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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 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;
+}
+