n];
  base_d2 = referenceBPs2[my_iindx[1]-n];
  qot     = qt = 0.;

  if(d1 == -1){
    r = vrna_urn() * Q_cM_rem;
    for(k = TURN + 2;
        k < n - 2 * TURN - 3;
        k++){

      if(Q_M_rem[my_iindx[1]-k]){

        if(Q_M2[k+1])
          for(cnt1 = k_min_Q_M2[k+1];
              cnt1 <= k_max_Q_M2[k+1];
              cnt1++)
            for(cnt2 = l_min_Q_M2[k+1][cnt1];
                cnt2 <= l_max_Q_M2[k+1][cnt1];
                cnt2 += 2){
              qot +=  Q_M_rem[my_iindx[1]-k]
                      * Q_M2[k+1][cnt1][cnt2/2]
                      * pf_params->expMLclosing;
              if(qot > r){
                backtrack_qm(vc, pstruc, d1, d2, 1, k);
                backtrack_qm2(vc, pstruc, cnt1, cnt2, k+1);
                return;
              }
            }

        if(Q_M2_rem[k+1]){
          qot +=  Q_M_rem[my_iindx[1]-k]
                  * Q_M2_rem[k+1]
                  * pf_params->expMLclosing;
          if(qot > r){
            backtrack_qm(vc, pstruc, d1, d2, 1, k);
            backtrack_qm2(vc, pstruc, d1, d2, k+1);
            return;
          }
        }

      }

      if(Q_M2_rem[k+1]){

        if(Q_M[my_iindx[1]-k])
          for(cnt1 = k_min_Q_M[my_iindx[1]-k];
              cnt1 <= k_max_Q_M[my_iindx[1]-k];
              cnt1++)
            for(cnt2 = l_min_Q_M[my_iindx[1]-k][cnt1];
                cnt2 <= l_max_Q_M[my_iindx[1]-k][cnt1];
                cnt2 += 2){
              qot +=  Q_M[my_iindx[1]-k][cnt1][cnt2/2]
                      * Q_M2_rem[k+1]
                      * pf_params->expMLclosing;
              if(qot > r){
                backtrack_qm(vc, pstruc, cnt1, cnt2, 1, k);
                backtrack_qm2(vc, pstruc, d1, d2, k+1);
                return;
              }
            }

      }

      da  = base_d1
            - referenceBPs1[my_iindx[1]-k]
            - referenceBPs1[my_iindx[k+1]-n];
      db  = base_d2
            - referenceBPs2[my_iindx[1]-k]
            - referenceBPs2[my_iindx[k+1]-n];

      if(     Q_M[my_iindx[1]-k]
          &&  Q_M2[k+1])
        for(cnt1 = k_min_Q_M[my_iindx[1]-k];
            cnt1 <= k_max_Q_M[my_iindx[1]-k];
            cnt1++)
          for(cnt2 = l_min_Q_M[my_iindx[1]-k][cnt1];
              cnt2 <= l_max_Q_M[my_iindx[1]-k][cnt1];
              cnt2 += 2)
            for(cnt3 = k_min_Q_M2[k+1];
                cnt3 <= k_max_Q_M2[k+1];
                cnt3++)
              for(cnt4 = l_min_Q_M2[k+1][cnt3];
                  cnt4 <= l_max_Q_M2[k+1][cnt3];
                  cnt4 += 2){
                if(     ((cnt1 + cnt3 + da) > maxD1)
                    ||  ((cnt2 + cnt4 + db) > maxD2)){
                  qot   +=  Q_M[my_iindx[1]-k][cnt1][cnt2/2]
                            * Q_M2[k+1][cnt3][cnt4/2]
                            * pf_params->expMLclosing;
                  if(qot > r){
                    backtrack_qm(vc, pstruc, cnt1, cnt2, 1, k);
                    backtrack_qm2(vc, pstruc, cnt3, cnt4, k+1);
                    return;
                  }
                }
              }

    }
  }
  else{
    r = vrna_urn() * Q_cM[d1][d2/2];
    for(k = TURN + 2;
        k < n - 2 * TURN - 3;
        k++){
      da  = base_d1
            - referenceBPs1[my_iindx[1]-k]
            - referenceBPs1[my_iindx[k+1]-n];
      db  = base_d2
            - referenceBPs2[my_iindx[1]-k]
            - referenceBPs2[my_iindx[k+1]-n];
        if(     Q_M[my_iindx[1]-k]
            &&  Q_M2[k+1])
          for(cnt1 = k_min_Q_M[my_iindx[1]-k];
              cnt1 <= k_max_Q_M[my_iindx[1]-k];
              cnt1++)
            for(cnt2 = l_min_Q_M[my_iindx[1]-k][cnt1];
                cnt2 <= l_max_Q_M[my_iindx[1]-k][cnt1];
                cnt2 += 2)
              for(cnt3 = k_min_Q_M2[k+1];
                  cnt3 <= k_max_Q_M2[k+1];
                  cnt3++)
                for(cnt4 = l_min_Q_M2[k+1][cnt3];
                    cnt4 <= l_max_Q_M2[k+1][cnt3];
                    cnt4 += 2)
                  if(     ((cnt1 + cnt3 + da) == d1)
                      &&  ((cnt2 + cnt4 + db) == d2)){
                    qot +=  Q_M[my_iindx[1]-k][cnt1][cnt2/2]
                            * Q_M2[k+1][cnt3][cnt4/2]
                            * pf_params->expMLclosing;
                    if(qot > r){
                      backtrack_qm(vc, pstruc, cnt1, cnt2, 1, k);
                      backtrack_qm2(vc, pstruc, cnt3, cnt4, k+1);
                      return;
                    }
                  }
    }
  }
  vrna_message_error("backtrack_qcM@2Dpfold.c: backtracking failed");
}

PRIVATE void
backtrack_qm2(vrna_fold_compound_t *vc,
              char *pstruc,
              int d1,
              int d2,
              unsigned int k){

  unsigned int  l, n, maxD1, maxD2, da, db,
                *referenceBPs1, *referenceBPs2;
  int           *my_iindx, *jindx, cnt1, cnt2, cnt3, cnt4,
                *k_min_Q_M1, *k_max_Q_M1,
                **l_min_Q_M1, **l_max_Q_M1;
  FLT_OR_DBL    r, qt, qot,
                ***Q_M2, ***Q_M1,
                *Q_M2_rem, *Q_M1_rem;

  vrna_exp_param_t  *pf_params;     /* holds all [unscaled] pf parameters */
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;

  n               = vc->length;
  my_iindx        = vc->iindx;
  jindx           = vc->jindx;
  referenceBPs1   = vc->referenceBPs1;
  referenceBPs2   = vc->referenceBPs2;
  maxD1           = vc->maxD1;
  maxD2           = vc->maxD2;

  Q_M1_rem        = matrices->Q_M1_rem;
  Q_M1            = matrices->Q_M1;
  l_min_Q_M1 = matrices->l_min_Q_M1;
  l_max_Q_M1 = matrices->l_max_Q_M1;
  k_min_Q_M1 = matrices->k_min_Q_M1;
  k_max_Q_M1 = matrices->k_max_Q_M1;

  Q_M2_rem        = matrices->Q_M2_rem;
  Q_M2            = matrices->Q_M2;

  qot = qt = 0.;

  if(d1 == -1){
    r = vrna_urn() * Q_M2_rem[k];
    for (l=k+TURN+1; l<n-TURN-1; l++){
      if(Q_M1_rem[jindx[l]+k]){
        if(Q_M1[jindx[n]+l+1]){
          for(cnt1 = k_min_Q_M1[jindx[n]+l+1];
              cnt1 <= k_max_Q_M1[jindx[n]+l+1];
              cnt1++)
            for(cnt2 = l_min_Q_M1[jindx[n]+l+1][cnt1];
                cnt2 <= l_max_Q_M1[jindx[n]+l+1][cnt1];
                cnt2 += 2){
              qot += Q_M1_rem[jindx[l]+k] * Q_M1[jindx[n]+l+1][cnt1][cnt2/2];
              if(qot > r){
                backtrack_qm1(vc, pstruc, d1, d2, k, l);
                backtrack_qm1(vc, pstruc, cnt1, cnt2, l+1, n);
                return;
              }
            }
        }
        if(Q_M1_rem[jindx[n]+l+1]){
          qot +=  Q_M1_rem[jindx[l]+k]
                  * Q_M1_rem[jindx[n]+l+1];
          if(qot > r){
            backtrack_qm1(vc, pstruc, d1, d2, k, l);
            backtrack_qm1(vc, pstruc, d1, d2, l+1, n);
            return;
          }
        }
      }
      if(Q_M1_rem[jindx[n]+l+1]){
        if(Q_M1[jindx[l]+k])
          for(cnt1 = k_min_Q_M1[jindx[l]+k];
              cnt1 <= k_max_Q_M1[jindx[l]+k];
              cnt1++)
            for(cnt2 = l_min_Q_M1[jindx[l]+k][cnt1];
                cnt2 <= l_max_Q_M1[jindx[l]+k][cnt1];
                cnt2 += 2){
              qot +=  Q_M1[jindx[l]+k][cnt1][cnt2/2]
                      * Q_M1_rem[jindx[n]+l+1];
              if(qot > r){
                backtrack_qm1(vc, pstruc, cnt1, cnt2, k, l);
                backtrack_qm1(vc, pstruc, d1, d2, l+1, n);
                return;
              }
            }
      }

      if(!Q_M1[jindx[l]+k]) continue;
      if(!Q_M1[jindx[n] + l + 1]) continue;

      da  = referenceBPs1[my_iindx[k]-n]
            - referenceBPs1[my_iindx[k]-l]
            - referenceBPs1[my_iindx[l+1]-n];
      db  = referenceBPs2[my_iindx[k]-n]
            - referenceBPs2[my_iindx[k]-l]
            - referenceBPs2[my_iindx[l+1]-n];
      for(cnt1 = k_min_Q_M1[jindx[l]+k];
          cnt1 <= k_max_Q_M1[jindx[l]+k];
          cnt1++)
        for(cnt2 = l_min_Q_M1[jindx[l]+k][cnt1];
            cnt2 <= l_max_Q_M1[jindx[l]+k][cnt1];
            cnt2 += 2){
          for(cnt3 = k_min_Q_M1[jindx[n] + l + 1];
              cnt3 <= k_max_Q_M1[jindx[n] + l + 1];
              cnt3++)
            for(cnt4 = l_min_Q_M1[jindx[n] + l + 1][cnt3];
                cnt4 <= l_max_Q_M1[jindx[n] + l + 1][cnt3];
                cnt4 += 2){
              if(    ((cnt1 + cnt3 + da) > maxD1)
                  || ((cnt2 + cnt4 + db) > maxD2)){
                qot +=  Q_M1[jindx[l]+k][cnt1][cnt2/2]
                        * Q_M1[jindx[n] + l + 1][cnt3][cnt4/2];
                if(qot > r){
                  backtrack_qm1(vc, pstruc, cnt1, cnt2, k, l);
                  backtrack_qm1(vc, pstruc, cnt3, cnt4, l+1, n);
                  return;
                }
              }
            }
        }
    }

  }
  else{
    r = vrna_urn() * Q_M2[k][d1][d2/2];
    for (l=k+TURN+1; l<n-TURN-1; l++){
      if(!Q_M1[jindx[l]+k]) continue;
      if(!Q_M1[jindx[n] + l + 1]) continue;

      da  = referenceBPs1[my_iindx[k]-n]
            - referenceBPs1[my_iindx[k]-l]
            - referenceBPs1[my_iindx[l+1]-n];
      db  = referenceBPs2[my_iindx[k]-n]
            - referenceBPs2[my_iindx[k]-l]
            - referenceBPs2[my_iindx[l+1]-n];
      for(cnt1 = k_min_Q_M1[jindx[l]+k];
          cnt1 <= k_max_Q_M1[jindx[l]+k];
          cnt1++)
        for(cnt2 = l_min_Q_M1[jindx[l]+k][cnt1];
            cnt2 <= l_max_Q_M1[jindx[l]+k][cnt1];
            cnt2 += 2){
          for(cnt3 = k_min_Q_M1[jindx[n] + l + 1];
              cnt3 <= k_max_Q_M1[jindx[n] + l + 1];
              cnt3++)
            for(cnt4 = l_min_Q_M1[jindx[n] + l + 1][cnt3];
                cnt4 <= l_max_Q_M1[jindx[n] + l + 1][cnt3];
                cnt4 += 2){
              if(     ((cnt1 + cnt3 + da) == d1)
                  &&  ((cnt2 + cnt4 + db) == d2)){
                qot +=  Q_M1[jindx[l]+k][cnt1][cnt2/2]
                        * Q_M1[jindx[n] + l + 1][cnt3][cnt4/2];
                if(qot > r){
                  backtrack_qm1(vc, pstruc, cnt1, cnt2, k, l);
                  backtrack_qm1(vc, pstruc, cnt3, cnt4, l+1, n);
                  return;
                }
              }
            }
        }
    }
  }
  vrna_message_error("backtrack_qm2@2Dpfold.c: backtracking failed");
}


PRIVATE void
backtrack(vrna_fold_compound_t *vc,
          char *pstruc,
          int d1,
          int d2,
          unsigned int i,
          unsigned int j) {

  FLT_OR_DBL      *scale;
  unsigned int    maxD1, maxD2, base_d1, base_d2, da, db;
  unsigned int    *referenceBPs1, *referenceBPs2;
  char            *ptype, *sequence;
  short           *S1, *reference_pt1, *reference_pt2;
  int             *my_iindx, *jindx, ij, cnt1, cnt2, cnt3, cnt4, *rtype;
  vrna_exp_param_t  *pf_params;     /* holds all [unscaled] pf parameters */
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  sequence    = vc->sequence;
  maxD1       = vc->maxD1;
  maxD2       = vc->maxD2;
  my_iindx    = vc->iindx;
  jindx       = vc->jindx;
  scale       = matrices->scale;
  ptype       = vc->ptype;
  rtype           = &(md->rtype[0]);
  S1              = vc->sequence_encoding;
  reference_pt1   = vc->reference_pt1;
  reference_pt2   = vc->reference_pt2;
  referenceBPs1   = vc->referenceBPs1;
  referenceBPs2   = vc->referenceBPs2;

  FLT_OR_DBL  ***Q_B, ***Q_M, ***Q_M1, *Q_B_rem, *Q_M_rem, *Q_M1_rem;
  int         *k_min_Q_M, *k_max_Q_M,*k_min_Q_M1, *k_max_Q_M1,*k_min_Q_B, *k_max_Q_B;
  int         **l_min_Q_M, **l_max_Q_M,**l_min_Q_M1, **l_max_Q_M1,**l_min_Q_B, **l_max_Q_B;

  Q_B = matrices->Q_B;
  k_min_Q_B = matrices->k_min_Q_B;
  k_max_Q_B = matrices->k_max_Q_B;
  l_min_Q_B = matrices->l_min_Q_B;
  l_max_Q_B = matrices->l_max_Q_B;

  Q_M = matrices->Q_M;
  k_min_Q_M = matrices->k_min_Q_M;
  k_max_Q_M = matrices->k_max_Q_M;
  l_min_Q_M = matrices->l_min_Q_M;
  l_max_Q_M = matrices->l_max_Q_M;

  Q_M1 = matrices->Q_M1;
  k_min_Q_M1 = matrices->k_min_Q_M1;
  k_max_Q_M1 = matrices->k_max_Q_M1;
  l_min_Q_M1 = matrices->l_min_Q_M1;
  l_max_Q_M1 = matrices->l_max_Q_M1;

  Q_B_rem   = matrices->Q_B_rem;
  Q_M_rem   = matrices->Q_M_rem;
  Q_M1_rem  = matrices->Q_M1_rem;

  do {
    double r, qbt1 = 0.;
    unsigned int k, l, u, u1;
    int type;

    pstruc[i-1] = '('; pstruc[j-1] = ')';

    r = 0.;
    ij = my_iindx[i]-j;

    if(d1 == -1){
      r= vrna_urn() * Q_B_rem[ij];
      if(r == 0.) vrna_message_error("backtrack@2Dpfold.c: backtracking failed\n");
      
      type = ptype[jindx[j] + i];
      u = j-i-1;
      base_d1 = ((unsigned int)reference_pt1[i] != j) ? 1 : -1;
      base_d2 = ((unsigned int)reference_pt2[i] != j) ? 1 : -1;

      da = base_d1 + referenceBPs1[ij];
      db = base_d2 + referenceBPs2[ij];

      /* hairpin ? */
      if((da > maxD1) || (db > maxD2))
        if(!(((type==3)||(type==4))&&no_closingGU))
          qbt1 = exp_E_Hairpin(u, type, S1[i+1], S1[j-1], sequence+i-1, pf_params) * scale[u+2];

      if (qbt1>=r) return; /* found the hairpin we're done */

      /* lets see if we form an interior loop */
      for (k=i+1; k<=MIN2(i+MAXLOOP+1,j-TURN-2); k++) {
        unsigned int u_pre, lmin;
        u1 = k-i-1;
        lmin = k + TURN + 1;
        u_pre = u1 + j;
        /* lmin = MAX2(k + TURN + 1, u1 + j - 1 - MAXLOOP) */
        if(u_pre > lmin + MAXLOOP) lmin = u_pre - 1 - MAXLOOP;
        for (l=lmin; l<j; l++) {
          int type_2;
          type_2 = ptype[jindx[l]+k];
          if (type_2) {
            cnt1 = cnt2 = -1;
            da = base_d1 + referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[k]-l];
            db = base_d2 + referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[k]-l];
            type_2 = rtype[type_2];
            FLT_OR_DBL tmp_en = exp_E_IntLoop(u1, j-l-1, type, type_2, S1[i+1], S1[j-1], S1[k-1], S1[l+1], pf_params) * scale[u1+j-l+1];

            if(Q_B_rem[my_iindx[k]-l] != 0.){
              qbt1 += Q_B_rem[my_iindx[k]-l] * tmp_en;
              if(qbt1 > r) goto backtrack_int_early_escape_rem;
            }

            if(Q_B[my_iindx[k]-l])
              for(cnt1 = k_min_Q_B[my_iindx[k]-l];
                  cnt1 <= k_max_Q_B[my_iindx[k]-l];
                  cnt1++)
                for(cnt2 = l_min_Q_B[my_iindx[k]-l][cnt1];
                    cnt2 <= l_max_Q_B[my_iindx[k]-l][cnt1];
                    cnt2 += 2)
                  if(((cnt1 + da) > maxD1) || ((cnt2 + db) > maxD2)){
                    qbt1 += Q_B[my_iindx[k]-l][cnt1][cnt2/2] * tmp_en;
                    if(qbt1 > r) goto backtrack_int_early_escape_rem;
                  }
          }
        }
      }
backtrack_int_early_escape_rem:
      if (l<j) {
        i=k; j=l;
        d1 = cnt1;
        d2 = cnt2;
      }
      else break;
    }
    else{

      if((d1 >= k_min_Q_B[ij]) && (d1 <= k_max_Q_B[ij]))
        if((d2 >= l_min_Q_B[ij][d1]) && (d2 <= l_max_Q_B[ij][d1]))
          r = vrna_urn() * Q_B[ij][d1][d2/2];

      if(r == 0.) vrna_message_error("backtrack@2Dpfold.c: backtracking failed\n");

      type = ptype[jindx[j] + i];
      u = j-i-1;
      base_d1 = ((unsigned int)reference_pt1[i] != j) ? 1 : -1;
      base_d2 = ((unsigned int)reference_pt2[i] != j) ? 1 : -1;

      da = base_d1 + referenceBPs1[ij];
      db = base_d2 + referenceBPs2[ij];

      /*hairpin contribution*/
      if((da == d1) && (db == d2))
        if(!(((type==3)||(type==4))&&no_closingGU))
          qbt1 = exp_E_Hairpin(u, type, S1[i+1], S1[j-1], sequence+i-1, pf_params) * scale[u+2];

      if (qbt1>=r) return; /* found the hairpin we're done */

      for (k=i+1; k<=MIN2(i+MAXLOOP+1,j-TURN-2); k++) {
        unsigned int u_pre, lmin;
        u1 = k-i-1;
        lmin = k + TURN + 1;
        u_pre = u1 + j;
        /* lmin = MAX2(k + TURN + 1, u1 + j - 1 - MAXLOOP) */
        if(u_pre > lmin + MAXLOOP) lmin = u_pre - 1 - MAXLOOP;
        for (l=lmin; l<j; l++) {
          int type_2;
          type_2 = ptype[jindx[l]+k];
          if (type_2) {
            da = base_d1 + referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[k]-l];
            db = base_d2 + referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[k]-l];
            type_2 = rtype[type_2];
            FLT_OR_DBL tmp_en = exp_E_IntLoop(u1, j-l-1, type, type_2, S1[i+1], S1[j-1], S1[k-1], S1[l+1], pf_params) * scale[u1+j-l+1];
            if(d1 >= da && d2 >= db)
              if((d1 - da >= k_min_Q_B[my_iindx[k]-l]) && (d1 - da <= k_max_Q_B[my_iindx[k]-l]))
                if((d2 - db >= l_min_Q_B[my_iindx[k]-l][d1 - da]) && (d2 - db <= l_max_Q_B[my_iindx[k]-l][d1 - da])){
                  cnt1 = d1 - da;
                  cnt2 = d2 - db;
                  qbt1 += Q_B[my_iindx[k]-l][cnt1][cnt2/2] * tmp_en;
                  if(qbt1 > r) goto backtrack_int_early_escape;
                }
          }
        }
      }

backtrack_int_early_escape:
      if (l<j) {
        i=k; j=l;
        d1 = cnt1;
        d2 = cnt2;
      }
      else break;
    }
  } while (1);

  /* backtrack in multi-loop */
  {
    double r, qt;
    unsigned int k, ii, jj;

    base_d1 = ((unsigned int)reference_pt1[i] != j) ? 1 : -1;
    base_d2 = ((unsigned int)reference_pt2[i] != j) ? 1 : -1;

    base_d1 += referenceBPs1[my_iindx[i]-j];
    base_d2 += referenceBPs2[my_iindx[i]-j];

    i++; j--;
    /* find the first split index */
    ii = my_iindx[i]; /* ii-j=[i,j] */
    jj = jindx[j]; /* jj+i=[j,i] */
    if(d1 == -1){
      /* get total contribution for current part */
      for (qt=0., k=i+1; k<j; k++){
        if(Q_M_rem[ii-k+1] != 0.){
          if(Q_M1[jj+k])
            for(cnt1 = k_min_Q_M1[jj+k];
                cnt1 <= k_max_Q_M1[jj+k];
                cnt1++)
              for(cnt2 = l_min_Q_M1[jj+k][cnt1];
                  cnt2 <= l_max_Q_M1[jj+k][cnt1];
                  cnt2 += 2)
                qt += Q_M_rem[ii-k+1] * Q_M1[jj+k][cnt1][cnt2/2];
          if(Q_M1_rem[jj+k] != 0.)
            qt += Q_M_rem[ii-k+1] * Q_M1_rem[jj+k];
        }
        if(Q_M1_rem[jj+k] != 0.){
          if(Q_M[ii-k+1])
            for(cnt1 = k_min_Q_M[ii-k+1];
                cnt1 <= k_max_Q_M[ii-k+1];
                cnt1++)
              for(cnt2 = l_min_Q_M[ii-k+1][cnt1];
                  cnt2 <= l_max_Q_M[ii-k+1][cnt1];
                  cnt2 += 2)
                qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1_rem[jj+k];
        }
        /* calculate introduced distance to reference structures */
        if(!Q_M[ii-k+1]) continue;
        if(!Q_M1[jj+k]) continue;
        da = base_d1 - referenceBPs1[my_iindx[i]-k+1] - referenceBPs1[my_iindx[k]-j];
        db = base_d2 - referenceBPs2[my_iindx[i]-k+1] - referenceBPs2[my_iindx[k]-j];
        /* collect all contributing energies */
        for(cnt1 = k_min_Q_M[ii-k+1];
            cnt1 <= k_max_Q_M[ii-k+1];
            cnt1++)
          for(cnt2 = l_min_Q_M[ii-k+1][cnt1];
              cnt2 <= l_max_Q_M[ii-k+1][cnt1];
              cnt2 += 2)
            for(cnt3 = k_min_Q_M1[jj+k];
                cnt3 <= k_max_Q_M1[jj+k];
                cnt3++)
              for(cnt4 = l_min_Q_M1[jj+k][cnt3];
                  cnt4 <= l_max_Q_M1[jj+k][cnt3];
                  cnt4 += 2)
                if(((cnt1 + cnt3 + da) > maxD1) || ((cnt2 + cnt4 + db) > maxD2))
                  qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1[jj+k][cnt3][cnt4/2];
      }
      /* throw the dice */
      r = vrna_urn() * qt;
      for (qt=0., k=i+1; k<j; k++) {
        cnt1 = cnt2 = cnt3 = cnt4 = -1;
        if(Q_M_rem[ii-k+1] != 0.){
          if(Q_M1_rem[jj+k] != 0){
            qt += Q_M_rem[ii-k+1] * Q_M1_rem[jj+k];
            if(qt >= r) goto backtrack_ml_early_escape;
          }
          if(Q_M1[jj+k])
            for(cnt3 = k_min_Q_M1[jj+k];
                cnt3 <= k_max_Q_M1[jj+k];
                cnt3++)
              for(cnt4 = l_min_Q_M1[jj+k][cnt3];
                  cnt4 <= l_max_Q_M1[jj+k][cnt3];
                  cnt4 += 2){
                qt += Q_M_rem[ii-k+1] * Q_M1[jj+k][cnt3][cnt4/2];
                if(qt >= r) goto backtrack_ml_early_escape;
              }
        }
        if(Q_M1_rem[jj+k] != 0.){
          cnt3 = cnt4 = -1;
          if(Q_M[ii-k+1])
            for(cnt1 = k_min_Q_M[ii-k+1];
                cnt1 <= k_max_Q_M[ii-k+1];
                cnt1++)
              for(cnt2 = l_min_Q_M[ii-k+1][cnt1];
                  cnt2 <= l_max_Q_M[ii-k+1][cnt1];
                  cnt2 += 2){
                qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1_rem[jj+k];
                if(qt >= r) goto backtrack_ml_early_escape;
              }
        }
        /* calculate introduced distance to reference structures */
        da = base_d1 - referenceBPs1[my_iindx[i]-k+1] - referenceBPs1[my_iindx[k]-j];
        db = base_d2 - referenceBPs2[my_iindx[i]-k+1] - referenceBPs2[my_iindx[k]-j];
        /* collect all contributing energies */
        if(!Q_M[ii-k+1]) continue;
        if(!Q_M1[jj+k]) continue;
        for(cnt1 = k_min_Q_M[ii-k+1];
            cnt1 <= k_max_Q_M[ii-k+1];
            cnt1++)
          for(cnt2 = l_min_Q_M[ii-k+1][cnt1];
              cnt2 <= l_max_Q_M[ii-k+1][cnt1];
              cnt2 += 2)
            for(cnt3 = k_min_Q_M1[jj+k];
                cnt3 <= k_max_Q_M1[jj+k];
                cnt3++)
              for(cnt4 = l_min_Q_M1[jj+k][cnt3];
                  cnt4 <= l_max_Q_M1[jj+k][cnt3];
                  cnt4 += 2)
                if(((cnt1 + cnt3 + da) > maxD1) || ((cnt2 + cnt4 + db) > maxD2)){
                  qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1[jj+k][cnt3][cnt4/2];
                  if (qt>=r) goto backtrack_ml_early_escape;
                }
      }
    }
    else{
      /* get total contribution */
      for (qt=0., k=i+1; k<j; k++){
        /* calculate introduced distance to reference structures */
        da = base_d1 - referenceBPs1[my_iindx[i]-k+1] - referenceBPs1[my_iindx[k]-j];
        db = base_d2 - referenceBPs2[my_iindx[i]-k+1] - referenceBPs2[my_iindx[k]-j];
        /* collect all contributing energies */
        if(d1 >= da && d2 >= db && Q_M[ii-k+1] && Q_M1[jj+k])
          for(cnt1 = k_min_Q_M[ii-k+1]; cnt1 <= MIN2(k_max_Q_M[ii-k+1], d1-da); cnt1++)
            for(cnt2 = l_min_Q_M[ii-k+1][cnt1]; cnt2 <= MIN2(l_max_Q_M[ii-k+1][cnt1], d2 - db); cnt2+=2)
              if((d1-cnt1-da >= k_min_Q_M1[jj+k]) && (d1-cnt1-da <= k_max_Q_M1[jj+k]))
                if((d2 - cnt2 - db >= l_min_Q_M1[jj+k][d1-da-cnt1]) && (d2 - cnt2 - db <= l_max_Q_M1[jj+k][d1-cnt1-da]))
                  qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1[jj+k][d1-da-cnt1][(d2-db-cnt2)/2];
      }
      r = vrna_urn() * qt;
      for (qt=0., k=i+1; k<j; k++) {
        /* calculate introduced distance to reference structures */
        da = base_d1 - referenceBPs1[my_iindx[i]-k+1] - referenceBPs1[my_iindx[k]-j];
        db = base_d2 - referenceBPs2[my_iindx[i]-k+1] - referenceBPs2[my_iindx[k]-j];
        /* collect all contributing energies */
        if(d1 >= da && d2 >= db && Q_M[ii-k+1] && Q_M1[jj+k])
          for(cnt1 = k_min_Q_M[ii-k+1]; cnt1 <= MIN2(k_max_Q_M[ii-k+1], d1-da); cnt1++)
            for(cnt2 = l_min_Q_M[ii-k+1][cnt1]; cnt2 <= MIN2(l_max_Q_M[ii-k+1][cnt1], d2 - db); cnt2+=2)
              if((d1-cnt1-da >= k_min_Q_M1[jj+k]) && (d1-cnt1-da <= k_max_Q_M1[jj+k]))
                if((d2 - cnt2 - db >= l_min_Q_M1[jj+k][d1-da-cnt1]) && (d2 - cnt2 - db <= l_max_Q_M1[jj+k][d1-cnt1-da])){
                  cnt3 = d1-da-cnt1;
                  cnt4 = d2-db-cnt2;
                  qt += Q_M[ii-k+1][cnt1][cnt2/2] * Q_M1[jj+k][cnt3][cnt4/2];
                  if (qt>=r) goto backtrack_ml_early_escape;
                }
      }
    }
    if (k>=j) vrna_message_error("backtrack failed, can't find split index ");

backtrack_ml_early_escape:

    backtrack_qm1(vc, pstruc, cnt3, cnt4, k, j);

    j = k-1;
    backtrack_qm(vc, pstruc, cnt1, cnt2, i, j);
  }
}

PRIVATE void
backtrack_qm1(vrna_fold_compound_t *vc,
              char *pstruc,
              int d1,
              int d2,
              unsigned int i,
              unsigned int j){

  /* i is paired to l, i<l<j; backtrack in qm1 to find l */
  FLT_OR_DBL      r, qt, *scale;
  unsigned int    maxD1, maxD2, da, db;
  unsigned int    *referenceBPs1, *referenceBPs2;
  char            *ptype;
  short           *S1;
  int             *my_iindx, *jindx, cnt1, cnt2;

  vrna_exp_param_t  *pf_params;     /* holds all [unscaled] pf parameters */
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  maxD1           = vc->maxD1;
  maxD2           = vc->maxD2;
  my_iindx        = vc->iindx;
  jindx           = vc->jindx;
  scale           = matrices->scale;
  ptype           = vc->ptype;
  S1              = vc->sequence_encoding;
  referenceBPs1   = vc->referenceBPs1;
  referenceBPs2   = vc->referenceBPs2;

  FLT_OR_DBL  ***Q_B, ***Q_M1, *Q_B_rem, *Q_M1_rem;
  int         *k_min_Q_M1, *k_max_Q_M1,*k_min_Q_B, *k_max_Q_B;
  int         **l_min_Q_M1, **l_max_Q_M1,**l_min_Q_B, **l_max_Q_B;

  Q_B = matrices->Q_B;
  k_min_Q_B = matrices->k_min_Q_B;
  k_max_Q_B = matrices->k_max_Q_B;
  l_min_Q_B = matrices->l_min_Q_B;
  l_max_Q_B = matrices->l_max_Q_B;

  Q_M1 = matrices->Q_M1;
  k_min_Q_M1 = matrices->k_min_Q_M1;
  k_max_Q_M1 = matrices->k_max_Q_M1;
  l_min_Q_M1 = matrices->l_min_Q_M1;
  l_max_Q_M1 = matrices->l_max_Q_M1;

  Q_B_rem   = matrices->Q_B_rem;
  Q_M1_rem  = matrices->Q_M1_rem;

  unsigned int ii, l;
  int type;

  r = 0.;

  /* find qm1 contribution */
  if(d1 == -1)
    r = vrna_urn() * Q_M1_rem[jindx[j]+i];
  else{
    if((d1 >= k_min_Q_M1[jindx[j]+i]) && (d1 <= k_max_Q_M1[jindx[j]+i]))
      if((d2 >= l_min_Q_M1[jindx[j]+i][d1]) && (d2 <= l_max_Q_M1[jindx[j]+i][d1]))
        r = vrna_urn() * Q_M1[jindx[j]+i][d1][d2/2];
  }
  if(r == 0.) vrna_message_error("backtrack_qm1@2Dpfold.c: backtracking failed\n");

  ii = my_iindx[i];
  for (qt=0., l=i+TURN+1; l<=j; l++) {
    type = ptype[jindx[l] + i];
    if (type){
      FLT_OR_DBL tmp = exp_E_MLstem(type, S1[i-1], S1[l+1], pf_params) * pow(pf_params->expMLbase, j-l) * scale[j-l];
      /* compute the introduced distance to reference structures */
      da = referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[i]-l];
      db = referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[i]-l];
      cnt1 = cnt2 = -1;
      if(d1 == -1){
        if(Q_B_rem[ii-l] != 0.){
          qt += Q_B_rem[ii-l] * tmp;
          if(qt >= r) goto backtrack_qm1_early_escape;
        }
        if(Q_B[ii-l])
          for(cnt1 = k_min_Q_B[ii-l];
              cnt1 <= k_max_Q_B[ii-l];
              cnt1++)
            for(cnt2 = l_min_Q_B[ii-l][cnt1];
                cnt2 <= l_max_Q_B[ii-l][cnt1];
                cnt2 += 2)
              if(((cnt1 + da) > maxD1) || ((cnt2 + db) > maxD2)){
                qt += Q_B[ii-l][cnt1][cnt2/2] * tmp;
                if(qt >= r) goto backtrack_qm1_early_escape;
              }
      }
      else{
        /* get energy contributions */
        if(d1 >= da && d2 >= db)
          if((d1 - da >= k_min_Q_B[ii-l]) && (d1 - da <= k_max_Q_B[ii-l]))
            if((d2 - db >= l_min_Q_B[ii-l][d1-da]) && (d2 - db <= l_max_Q_B[ii-l][d1-da])){
              cnt1 = d1 - da;
              cnt2 = d2 - db;
              qt += Q_B[ii-l][cnt1][cnt2/2] * tmp;
              if (qt>=r) goto backtrack_qm1_early_escape;
            }
      }
    }
  }
  if (l>j) vrna_message_error("backtrack failed in qm1");
backtrack_qm1_early_escape:

  backtrack(vc, pstruc, cnt1, cnt2, i,l);
}

PRIVATE void
backtrack_qm( vrna_fold_compound_t *vc,
              char *pstruc,
              int d1,
              int d2,
              unsigned int i,
              unsigned int j){

  /* divide multiloop into qm and qm1  */
  FLT_OR_DBL      r, *scale;
  unsigned int    maxD1, maxD2, da, db, da2, db2;
  unsigned int    *referenceBPs1, *referenceBPs2;
  int             *my_iindx, *jindx, cnt1, cnt2, cnt3, cnt4;

  vrna_exp_param_t  *pf_params;     /* holds all [unscaled] pf parameters */
  vrna_md_t         *md;
  vrna_mx_pf_t      *matrices;

  pf_params         = vc->exp_params;
  md                = &(pf_params->model_details);
  matrices          = vc->exp_matrices;
  maxD1       = vc->maxD1;
  maxD2       = vc->maxD2;
  my_iindx    = vc->iindx;
  jindx       = vc->jindx;
  scale       = matrices->scale;
  referenceBPs1  = vc->referenceBPs1;
  referenceBPs2  = vc->referenceBPs2;

  FLT_OR_DBL  ***Q_M, ***Q_M1, *Q_M_rem, *Q_M1_rem;
  int         *k_min_Q_M, *k_max_Q_M,*k_min_Q_M1, *k_max_Q_M1;
  int         **l_min_Q_M, **l_max_Q_M,**l_min_Q_M1, **l_max_Q_M1;

  Q_M = matrices->Q_M;
  k_min_Q_M = matrices->k_min_Q_M;
  k_max_Q_M = matrices->k_max_Q_M;
  l_min_Q_M = matrices->l_min_Q_M;
  l_max_Q_M = matrices->l_max_Q_M;

  Q_M1 = matrices->Q_M1;
  k_min_Q_M1 = matrices->k_min_Q_M1;
  k_max_Q_M1 = matrices->k_max_Q_M1;
  l_min_Q_M1 = matrices->l_min_Q_M1;
  l_max_Q_M1 = matrices->l_max_Q_M1;
  Q_M_rem   = matrices->Q_M_rem;
  Q_M1_rem  = matrices->Q_M1_rem;

  double qmt = 0;
  unsigned int k;
  while(j>i){
    /* now backtrack  [i ... j] in qm[] */

    /* find qm contribution */
    if(d1 == -1)
      r = vrna_urn() * Q_M_rem[my_iindx[i]-j];
    else{
      if(Q_M[my_iindx[i]-j])
        if((d1 >= k_min_Q_M[my_iindx[i]-j]) && (d1 <= k_max_Q_M[my_iindx[i]-j]))
          if((d2 >= l_min_Q_M[my_iindx[i]-j][d1]) && (d2 <= l_max_Q_M[my_iindx[i]-j][d1]))
            r = vrna_urn() * Q_M[my_iindx[i]-j][d1][d2/2];
    }
    if(r == 0.) vrna_message_error("backtrack_qm@2Dpfold.c: backtracking failed in finding qm contribution\n");

    qmt = 0.;
    if(d1 == -1){
      if(Q_M1_rem[jindx[j]+i] != 0.){
        qmt += Q_M1_rem[jindx[j]+i];
        if(qmt >= r){
          backtrack_qm1(vc, pstruc, d1, d2, i, j);
          return;
        }
      }

      for(k=i+1; k<=j; k++){
        FLT_OR_DBL tmp = pow(pf_params->expMLbase, k-i) * scale[k-i];
        if(Q_M1_rem[jindx[j]+k] != 0.){
          qmt += Q_M1_rem[jindx[j]+k] * tmp;
          if(qmt >= r){
            backtrack_qm1(vc, pstruc, d1, d2, k, j);
            return;
          }
        }
        da2 = referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[k]-j];
        db2 = referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[k]-j];
        if(Q_M1[jindx[j]+k])
          for(cnt1 = k_min_Q_M1[jindx[j]+k];
              cnt1 <= k_max_Q_M1[jindx[j]+k];
              cnt1++)
            for(cnt2 = l_min_Q_M1[jindx[j]+k][cnt1];
                cnt2 <= l_max_Q_M1[jindx[j]+k][cnt1];
                cnt2 += 2)
              if(((cnt1 + da2) > maxD1) || ((cnt2 + db2) > maxD2)){
                qmt += Q_M1[jindx[j]+k][cnt1][cnt2/2] * tmp;
                if(qmt >= r){
                  backtrack_qm1(vc, pstruc, cnt1, cnt2, k, j);
                  return;
                }
              }

        da = da2 - referenceBPs1[my_iindx[i]-k+1];
        db = db2 - referenceBPs2[my_iindx[i]-k+1];

        cnt1 = cnt2 = cnt3 = cnt4 = -1;
        if(Q_M_rem[my_iindx[i]-k+1] != 0.){
          if(Q_M1_rem[jindx[j]+k] != 0.){
            qmt += Q_M_rem[my_iindx[i]-k+1] * Q_M1_rem[jindx[j]+k];
            if(qmt >= r) goto backtrack_qm_early_escape;
          }
          if(Q_M1[jindx[j]+k])
            for(cnt3 = k_min_Q_M1[jindx[j]+k];
                cnt3 <= k_max_Q_M1[jindx[j]+k];
                cnt3++)
              for(cnt4 = l_min_Q_M1[jindx[j]+k][cnt3];
                  cnt4 <= l_max_Q_M1[jindx[j]+k][cnt3];
                  cnt4 += 2){
                qmt += Q_M_rem[my_iindx[i]-k+1] * Q_M1[jindx[j]+k][cnt3][cnt4/2];
                if(qmt >= r) goto backtrack_qm_early_escape;
              }
        }
        if(Q_M1_rem[jindx[j]+k] != 0.){
          cnt3 = cnt4 = -1;
          if(Q_M[my_iindx[i]-k+1])
            for(cnt1 = k_min_Q_M[my_iindx[i]-k+1];
                cnt1 <= k_max_Q_M[my_iindx[i]-k+1];
                cnt1++)
              for(cnt2 = l_min_Q_M[my_iindx[i]-k+1][cnt1];
                  cnt2 <= l_max_Q_M[my_iindx[i]-k+1][cnt1];
                  cnt2 += 2){
                qmt += Q_M[my_iindx[i]-k+1][cnt1][cnt2/2] * Q_M1_rem[jindx[j]+k];
                if(qmt >= r) goto backtrack_qm_early_escape;
              }
        }

        if(!Q_M[my_iindx[i]-k+1]) continue;
        if(!Q_M1[jindx[j]+k]) continue;
        for(cnt1 = k_min_Q_M[my_iindx[i]-k+1];
            cnt1 <= k_max_Q_M[my_iindx[i]-k+1];
            cnt1++)
          for(cnt2 = l_min_Q_M[my_iindx[i]-k+1][cnt1];
              cnt2 <= l_max_Q_M[my_iindx[i]-k+1][cnt1];
              cnt2 += 2)
            for(cnt3 = k_min_Q_M1[jindx[j]+k];
                cnt3 <= k_max_Q_M1[jindx[j]+k];
                cnt3++)
              for(cnt4 = l_min_Q_M1[jindx[j]+k][cnt3];
                  cnt4 <= l_max_Q_M1[jindx[j]+k][cnt3];
                  cnt4 += 2)
                if(((cnt1 + cnt3 + da) > maxD1) || ((cnt2 + cnt4 + db) > maxD2)){
                  qmt += Q_M[my_iindx[i]-k+1][cnt1][cnt2/2] * Q_M1[jindx[j]+k][cnt3][cnt4/2];
                  if(qmt >= r) goto backtrack_qm_early_escape;
                }
      }

    }
    else{
      /* find corresponding qm1 contribution */
      if(Q_M1[jindx[j]+i])
        if((d1 >= k_min_Q_M1[jindx[j]+i]) && (d1 <= k_max_Q_M1[jindx[j]+i]))
          if((d2 >= l_min_Q_M1[jindx[j]+i][d1]) && (d2 <= l_max_Q_M1[jindx[j]+i][d1])){
            qmt = Q_M1[jindx[j]+i][d1][d2/2];
          }

      k=i;
      if(qmt<r){
        for(k=i+1; k<=j; k++){
          /* calculate introduced distancies to reference structures */
          da2 = referenceBPs1[my_iindx[i]-j] - referenceBPs1[my_iindx[k]-j];
          db2 = referenceBPs2[my_iindx[i]-j] - referenceBPs2[my_iindx[k]-j];
          da = da2 - referenceBPs1[my_iindx[i]-k+1];
          db = db2 - referenceBPs2[my_iindx[i]-k+1];


          FLT_OR_DBL tmp = pow(pf_params->expMLbase, k-i) * scale[k-i];

          /* collect unpaired + qm1 contributions */
          if(d1 >= da2 && d2 >= db2)
            if((d1 - da2 >= k_min_Q_M1[jindx[j]+k]) && (d1 - da2 <= k_max_Q_M1[jindx[j]+k]))
              if((d2 - db2 >= l_min_Q_M1[jindx[j]+k][d1-da2]) && (d2 - db2 <= l_max_Q_M1[jindx[j]+k][d1-da2])){
                cnt3 = d1-da2;
                cnt4 = d2-db2;
                qmt += Q_M1[jindx[j]+k][cnt3][cnt4/2] * tmp;
                if(qmt >= r){
                  backtrack_qm1(vc, pstruc, cnt3, cnt4, k, j);
                  return;
                }
              }

          /* collect qm + qm1 contributions */
          if(d1 >= da && d2 >= db && Q_M[my_iindx[i]-k+1] && Q_M1[jindx[j]+k])
            for(cnt1 = k_min_Q_M[my_iindx[i]-k+1]; cnt1 <= MIN2(k_max_Q_M[my_iindx[i]-k+1], d1 - da); cnt1++)
              for(cnt2 = l_min_Q_M[my_iindx[i]-k+1][cnt1]; cnt2 <= MIN2(l_max_Q_M[my_iindx[i]-k+1][cnt1], d2 - db); cnt2+=2)
                if((d1 - da - cnt1 >= k_min_Q_M1[jindx[j]+k]) && (d1 - da - cnt1 <= k_max_Q_M1[jindx[j]+k]))
                  if((d2 - db - cnt2 >= l_min_Q_M1[jindx[j]+k][d1-da-cnt1]) && (d2 - db - cnt2 <= l_max_Q_M1[jindx[j]+k][d1-da-cnt1])){
                    cnt3 = d1 - da - cnt1;
                    cnt4 = d2 - db - cnt2;
                    qmt += Q_M[my_iindx[i]-k+1][cnt1][cnt2/2] * Q_M1[jindx[j]+k][cnt3][cnt4/2];
                    if(qmt >= r) goto backtrack_qm_early_escape;
                  }
        }
      }
      else{
        backtrack_qm1(vc, pstruc, d1, d2, k, j);
        return;
      }
    }

    if(k>j) vrna_message_error("backtrack_qm@2Dpfold.c: backtrack failed in qm");

backtrack_qm_early_escape:

    backtrack_qm1(vc, pstruc, cnt3, cnt4, k, j);

    if(k<i+TURN) break; /* no more pairs */

    d1 = cnt1;
    d2 = cnt2;


    if(d1 == referenceBPs1[my_iindx[i]-k+1] && d2 == referenceBPs2[my_iindx[i]-k+1]){
      /* is interval [i,k] totally unpaired? */
      FLT_OR_DBL tmp = pow(pf_params->expMLbase, k-i) * scale[k-i];
      r = vrna_urn() * (Q_M[my_iindx[i]-k+1][d1][d2/2] + tmp);
      if(tmp >= r) return; /* no more pairs */
    }
    j = k-1;
  }
}




PRIVATE void  adjustArrayBoundaries(FLT_OR_DBL ***array,
                                    int *k_min, int *k_max,
                                    int **l_min, int **l_max,
                                    int k_min_post, int k_max_post,
                                    int *l_min_post, int *l_max_post){

  int cnt1;
  int k_diff_pre  = k_min_post - *k_min;
  int mem_size    = k_max_post - k_min_post + 1;

  if(k_min_post < INF){
    /* free all the unused memory behind actual data */
    for(cnt1 = k_max_post + 1; cnt1 <= *k_max; cnt1++){
      (*array)[cnt1] += (*l_min)[cnt1]/2;
      free((*array)[cnt1]);
    }

    /* free unused memory before actual data */
    for(cnt1 = *k_min; cnt1 < k_min_post; cnt1++){
      (*array)[cnt1] += (*l_min)[cnt1]/2;
      free((*array)[cnt1]);
    }
    /* move data to front and thereby eliminating unused memory in front of actual data */
    if(k_diff_pre > 0){
      memmove((FLT_OR_DBL **)(*array),((FLT_OR_DBL **)(*array)) + k_diff_pre, sizeof(FLT_OR_DBL *) * mem_size);
      memmove((int *) (*l_min),((int *) (*l_min)) + k_diff_pre, sizeof(int)   * mem_size);
      memmove((int *) (*l_max),((int *) (*l_max)) + k_diff_pre, sizeof(int)   * mem_size);
    }

    /* reallocating memory to actual size used */
    *array  +=  *k_min;
    *array  =   (FLT_OR_DBL **)realloc(*array, sizeof(FLT_OR_DBL *) * mem_size);
    *array  -=  k_min_post;

    *l_min  +=  *k_min;
    *l_min  =   (int *)realloc(*l_min, sizeof(int) * mem_size);
    *l_min  -=   k_min_post;

    *l_max  +=  *k_min;
    *l_max  =   (int *)realloc(*l_max, sizeof(int) * mem_size);
    *l_max  -=  k_min_post;


    for(cnt1 = k_min_post; cnt1 <= k_max_post; cnt1++){
      if(l_min_post[cnt1] < INF){
        /* new memsize */
        mem_size        = (l_max_post[cnt1] - l_min_post[cnt1] + 1)/2 + 1;
        /* reshift the pointer */
        (*array)[cnt1]  += (*l_min)[cnt1]/2;

        int shift       = (l_min_post[cnt1]%2 == (*l_min)[cnt1]%2) ? 0 : 1;
        /* eliminate unused memory in front of actual data */
        unsigned int    start = (l_min_post[cnt1] - (*l_min)[cnt1])/2 + shift;
        if(start > 0)
          memmove((FLT_OR_DBL *)((*array)[cnt1]), (FLT_OR_DBL *)((*array)[cnt1])+start, sizeof(FLT_OR_DBL) * mem_size);
        (*array)[cnt1]  = (FLT_OR_DBL *) realloc((*array)[cnt1], sizeof(FLT_OR_DBL) * mem_size);

        (*array)[cnt1]  -= l_min_post[cnt1]/2;
      }
      else{
        /* free according memory */
        (*array)[cnt1] += (*l_min)[cnt1]/2;
        free((*array)[cnt1]);
      }

      (*l_min)[cnt1] = l_min_post[cnt1];
      (*l_max)[cnt1] = l_max_post[cnt1];
    }
  }
  else{
    /* we have to free all unused memory */
    for(cnt1 = *k_min; cnt1 <= *k_max; cnt1++){
      (*array)[cnt1] += (*l_min)[cnt1]/2;
      free((*array)[cnt1]);
    }
    (*l_min) += *k_min;
    (*l_max) += *k_min;
    free(*l_min);
    free(*l_max);
    (*array) += *k_min;
    free(*array);
    *array = NULL;
  }

  l_min_post  += *k_min;
  l_max_post  += *k_min;
  *k_min      = k_min_post;
  *k_max      = k_max_post;

  free(l_min_post);
  free(l_max_post);
}


PRIVATE INLINE void preparePosteriorBoundaries(int size, int shift, int *min_k, int *max_k, int **min_l, int **max_l){
  int i;
  *min_k  = INF;
  *max_k  = 0;

  *min_l  = (int *)vrna_alloc(sizeof(int) * size);
  *max_l  = (int *)vrna_alloc(sizeof(int) * size);

  for(i = 0; i < size; i++){
    (*min_l)[i] = INF;
    (*max_l)[i] = 0;
  }

  *min_l  -= shift;
  *max_l  -= shift;
}

PRIVATE INLINE void updatePosteriorBoundaries(int d1, int d2, int *min_k, int *max_k, int **min_l, int **max_l){
  (*min_l)[d1]  = MIN2((*min_l)[d1], d2);
  (*max_l)[d1]  = MAX2((*max_l)[d1], d2);
  *min_k        = MIN2(*min_k, d1);
  *max_k        = MAX2(*max_k, d1);
}

PRIVATE INLINE  void  prepareBoundaries(int min_k_pre, int max_k_pre, int min_l_pre, int max_l_pre, int bpdist, int *min_k, int *max_k, int **min_l, int **max_l){
  int cnt;
  int mem = max_k_pre - min_k_pre + 1;

  *min_k  = min_k_pre;
  *max_k  = max_k_pre;
  *min_l  = (int *) vrna_alloc(sizeof(int) * mem);
  *max_l  = (int *) vrna_alloc(sizeof(int) * mem);

  *min_l  -= min_k_pre;
  *max_l  -= min_k_pre;

  /* for each k guess the according minimum l*/
  for(cnt = min_k_pre; cnt <= max_k_pre; cnt++){
    (*min_l)[cnt] = min_l_pre;
    (*max_l)[cnt] = max_l_pre;
    while((*min_l)[cnt] + cnt < bpdist) (*min_l)[cnt]++;
    if((bpdist % 2) != (((*min_l)[cnt] + cnt) % 2)) (*min_l)[cnt]++;
  }
}

PRIVATE INLINE  void  prepareArray(FLT_OR_DBL ***array, int min_k, int max_k, int *min_l, int *max_l){
  int i, mem;
  *array  = (FLT_OR_DBL **)vrna_alloc(sizeof(FLT_OR_DBL *) * (max_k - min_k + 1));
  *array  -= min_k;

  for(i = min_k; i <= max_k; i++){
    mem         = (max_l[i] - min_l[i] + 1)/2 + 1;
    (*array)[i] = (FLT_OR_DBL *)vrna_alloc(sizeof(FLT_OR_DBL) * mem);
    (*array)[i] -= min_l[i]/2;
  }
}

/*
#################################
# DEPRECATED FUNCTIONS BELOW    #
#################################
*/
PRIVATE void
crosslink(TwoDpfold_vars *vars){

  vrna_fold_compound_t  *c;
  vrna_mx_pf_t        *m;

  c                     = vars->compatibility;
  m                     = c->exp_matrices;

  vars->sequence      = c->sequence;
  vars->seq_length    = c->length;
  vars->reference_pt1 = c->reference_pt1;
  vars->reference_pt2 = c->reference_pt2;
  vars->referenceBPs1 = c->referenceBPs1;
  vars->referenceBPs2 = c->referenceBPs2;
  vars->mm1           = c->mm1;
  vars->mm2           = c->mm2;
  vars->bpdist        = c->bpdist;
  vars->dangles       = c->exp_params->model_details.dangles;
  vars->circ          = c->exp_params->model_details.circ;
  vars->temperature   = c->exp_params->model_details.temperature;
  vars->init_temp     = c->exp_params->model_details.temperature;
  vars->pf_scale      = c->exp_params->pf_scale;
  vars->pf_params     = c->exp_params;

  vars->scale         = m->scale;
  vars->ptype         = c->ptype_pf_compat;
  vars->S             = c->sequence_encoding2;
  vars->S1            = c->sequence_encoding;

  vars->jindx         = c->jindx;
  vars->my_iindx      = c->iindx;
  vars->maxD1         = c->maxD1;
  vars->maxD2         = c->maxD2;

  vars->Q                = m->Q;
  vars->l_min_values     = m->l_min_Q;
  vars->l_max_values     = m->l_max_Q;
  vars->k_min_values     = m->k_min_Q;
  vars->k_max_values     = m->k_max_Q;

  vars->Q_B              = m->Q_B;
  vars->l_min_values_b   = m->l_min_Q_B;
  vars->l_max_values_b   = m->l_max_Q_B;
  vars->k_min_values_b   = m->k_min_Q_B;
  vars->k_max_values_b   = m->k_max_Q_B;

  vars->Q_M              = m->Q_M;
  vars->l_min_values_m   = m->l_min_Q_M;
  vars->l_max_values_m   = m->l_max_Q_M;
  vars->k_min_values_m   = m->k_min_Q_M;
  vars->k_max_values_m   = m->k_max_Q_M;

  vars->Q_M1             = m->Q_M1;
  vars->l_min_values_m1  = m->l_min_Q_M1;
  vars->l_max_values_m1  = m->l_max_Q_M1;
  vars->k_min_values_m1  = m->k_min_Q_M1;
  vars->k_max_values_m1  = m->k_max_Q_M1;

  vars->Q_M2_rem         = m->Q_M2_rem;
  vars->Q_M2             = m->Q_M2;
  vars->l_min_values_m2  = m->l_min_Q_M2;
  vars->l_max_values_m2  = m->l_max_Q_M2;
  vars->k_min_values_m2  = m->k_min_Q_M2;
  vars->k_max_values_m2  = m->k_max_Q_M2;

  vars->Q_c               = m->Q_c;
  vars->Q_cH              = m->Q_cH;
  vars->Q_cI              = m->Q_cI;
  vars->Q_cM              = m->Q_cM;
  vars->Q_c_rem           = m->Q_c_rem;
  vars->Q_cH_rem          = m->Q_cH_rem;
  vars->Q_cI_rem          = m->Q_cI_rem;
  vars->Q_cM_rem          = m->Q_cM_rem;

  vars->Q_rem             = m->Q_rem;
  vars->Q_B_rem           = m->Q_B_rem;
  vars->Q_M_rem           = m->Q_M_rem;
  vars->Q_M1_rem          = m->Q_M1_rem;
}

PUBLIC char *
TwoDpfold_pbacktrack( TwoDpfold_vars *vars,
                      int d1,
                      int d2){

  return vrna_pbacktrack_TwoD(vars->compatibility, d1, d2);
}

PUBLIC char *
TwoDpfold_pbacktrack5(TwoDpfold_vars *vars,
                      int d1,
                      int d2,
                      unsigned int length){

  return vrna_pbacktrack5_TwoD(vars->compatibility, d1, d2, length);
}

PUBLIC TwoDpfold_vars *
get_TwoDpfold_variables(const char *seq,
                        const char *structure1,
                        char *structure2,
                        int circ){

  vrna_md_t           md;
  TwoDpfold_vars      *vars;
  vrna_fold_compound_t  *c;
  vrna_mx_mfe_t       *m;

  set_model_details(&md);
  md.circ = circ;

  vars = (TwoDpfold_vars *)malloc(sizeof(TwoDpfold_vars));
  vars->compatibility = vrna_fold_compound_TwoD(seq, structure1, structure2, &md, VRNA_OPTION_PF);

  crosslink(vars);

  return vars;
}

PUBLIC void
destroy_TwoDpfold_variables(TwoDpfold_vars *vars){

  if(vars == NULL) return;

  vrna_fold_compound_free(vars->compatibility);

  free(vars);
}

vrna_sol_TwoD_pf_t *
TwoDpfoldList(TwoDpfold_vars *vars,
              int distance1,
              int distance2){

  vrna_sol_TwoD_pf_t *sol;

  sol = vrna_pf_TwoD(vars->compatibility, distance1, distance2);

  crosslink(vars);

  return sol;
}