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/* 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);
}
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