| /* statistics/wvariance_source.c |
| * |
| * Copyright (C) 1996, 1997, 1998, 1999, 2000 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 2 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,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,factor) (const BASE w[], const size_t wstride, const size_t n) |
| { |
| /* Find the factor ``N/(N-1)'' which multiplies the raw std dev */ |
| |
| 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); |
| } |