frqtab.c

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    --fx; s_x += *fx * *fx; }   /* compute sum_x N(x)^2 */
  for (fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; ) {
    if (*--fy <= 0) continue;   /* skip empty rows */
    t = 0;                      /* process a conditional distribution */
    c = ftab->frq_xy +ftab->xcnt;
    for (fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c)
      if (*--fx > 0) t += (*c)[y]*(*c)[y];
    w_xy += t / *fy;            /* sum_y 1/N(y) sum_x N(x,y)^2 */
  }

  t = ftab->known; t *= t;      /* compute N^2 */
  switch (measure & 0xff) {     /* evaluate the measure code */
    case FEM_GINIMOD:           /* modified Gini index */
      if (s_x <= 0) return 0;   /* check the denominator */
      gini = s_xy / s_x - s_y / t;                     break;
    case FEM_RELIEF:            /* relief measure */
      if ((s_y <= 0) || (t -s_y <= 0)) return 0;
      gini = s_xy / s_y - (s_x -s_xy) / (t -s_y);      break;
    default:                    /* symmetric Gini index */
      t = 2*t -s_x -s_y;        /* compute and */
      if (t <= 0) return 0;     /* check the denominator */
      gini = ((w_xy +w_yx) *ftab->known -s_x -s_y) /t; break;
  }                             /* compute requested measure */
  if (measure & FEF_WGTD) return gini *(ftab->known/ftab->frq);
  return gini;                  /* return Gini index/relief measure */
}  /* _gini() */

/*--------------------------------------------------------------------*/

static double _wdiff (FRQTAB *ftab, int measure, double *params)
{                               /* --- weighted sum of differences */
  int    x, y, m;               /* loop variables, integer exponent */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double e, s, t;               /* exponent of difference, buffers */
  double sum;                   /* sum of weighted differences */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  e = (params) ? *params : 1.0; /* get the sensitivity parameter */
  if      (e <= 0.0) e = 1.0;   /* an exponent less than 0 is useless */
  if      (e == 1.0) m = 1;     /* (exponent of absolute difference) */
  else if (e == 2.0) m = 2;     /* and create a flag to distinguish */
  else               m = 0;     /* the two simplest special cases */
  sum = 0;                      /* traverse the joint distribution */
  c = ftab->frq_xy +ftab->xcnt; /* and the column distribution */
  for (fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx <= 0) continue;   /* skip empty and combined columns */
    s   = 0;                    /* traverse the row distribution */
    fxy = *c +ftab->ycnt;       /* and the rows of the column */
    fy  = ftab->frq_y +(y = ftab->ycnt);
    switch (m) {                /* distinguish special cases */
      case  1: while (--y >= 0){/* if exponent for difference is 1 */
                 t  = *fx * *--fy -*--fxy *ftab->known;
                 s += *fxy *fabs(t);
               } break;         /* sum weighted absolute differences */
      case  2: while (--y >= 0){/* if exponent for difference is 2 */
                 t  = *fx * *--fy -*--fxy *ftab->known;
                 s += *fxy *t *t;
               } break;         /* sum weighted squared differences */
      default: while (--y >= 0){/* if any other exponent */
                 t  = *fx * *--fy -*--fxy *ftab->known;
                 s += *fxy *pow(fabs(t), e);
               } break;         /* raise the differences to */
    }                           /* the given power and sum them */
    sum += s;                   /* sum the results for the columns */
  }
  t = ftab->known;              /* normalize the sum */
  return sum /(pow(t*t, e) *((measure & FEF_WGTD) ? ftab->frq : t));
}  /* _wdiff() */               /* return sum of weighted differences */

/*--------------------------------------------------------------------*/

static double _chi2 (FRQTAB *ftab, int measure, double *params)
{                               /* --- chi^2 measure */
  int    x, y;                  /* loop variables */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double s, t, p;               /* temporary buffers */
  double chi2;                  /* chi^2 measure */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  chi2 = 0;                     /* traverse the joint distribution */
  c = ftab->frq_xy +ftab->xcnt; /* and the column distribution */
  for (fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx <= 0) continue;   /* skip empty and combined columns */
    s   = 0;                    /* traverse the rows of the column */ 
    fxy = *c +ftab->ycnt;       /* and the row distribution */
    for (fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; ) {
      --fxy;                    /* go to the next row */
      if (*--fy <= 0) continue; /* traverse non-empty rows */
      p = *fx * *fy;            /* compute (N(x)N(y) - N N(x,y))^2 */
      t = p -*fxy *ftab->known; /*       / (N(x)N(y))              */
      s += t *t /p;             /* and sum these values */
    }
    chi2 += s;                  /* sum the results for the columns */
  }                             /* (results in chi^2 *N) */
  if ((measure & 0xff) == FEM_CHI2NRM) {
    t = (ftab->xcnt-1) *(ftab->ycnt-1);
    if (t > 0) chi2 /= t;       /* normalize the chi^2 measure by */
  }                             /* dividing by the degrees of freedom */
  return chi2 /((measure & FEF_WGTD) ? ftab->frq : ftab->known);
}  /* _chi2() */                /* return the chi^2 measure */

/*--------------------------------------------------------------------*/

static double _wevid (FRQTAB *ftab, int measure, double *params)
{                               /* --- weight of evidence */
  int    x, y;                  /* loop variables */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double outer, inner;          /* inner and outer sum */
  double a, b, z;               /* temporary buffers */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  outer = 0;                    /* traverse the joint distribution */
  c = ftab->frq_xy +ftab->xcnt; /* and the column distribution */
  for (fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx <= 0) continue;   /* skip empty and combined columns */
    inner = 0;                  /* traverse the rows of the column */
    fxy   = *c +ftab->ycnt;     /* and the row distribution */
    for (fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; ) {
      z = *--fy * *--fxy;       /* compute the common term */
      a = *fxy* ftab->known -z; /* and the terms of */
      b = *fx * *fy         -z; /* the odds fraction */
      if ((a >= EPSILON) && (b >= EPSILON))
        inner += *fy *fabs(log(a/b));
    }                           /* compute the inner sum */
    outer += *fx *inner;        /* compute the outer sum */
  }
  outer /= LN_2 *ftab->known;   /* scale and return the result */
  return outer /((measure & FEF_WGTD) ? ftab->frq : ftab->known);
}  /* _wevid() */

/*--------------------------------------------------------------------*/

static double _relev (FRQTAB *ftab, int measure, double *params)
{                               /* --- relevance */
  int    x, y;                  /* loop variables */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double max, tmp;              /* (maximal) frequency ratio */
  double relev = 0, sum;        /* relevance measure, buffer */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  c = ftab->frq_xy +ftab->xcnt; /* traverse the joint distribution */
  for (fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx <= 0) continue;   /* skip empty and combined columns */
    max = sum = 0;              /* traverse the rows of the column */
    fxy = *c +ftab->ycnt;       /* and the row distribution */
    for (fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; ) {
      --fy;                     /* go to the next row */
      if (*--fxy <= 0) continue;/* skip zero frequencies */
      tmp = *fxy / *fy;         /* compute the frequency ratio */
      if (tmp <= max) sum += tmp;
      else          { sum += max; max = tmp; }
    }                           /* sum ratios with the exception */
    relev += sum;               /* of the/one maximal ratio */
  }
  relev = 1 -relev /(ftab->ycnt-1);
  if (measure & FEF_WGTD) return relev *(ftab->known/ftab->frq);
  return relev;                 /* return the relevance measure */
}  /* _relev() */

/*--------------------------------------------------------------------*/

static double _bdm (FRQTAB *ftab, int measure, double *params)
{                               /* --- Bayesian-Dirichlet metric */
  int    x, y;                  /* loop variables */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double p, s, a;               /* (sum of) prior(s), sensitivity */
  double bdm, r, t, z;          /* Bayesian-Dirichlet metric, buffers */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  a = (params && (params[0]+1 > 0)) ? params[0]+1 : 1;
  a *= a;                       /* get the sensitivity parameter */
  p = (params && (params[1] !=  0)) ? params[1]   : 1;
  if (p < 0) p /= -ftab->ycnt;  /* get the prior/equiv. sample size */
  for (r = 0, fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; )
    r += logGa(*--fy *a +p);    /* process the class distribution */
  s  =  ftab->ycnt *p;          /* and compute the reference value */
  r += -ftab->ycnt *logGa(p) +(logGa(s) -logGa(ftab->known *a +s));
  if (params && (params[1] < 0))/* adapt prior for l. equiv. version */
    s = ftab->ycnt *(p /= ftab->xcnt);
  z = logGa(s) -ftab->ycnt *logGa(p);
  c = ftab->frq_xy +ftab->xcnt; /* process the joint distribution */
  for (bdm = 0, fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx < 0) continue;    /* skip empty and combined columns */
    for (t = 0, fxy = *c +(y = ftab->ycnt); --y >= 0; )
      t += logGa(*--fxy *a +p); /* process a conditional distribution */
    bdm += t +z -logGa(*fx *a +s);
  }                             /* sum the results over the columns */
  bdm -= r;                     /* and return the weighted BD metric */
  return bdm /(LN_2 *((measure & FEF_WGTD) ? ftab->frq : ftab->known));
}  /* _bdm() */

/*--------------------------------------------------------------------*/

static double _bdmod (FRQTAB *ftab, int measure, double *params)
{                               /* --- modified BD / K2 metric 2 */
  int    x, y;                  /* loop variables */
  double **c;                   /* to traverse the table columns */
  double *fx, *fy, *fxy;        /* to traverse the frequencies */
  double p, a;                  /* prior and sensitivity */
  double bdm, r, t, z;          /* Bayesian-Dirichlet metric, buffers */

  assert(ftab);                 /* check the function argument */
  if (ftab->known < EPSILON) return 0;
  a = (params && (params[0] >= 0)) ? params[0] : 0;
  if (a < 0) a = 0;             /* get the sensitivity parameter */
  p = (params && (params[1] != 0)) ? params[1] : 1;
  if (p < 0) p /= -ftab->ycnt;  /* get the prior/equiv. sample size */
  for (r = 0, fy = ftab->frq_y +(y = ftab->ycnt); --y >= 0; ) {
    z = *--fy *a +p; r += logGa(z +*fy) -logGa(z); }
  z  = ftab->known *a +ftab->ycnt *p;    /* process the */
  r += logGa(z) -logGa(z +ftab->known);  /* class distribution */
  if (params && (params[1] < 0))/* adapt the prior for the */
    p /= ftab->xcnt;            /* likelihood equivalent version */
  c = ftab->frq_xy +ftab->xcnt; /* and the column distribution */
  for (bdm = 0, fx = ftab->frq_x +(x = ftab->xcnt); --x >= 0; --c) {
    if (*--fx < 0) continue;    /* skip empty and combined columns */
    for (t = 0, fxy = *c +(y = ftab->ycnt); --y >= 0; ) {
      z = *--fxy *a +p; t += logGa(z +*fxy) -logGa(z); }
    z = *fx *a +ftab->ycnt *p;  /* process a conditional distribution */
    bdm += t +(logGa(z) -logGa(z +*fx));
  }                             /* sum the results over the columns */
  bdm -= r;                     /* and return the weighted BD metric */
  return bdm /(LN_2 *((measure & FEF_WGTD) ? ftab->frq : ftab->known));
}  /* _bdmod() */