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/* statistics/lag1_source.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000, 2007 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 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 program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
double
FUNCTION(gsl_stats,lag1_autocorrelation) (const BASE data[], const size_t stride, const size_t n)
{
const double mean = FUNCTION(gsl_stats,mean) (data, stride, n);
return FUNCTION(gsl_stats,lag1_autocorrelation_m)(data, stride, n, mean);
}
double
FUNCTION(gsl_stats,lag1_autocorrelation_m) (const BASE data[], const size_t stride, const size_t size, const double mean)
{
/* Compute the lag-1 autocorrelation of a dataset using the
recurrence relation */
size_t i;
long double r1 ;
long double q = 0 ;
long double v = (data[0 * stride] - mean) * (data[0 * stride] - mean) ;
for (i = 1; i < size ; i++)
{
const long double delta0 = (data[(i-1) * stride] - mean);
const long double delta1 = (data[i * stride] - mean);
q += (delta0 * delta1 - q)/(i + 1);
v += (delta1 * delta1 - v)/(i + 1);
}
r1 = q / v ;
return r1;
}
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