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/*
* Unofficial release 1.3.0
* B I N G
*
*/
/* $Id: lin_reg.c,v 1.4 1999/10/16 07:07:58 fgouget Exp $ */
#include <math.h>
#include <float.h>
#include "lin_reg.h"
/*
* The linear regression stuff.
* The basic formula used to do the linear regression are given below but
* for more details you should see a maths book.
*
* We have a set of n samples (xi,yi). Then if we write
*
* y = a * x + b
*
* the a and b that best approximate the samples are given by:
*
* a = Covariance ( xi , yi ) / Variance ( xi )
*
* b = Covariance ( xi , yi ) / Variance (xi) * Mean ( xi ) - Mean ( yi )
*
* Note that in bing we only care about a.
*
* To compute a we maintain the variables below:
*
* sum_x = Sum ( xi )
* sum_x2 = Sum ( xi * xi )
* sum_y = Sum ( yi )
* sum_xy = Sum ( xi * yi )
*
* And then the covariance and variance can be computed as:
*
* Covariance ( xi , yi ) = ( sum_xy - sum_x * sum_y / n ) / ( n - 1 )
*
* Variance ( xi ) = ( sum_x2 - sum_x * sum_x / n ) / ( n - 1 )
*
* Thus:
*
* n * sum_xy - sum_x * sum_y
* a = ----------------------------
* n * sum_x2 - sum_x * sum_x
*
* sum_x2 * sum_y - sum_x * sum_xy
* b = ---------------------------------
* n * sum_x2 - sum_x * sum_x
*
*
* We also compute the correlation value so that we know whether the stats
* indeed look like a line or not. The correlation is computed from the
* following formula:
*
* Corr (xi , yi ) = Covariance ( xi , yi ) / Sqrt ( Variance ( xi ) / Variance ( yi ) )
*
* i.e.
*
* n * sum_xy - sum_x * sum_y
* Corr (xi , yi ) = -------------------------------------------------------------------------
* Sqrt( ( n * sum_x2 - sum_x * sum_x ) * ( n * sum_y2 - sum_y * sum_y ) )
*
*/
void linreg_update(linreg_t* linreg)
{
if (linreg->nb_samples>1) {
/*
* This function computes the end result from the computed
* intermediate statistics.
*/
linreg->a=(linreg->sum_xy-linreg->sum_x*linreg->sum_y/linreg->nb_samples)/
(linreg->sum_x2-linreg->sum_x*linreg->sum_x/linreg->nb_samples);
linreg->b=(linreg->sum_x2*linreg->sum_y-linreg->sum_x*linreg->sum_xy)/
(linreg->nb_samples*linreg->sum_x2-linreg->sum_x*linreg->sum_x);
linreg->corr=(linreg->sum_xy-linreg->sum_x*linreg->sum_y/linreg->nb_samples)/
sqrt((linreg->sum_x2-linreg->sum_x*linreg->sum_x/linreg->nb_samples) *
(linreg->sum_y2-linreg->sum_y*linreg->sum_y/linreg->nb_samples)
);
} else {
linreg->a=0;
linreg->b=0;
linreg->corr=0;
}
}
int linreg_init(linreg_t *linreg)
{
linreg->nb_samples=0;
linreg->sum_x=0.0;
linreg->sum_y=0.0;
linreg->sum_x2=0.0;
linreg->sum_y2=0.0;
linreg->sum_xy=0.0;
linreg->a=0.0;
linreg->b=0.0;
linreg->corr=0.0;
return 0;
}
int linreg_add_all(linreg_t *linreg,int nb_samples, int* x, double* y, int update)
{
int i;
/* Initialise the results data structure */
for (i=0;i<nb_samples;i++) {
if (y[i]==DBL_MAX)
continue;
linreg->sum_x+=x[i];
linreg->sum_y+=y[i];
linreg->sum_x2+=x[i]*x[i];
linreg->sum_y2+=y[i]*y[i];
linreg->sum_xy+=x[i]*y[i];
linreg->nb_samples++;
}
/* Update the regression results */
if (update!=0)
linreg_update(linreg);
return 0;
}
int linreg_del_sample(linreg_t *linreg, int x, double y, int update)
{
linreg->nb_samples--;
linreg->sum_x-=x;
linreg->sum_y-=y;
linreg->sum_x2-=x*x;
linreg->sum_y2-=y*y;
linreg->sum_xy-=x*y;
/* Update the regression results */
if (update!=0)
linreg_update(linreg);
return 0;
}
int linreg_add_sample(linreg_t *linreg, int x, double y, int update)
{
linreg->nb_samples++;
linreg->sum_x+=x;
linreg->sum_y+=y;
linreg->sum_x2+=x*x;
linreg->sum_y2+=y*y;
linreg->sum_xy+=x*y;
/* Update the regression results */
if (update!=0)
linreg_update(linreg);
return 0;
}
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