/* histogram/stat2d.c

 * Copyright (C) 2002  Achim Gaedke

 *

 * 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 histogram/stat2d.c:

 * Routine to return statistical values of the content of a 2D hisogram. 

 *

 * Contains the routines:

 * gsl_histogram2d_sum sum up all bin values

 * gsl_histogram2d_xmean determine mean of x values

 * gsl_histogram2d_ymean determine mean of y values

 *

 * Author: Achim Gaedke Achim.Gaedke@zpr.uni-koeln.de

 * Jan. 2002

 *

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

#include <config.h>

#include <math.h>

#include <gsl/gsl_errno.h>

#include <gsl/gsl_histogram2d.h>

/*

  sum up all bins of histogram2d

 */

double

gsl_histogram2d_sum (const gsl_histogram2d * h)

{

  const size_t n = h->nx * h->ny;

  double sum = 0;

  size_t i = 0;

  while (i < n)

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

  return sum;

}

double

gsl_histogram2d_xmean (const gsl_histogram2d * h)

{

  const size_t nx = h->nx;

  const size_t ny = h->ny;

  size_t i;

  size_t j;

  /* 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 < nx; i++)

    {

      double xi = (h->xrange[i + 1] + h->xrange[i]) / 2.0;

      double wi = 0;

      for (j = 0; j < ny; j++)

        {

          double wij = h->bin[i * ny + j];

          if (wij > 0)

            wi += wij;

        }

      if (wi > 0)

        {

          W += wi;

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

        }

    }

  return wmean;

}

double

gsl_histogram2d_ymean (const gsl_histogram2d * h)

{

  const size_t nx = h->nx;

  const size_t ny = h->ny;

  size_t i;

  size_t j;

  /* 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 (j = 0; j < ny; j++)

    {

      double yj = (h->yrange[j + 1] + h->yrange[j]) / 2.0;

      double wj = 0;

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

        {

          double wij = h->bin[i * ny + j];

          if (wij > 0)

            wj += wij;

        }

      if (wj > 0)

        {

          W += wj;

          wmean += (yj - wmean) * (wj / W);

        }

    }

  return wmean;

}

double

gsl_histogram2d_xsigma (const gsl_histogram2d * h)

{

  const double xmean = gsl_histogram2d_xmean (h);

  const size_t nx = h->nx;

  const size_t ny = h->ny;

  size_t i;

  size_t j;

  /* 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 wvariance = 0;

  long double W = 0;

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

    {

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

      double wi = 0;

      for (j = 0; j < ny; j++)

        {

          double wij = h->bin[i * ny + j];

          if (wij > 0)

            wi += wij;

        }

      if (wi > 0)

        {

          W += wi;

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

        }

    }

  {

    double xsigma = sqrt (wvariance);

    return xsigma;

  }

}

double

gsl_histogram2d_ysigma (const gsl_histogram2d * h)

{

  const double ymean = gsl_histogram2d_ymean (h);

  const size_t nx = h->nx;

  const size_t ny = h->ny;

  size_t i;

  size_t j;

  /* 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 wvariance = 0;

  long double W = 0;

  for (j = 0; j < ny; j++)

    {

      double yj = (h->yrange[j + 1] + h->yrange[j]) / 2.0 - ymean;

      double wj = 0;

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

        {

          double wij = h->bin[i * ny + j];

          if (wij > 0)

            wj += wij;

        }

      if (wj > 0)

        {

          W += wj;

          wvariance += ((yj * yj) - wvariance) * (wj / W);

        }

    }

  {

    double ysigma = sqrt (wvariance);

    return ysigma;

  }

}

double

gsl_histogram2d_cov (const gsl_histogram2d * h)

{

  const double xmean = gsl_histogram2d_xmean (h);

  const double ymean = gsl_histogram2d_ymean (h);

  const size_t nx = h->nx;

  const size_t ny = h->ny;

  size_t i;

  size_t j;

  /* 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 wcovariance = 0;

  long double W = 0;

  for (j = 0; j < ny; j++)

    {

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

        {

          double xi = (h->xrange[i + 1] + h->xrange[i]) / 2.0 - xmean;

          double yj = (h->yrange[j + 1] + h->yrange[j]) / 2.0 - ymean;

          double wij = h->bin[i * ny + j];

          if (wij > 0)

            {

              W += wij;

              wcovariance += ((xi * yj) - wcovariance) * (wij / W);

            }

        }

    }

  return wcovariance;

}