text: /*
    Copyright (c) 2010 Dirk Willrodt <willrodt@zbh.uni-hamburg.de>
    Copyright (c) 2010 Center for Bioinformatics, University of Hamburg
  
    Permission to use, copy, modify, and distribute this software for any
    purpose with or without fee is hereby granted, provided that the above
    copyright notice and this permission notice appear in all copies.
  
    THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
    WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
    MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
    ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
    WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
    ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
    OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
  */
  
  #include <math.h>
  #include <float.h>
  
  #include "core/array2dim_api.h"
  #include "core/assert_api.h"
  #include "core/log_api.h"
  #include "core/mathsupport_api.h"
  #include "core/unused_api.h"
  #include "match/shu-divergence.h"
  
  static double pmax(double M, /* M value should be explored by simulation ??? */
              GtUword x,
              double p,
              GtUword subjectLength,
              int *thresholdReached,
              double *ln_n_fac,
              double *s1,
              GT_UNUSED GtUword n_s)
  {
  
    GtUword k;
    double s = 0.0, ln_x_choose_k;
    double ln, ln1, m1, m, delta;
  
    gt_assert(x <= n_s && " The maximum number of elements in the array s1 "
              "should be increased!");
    if (s1[x] != 0.0)
      return s1[x];
  
    for (k = 0; k <= x; k++) {
      double m_a, m_b, m_c, m_d, m_e;
      if (x == k)
        ln_x_choose_k = 0.0;
      else
        ln_x_choose_k =  ln_n_fac[x] - ln_n_fac[k] - ln_n_fac[x-k];
  
      m_a = pow (2.0, (double) x);
      m_b = pow (p, (double) k);
      m_c = pow (0.5 - p, (double) x - k);
      m_d = pow (p, (double) k);
      m_e = pow (0.5 - p, (double) x -k);
      m = (m_a * m_b * m_c * pow (1.0 - m_d * m_e, (double) subjectLength));
      /* this is ok even with double, because of next if!*/
      if (m == 0.0)
        delta = 0.0;
      else if (M <= m) {
        ln = log(m);
        if (ln == -HUGE_VAL)
          delta = 0.0;
        else
          delta = exp (ln + ln_x_choose_k);
      }
      else {
        double delta_a, delta_b;
        m1 = 1 + m;  /* for small values of m - to avoid overflow (-INF) */
        ln1 = log(m1);
        delta_a = exp (ln1 + ln_x_choose_k);
        delta_b = exp (ln_x_choose_k);
        delta = delta_a - delta_b;
      }
      s += delta;
      if (s >= 1.0) {
        s = 1.0;
        *thresholdReached = 1;
        break;
      }
    }  /* end for */
    s1[x] = s;
    return s;
  }
  
  static double expShulen(double T, /* absolute error */
                   double M, /* min logarithm */
                   double d,
                   double p,
                   GtUword subjectLength,
                   double *ln_n_fac,
                   double *s1,
                   GtUword n_s)
  {
    GtUword i;
    int thresholdReached = 0;
  
    double prob_i, probOld, delta, factor;
  
    double e = 0.0;    /* expectation */
    double t = 1.0 - d;
    double p_t = t;
  
    probOld  = 0.0;
  
    /*since for i = 0, the whole expression is 0*/
    for (i = 1LU; i < subjectLength; i++) {
      factor = 1.0 - p_t;
      if (!thresholdReached) {
        prob_i = factor * pmax(M, i, p,
                               subjectLength,
                               &thresholdReached,
                               ln_n_fac,
                               s1,
                               n_s);
      }
      else
        prob_i = factor;  /* prob_i = factor * s, where s = 1 */
      delta = (prob_i - probOld) * i;  /* delta should always be positive */
      gt_assert(gt_double_equals_double(delta, 0.0) ||
                gt_double_larger_double(delta, 0.0));
      e += delta;    /* expectation of avg shulen length(Q, S) */
      /* check error */
      if (1.0 <= e && delta / e <= T)
        break;
      p_t *= t;
      probOld = prob_i;
    }
    return e;
  }
  
  /* calculate divergence */
  double gt_divergence(double E, /* relative error for divergence calculation */
                     double T, /* absolute error for exp shulen*/
                     double M, /* minimum for logarithm */
                     double threshold, /* abs error for divergence */
                     double shulen,
                     GtUword subjectLength,
                     double gc,
                     double *ln_n_fac,
                     GtUword n_s)
  {
    double p, q,
           du, dl, dm, d, exp_shulen;
    double *s1;
    s1 = gt_calloc((size_t) n_s + 1, sizeof (double));
  
    p = gc / 2;
    q = (1.0 - gc) / 2.0;
    du = 0.0;
    dl = 1.0 - (2 * p * p + 2 * q * q);  /* dl < 0.75 */
  
    while (gt_double_smaller_double(threshold, (dl - du) / 2.0)) {
      dm = (du + dl) / 2.0;
      exp_shulen = expShulen(T, M, dm, p, subjectLength, ln_n_fac, s1, n_s);
      if (gt_double_smaller_double(shulen, exp_shulen))
        du = dm;
      else
        dl = dm;
      /* test the relative error between du and dl; if it is smaller than some
       * threshold, then break !! */
      if (fabs (dl - du) / dl <= E)
        break;
    }
    d = (du + dl) / 2.0;
    gt_free(s1);
    return d;
  }
  
  double *gt_get_ln_n_fac(GtUword n)
  {
    GtUword i;
    double *ln_n_fac;
  
    ln_n_fac = gt_calloc((size_t) n + 1, sizeof (double));
  
    ln_n_fac[0] = log(1.0);
    for (i = 1UL; i <= n; i++) {
      ln_n_fac[i] = log((double) i) + ln_n_fac[i-1];
    }
    return ln_n_fac;
  }
  
  double gt_calculateKr(double d)
  {
    double kr = -0.75 * log (1 - 4.0 / 3.0 * d);
    return kr;
  }
  