/* statistics/variance_source.c

 * 

 * Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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,variance) (const BASE data[], const size_t stride, const size_t n, const double mean);

static double 

FUNCTION(compute,tss) (const BASE data[], const size_t stride, const size_t n, const double mean);

static double

FUNCTION(compute,variance) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  /* takes a dataset and finds the variance */

  long double variance = 0 ;

  size_t i;

  /* find the sum of the squares */

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

    {

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

      variance += (delta * delta - variance) / (i + 1);

    }

  return variance ;

}

static double

FUNCTION(compute,tss) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

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

  long double tss = 0 ;

  size_t i;

  /* find the sum of the squares */

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

    {

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

      tss += delta * delta;

    }

  return tss ;

}

double 

FUNCTION(gsl_stats,variance_with_fixed_mean) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  const double variance = FUNCTION(compute,variance) (data, stride, n, mean);

  return variance;

}

double 

FUNCTION(gsl_stats,sd_with_fixed_mean) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  const double variance = FUNCTION(compute,variance) (data, stride, n, mean);

  const double sd = sqrt (variance);

  return sd;

}

double 

FUNCTION(gsl_stats,variance_m) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  const double variance = FUNCTION(compute,variance) (data, stride, n, mean);

  return variance * ((double)n / (double)(n - 1));

}

double 

FUNCTION(gsl_stats,sd_m) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  const double variance = FUNCTION(compute,variance) (data, stride, n, mean);

  const double sd = sqrt (variance * ((double)n / (double)(n - 1)));

  return sd;

}

double 

FUNCTION(gsl_stats,variance) (const BASE data[], const size_t stride, const size_t n)

{

  const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);

  return FUNCTION(gsl_stats,variance_m)(data, stride, n, mean);

}

double 

FUNCTION(gsl_stats,sd) (const BASE data[], const size_t stride, const size_t n)

{

  const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);

  return FUNCTION(gsl_stats,sd_m) (data, stride, n, mean);

}

double 

FUNCTION(gsl_stats,tss_m) (const BASE data[], const size_t stride, const size_t n, const double mean)

{

  const double tss = FUNCTION(compute,tss) (data, stride, n, mean);

  return tss;

}

double 

FUNCTION(gsl_stats,tss) (const BASE data[], const size_t stride, const size_t n)

{

  const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);

  return FUNCTION(gsl_stats,tss_m)(data, stride, n, mean);

}