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/* statistics/wvariance_source.c
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*
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* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007, 2010 Jim Davies, Brian Gough
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*
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* This program is free software; you can redistribute it and/or modify
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* it under the terms of the GNU General Public License as published by
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* the Free Software Foundation; either version 3 of the License, or (at
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* your option) any later version.
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*
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* This program is distributed in the hope that it will be useful, but
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* WITHOUT ANY WARRANTY; without even the implied warranty of
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* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
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* General Public License for more details.
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*
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* You should have received a copy of the GNU General Public License
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* along with this program; if not, write to the Free Software
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* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
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*/
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static double
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FUNCTION(compute,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean);
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static double
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FUNCTION(compute,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean);
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static double
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FUNCTION(compute,factor) (const BASE w[], const size_t wstride, const size_t n);
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static double
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FUNCTION(compute,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)
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{
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/* takes a dataset and finds the weighted variance */
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long double wvariance = 0 ;
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long double W = 0;
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size_t i;
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/* find the sum of the squares */
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for (i = 0; i < n; i++)
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{
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BASE wi = w[i * wstride];
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if (wi > 0) {
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const long double delta = (data[i * stride] - wmean);
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W += wi ;
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wvariance += (delta * delta - wvariance) * (wi / W);
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}
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}
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return wvariance ;
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}
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static double
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FUNCTION(compute,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n, const double wmean)
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{
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/* takes a dataset and finds the weighted sum of squares about wmean*/
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long double wtss = 0 ;
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size_t i;
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/* find the sum of the squares */
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for (i = 0; i < n; i++)
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{
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BASE wi = w[i * wstride];
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if (wi > 0) {
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const long double delta = (data[i * stride] - wmean);
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wtss += wi * delta * delta;
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}
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}
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return wtss ;
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}
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static double
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FUNCTION(compute,factor) (const BASE w[], const size_t wstride, const size_t n)
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{
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/* Find the factor ``N/(N-1)'' which multiplies the raw std dev
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see the file doc/statnotes.tex for the derivation */
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long double a = 0 ;
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long double b = 0;
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long double factor;
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size_t i;
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/* find the sum of the squares */
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for (i = 0; i < n; i++)
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{
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BASE wi = w[i * wstride];
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if (wi > 0)
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{
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a += wi ;
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b += wi * wi ;
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}
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}
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factor = (a*a) / ((a*a) - b);
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return factor ;
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}
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double
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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)
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{
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const double wvariance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);
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return wvariance;
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}
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double
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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)
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{
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const double wvariance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);
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const double wsd = sqrt (wvariance);
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return wsd;
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}
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double
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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)
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{
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const double variance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);
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const double scale = FUNCTION(compute,factor)(w, wstride, n);
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return scale * variance;
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}
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double
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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)
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{
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const double variance = FUNCTION(compute,wvariance) (w, wstride, data, stride, n, wmean);
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const double scale = FUNCTION(compute,factor)(w, wstride, n);
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const double wsd = sqrt(scale * variance) ;
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return wsd;
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}
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double
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FUNCTION(gsl_stats,wsd) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)
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{
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const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);
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return FUNCTION(gsl_stats,wsd_m) (w, wstride, data, stride, n, wmean) ;
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}
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double
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FUNCTION(gsl_stats,wvariance) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)
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{
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const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);
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return FUNCTION(gsl_stats,wvariance_m)(w, wstride, data, stride, n, wmean);
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}
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double
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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)
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{
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const double wtss = FUNCTION(compute,wtss) (w, wstride, data, stride, n, wmean);
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return wtss;
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}
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double
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FUNCTION(gsl_stats,wtss) (const BASE w[], const size_t wstride, const BASE data[], const size_t stride, const size_t n)
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{
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const double wmean = FUNCTION(gsl_stats,wmean) (w, wstride, data, stride, n);
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return FUNCTION(gsl_stats,wtss_m)(w, wstride, data, stride, n, wmean);
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}
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