/* statistics/wvariance_source.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007, 2010 Jim Davies, Brian Gough

 * 

 * This program 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 program; if not, write to the Free Software

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

 */

static double 

FUNCTION(compute,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean);

static double 

FUNCTION(compute,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean);

static double

FUNCTION(compute,factor) (const BASE w[], const size_t wstride, const size_t n);

static double

FUNCTION(compute,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  /* takes a dataset and finds the weighted variance */

  long double wvariance = 0 ;

  long double W = 0;

  size_t i;

  /* find the sum of the squares */

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

    {

      BASE wi = w[i * wstride];

      if (wi > 0) {

        const long double delta = (data[i * stride] - wmean);

        W += wi ;

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

      }

    }

  return wvariance ;

}

static double

FUNCTION(compute,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  /* takes a dataset and finds the weighted sum of squares about wmean*/

  long double wtss = 0 ;

  size_t i;

  /* find the sum of the squares */

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

    {

      BASE wi = w[i * wstride];

      if (wi > 0) {

        const long double delta = (data[i * stride] - wmean);

        wtss += wi * delta * delta;

      }

    }

  return wtss ;

}

static double

FUNCTION(compute,factor) (const BASE w[], const size_t wstride, const size_t n)

{

  /* Find the factor ``N/(N-1)'' which multiplies the raw std dev 

     see the file doc/statnotes.tex for the derivation */

  long double a = 0 ;

  long double b = 0;

  long double factor;

  size_t i;

  /* find the sum of the squares */

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

    {

      BASE wi = w[i * wstride];

      if (wi > 0)

        {

          a += wi ;

          b += wi * wi ;

        }

    }

  factor = (a*a) / ((a*a) - b);

  return factor ;

}

double 

FUNCTION(gsl_stats,wvariance_with_fixed_mean) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  const double wvariance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);

  return wvariance;

}

double 

FUNCTION(gsl_stats,wsd_with_fixed_mean) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  const double wvariance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);

  const double wsd = sqrt (wvariance);

  return wsd;

}

double 

FUNCTION(gsl_stats,wvariance_m) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  const double variance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);

  const double scale = FUNCTION(compute,factor)(w, wstride, n);

  return scale * variance;

}

double 

FUNCTION(gsl_stats,wsd_m) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  const double variance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);

  const double scale = FUNCTION(compute,factor)(w, wstride, n);

  const double wsd = sqrt(scale * variance) ;

  return wsd;

}

double 

FUNCTION(gsl_stats,wsd) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)

{

  const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);

  return FUNCTION(gsl_stats,wsd_m) (w, wstride, data, stride, n, wmean) ;

}

double 

FUNCTION(gsl_stats,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)

{

  const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);

  return FUNCTION(gsl_stats,wvariance_m)(w, wstride, data, stride, n, wmean);

}

double 

FUNCTION(gsl_stats,wtss_m) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)

{

  const double wtss = FUNCTION(compute,wtss) (w, wstride, data, stride, n, wmean);

  return wtss;

}

double 

FUNCTION(gsl_stats,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)

{

  const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);

  return FUNCTION(gsl_stats,wtss_m)(w, wstride, data, stride, n, wmean);

}