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/* 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 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 library; if not, write to the Free Software Foundation, Inc.,
* 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, 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;
/* Use a two-pass algorithm for stability. Could also use a single
pass formula, 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;
}
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