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/* 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);
}
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