| /* gsl_histogram_stat.c |
| * Copyright (C) 2000 Simone Piccardi |
| * |
| * This library 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 library; if not, write to the |
| * Free Software Foundation, Inc., 59 Temple Place - Suite 330, |
| * Boston, MA 02111-1307, USA. |
| */ |
| /*************************************************************** |
| * |
| * File gsl_histogram_stat.c: |
| * Routines for statisticalcomputations on histograms. |
| * Need GSL library and header. |
| * Contains the routines: |
| * gsl_histogram_mean compute histogram mean |
| * gsl_histogram_sigma compute histogram sigma |
| * |
| * Author: S. Piccardi |
| * Jan. 2000 |
| * |
| ***************************************************************/ |
| #include <config.h> |
| #include <stdlib.h> |
| #include <math.h> |
| #include <gsl/gsl_errno.h> |
| #include <gsl/gsl_histogram.h> |
| |
| /* FIXME: We skip negative values in the histogram h->bin[i] < 0, |
| since those correspond to negative weights (BJG) */ |
| |
| double |
| gsl_histogram_mean (const gsl_histogram * h) |
| { |
| const size_t n = h->n; |
| size_t i; |
| |
| /* Compute the bin-weighted arithmetic mean M of a histogram using the |
| recurrence relation |
| |
| M(n) = M(n-1) + (x[n] - M(n-1)) (w(n)/(W(n-1) + w(n))) |
| W(n) = W(n-1) + w(n) |
| |
| */ |
| |
| long double wmean = 0; |
| long double W = 0; |
| |
| for (i = 0; i < n; i++) |
| { |
| double xi = (h->range[i + 1] + h->range[i]) / 2; |
| double wi = h->bin[i]; |
| |
| if (wi > 0) |
| { |
| W += wi; |
| wmean += (xi - wmean) * (wi / W); |
| } |
| } |
| |
| return wmean; |
| } |
| |
| double |
| gsl_histogram_sigma (const gsl_histogram * h) |
| { |
| const size_t n = h->n; |
| size_t i; |
| |
| long double wvariance = 0 ; |
| long double wmean = 0; |
| long double W = 0; |
| |
| /* FIXME: should use a single pass formula here, as given in |
| N.J.Higham 'Accuracy and Stability of Numerical Methods', p.12 */ |
| |
| /* Compute the mean */ |
| |
| for (i = 0; i < n; i++) |
| { |
| double xi = (h->range[i + 1] + h->range[i]) / 2; |
| double wi = h->bin[i]; |
| |
| if (wi > 0) |
| { |
| W += wi; |
| wmean += (xi - wmean) * (wi / W); |
| } |
| } |
| |
| /* Compute the variance */ |
| |
| W = 0.0; |
| |
| for (i = 0; i < n; i++) |
| { |
| double xi = ((h->range[i + 1]) + (h->range[i])) / 2; |
| double wi = h->bin[i]; |
| |
| if (wi > 0) { |
| const long double delta = (xi - wmean); |
| W += wi ; |
| wvariance += (delta * delta - wvariance) * (wi / W); |
| } |
| } |
| |
| { |
| double sigma = sqrt (wvariance) ; |
| return sigma; |
| } |
| } |
| |
| |
| /* |
| sum up all bins of histogram |
| */ |
| |
| double |
| gsl_histogram_sum(const gsl_histogram * h) |
| { |
| double sum=0; |
| size_t i=0; |
| size_t n; |
| n=h->n; |
| |
| while(i < n) |
| sum += h->bin[i++]; |
| |
| return sum; |
| } |
| |