/* gsl_histogram_stat.c

 * Copyright (C) 2000  Simone Piccardi

 *

 * This library is free software; you can redistribute it and/or

 * modify it under the terms of the GNU General Public License as

 * published by the Free Software Foundation; either version 3 of the

 * License, or (at your option) any later version.

 *

 * This program is distributed in the hope that it will be useful,

 * but WITHOUT ANY WARRANTY; without even the implied warranty of

 * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the GNU

 * General Public License for more details.

 *

 * You should have received a copy of the GNU General Public License along

 * with this library; if not, write to the Free Software Foundation, Inc.,

 * 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.

 */

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

 *

 * File gsl_histogram_stat.c: 

 * Routines for statisticalcomputations on histograms. 

 * Need GSL library and header.

 * Contains the routines:

 * gsl_histogram_mean    compute histogram mean

 * gsl_histogram_sigma   compute histogram sigma

 *

 * Author: S. Piccardi

 * Jan. 2000

 *

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

#include <config.h>

#include <stdlib.h>

#include <math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_histogram.h>

/* FIXME: We skip negative values in the histogram h->bin[i] < 0,

   since those correspond to negative weights (BJG) */

double

gsl_histogram_mean (const gsl_histogram * h)

{

  const size_t n = h->n;

  size_t i;

  /* Compute the bin-weighted arithmetic mean M of a histogram using the

     recurrence relation

     M(n) = M(n-1) + (x[n] - M(n-1)) (w(n)/(W(n-1) + w(n))) 

     W(n) = W(n-1) + w(n)

   */

  long double wmean = 0;

  long double W = 0;

  for (i = 0; i < n; i++)

    {

      double xi = (h->range[i + 1] + h->range[i]) / 2;

      double wi = h->bin[i];

      if (wi > 0)

        {

          W += wi;

          wmean += (xi - wmean) * (wi / W);

        }

    }

  return wmean;

}

double

gsl_histogram_sigma (const gsl_histogram * h)

{

  const size_t n = h->n;

  size_t i;

  long double wvariance = 0 ;

  long double wmean = 0;

  long double W = 0;

  /* Use a two-pass algorithm for stability.  Could also use a single

     pass formula, as given in N.J.Higham 'Accuracy and Stability of

     Numerical Methods', p.12 */

  /* Compute the mean */

  for (i = 0; i < n; i++)

    {

      double xi = (h->range[i + 1] + h->range[i]) / 2;

      double wi = h->bin[i];

      if (wi > 0)

        {

          W += wi;

          wmean += (xi - wmean) * (wi / W);

        }

    }

  /* Compute the variance */

  W = 0.0;

  for (i = 0; i < n; i++)

    {

      double xi = ((h->range[i + 1]) + (h->range[i])) / 2;

      double wi = h->bin[i];

      if (wi > 0) {

        const long double delta = (xi - wmean);

        W += wi ;

        wvariance += (delta * delta - wvariance) * (wi / W);

      }

    }

  {

    double sigma = sqrt (wvariance) ;

    return sigma;

  }

}

/*

  sum up all bins of histogram

 */

double 

gsl_histogram_sum(const gsl_histogram * h)

{

  double sum=0;

  size_t i=0;

  size_t n;

  n=h->n;

  while(i < n)

    sum += h->bin[i++];

  return sum;

}