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/*
Theseus - maximum likelihood superpositioning of macromolecular structures
Copyright (C) 2004-2015 Douglas L. Theobald
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 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 program; if not, write to the:
Free Software Foundation, Inc.,
59 Temple Place, Suite 330,
Boston, MA 02111-1307 USA
-/_|:|_|_\-
*/
#include <stdio.h>
#include <math.h>
#include <float.h>
#include <gsl/gsl_rng.h>
#include <gsl/gsl_randist.h>
#include "statistics.h"
#include "DLTmath.h"
#include "normal_dist.h"
/* The normal distribution has the form
*/
double
normal_dev(const double mean, const double var, const gsl_rng *r2)
{
return (gsl_ran_gaussian_ziggurat(r2, sqrt(var)) + mean);
}
/* double */
/* normal_dev(const double mean, const double var, const gsl_rng *r2) */
/* { */
/* double fac, r, v1, v2; */
/* */
/* do */
/* { */
/* v1 = 2.0 * gsl_rng_uniform(r2) - 1.0; */
/* v2 = 2.0 * gsl_rng_uniform(r2) - 1.0; */
/* r = v1*v1 + v2*v2; */
/* } */
/* while (r >= 1.0); */
/* */
/* fac = sqrt(-2.0 * log(r) / r); */
/* */
/* return (v2 * fac * sqrt(var) + mean); */
/* } */
double
normal_pdf(const double x, const double mean, const double var)
{
double p, term;
if (var == 0.0)
{
if (x == mean)
return(1.0);
else
return(0.0);
}
term = x - mean;
p = (1.0 / sqrt(2.0 * MY_PI * var)) * exp(-term * term / (2.0 * var));
return (p);
}
double
normal_lnpdf(const double x, const double mean, const double var)
{
double p;
p = (-0.5 * log(2.0 * MY_PI * var)) - (mysquare(x - mean) / (2.0 * var));
return (p);
}
double
normal_cdf(const double x, const double mean, const double var)
{
double p;
p = 0.5 * (1.0 + erf((x - mean) / (sqrt(2.0 * var))));
return (p);
}
double
normal_sdf(const double x, const double mean, const double var)
{
double p;
p = 0.5 * erfc((x - mean) / (sqrt(2.0 * var)));
return (p);
}
double
normal_int(const double x, const double y, const double mean, const double var)
{
double p, xn, yn;
xn = (x - mean) / (sqrt(2.0 * var));
yn = (y - mean) / (sqrt(2.0 * var));
if ((x + y) < 2.0 * mean)
p = 0.5 * (erf(yn) - erf(xn));
else
p = 0.5 * (erfc(xn) - erfc(yn));
return (p);
}
double
normal_logL(const double mean, const double var)
{
return(-log(sqrt(var * 2.0 * MY_PI * MY_E)));
}
/* maximum likelihood fit of data to a normal distribution */
/* screw bias, it's overblown */
double
normal_fit(const double *x, const int n, double *mean, double *var, double *logL)
{
double nd = (double) n;
double ave, variance, verror;
int i;
ave = 0.0;
for (i = 0; i < n; ++i)
ave += x[i];
ave /= nd;
variance = verror = 0.0;
for (i = 0; i < n; ++i)
{
variance += mysquare(x[i] - ave);
verror += (x[i] - ave);
}
verror = mysquare(verror) / nd;
variance = (variance - verror) / nd; /* more accurate corrected two-pass algorithm */
/* with no rounding error, verror = 0 */
*mean = ave;
*var = variance;
/* printf("\n\nnormal logL %e\n", normal_logL(*mean, *var)); */
return(chi_sqr_adapt(x, n, 0, logL, *mean, *var, normal_pdf, normal_lnpdf, normal_int));
}
double
normal_fit_w(const double *x, const int n, const double *wts, double *mean,
double *var, double *logL)
{
double ave, variance, tmp, wtsum;
int i;
ave = wtsum = 0.0;
for (i = 0; i < n; ++i)
{
ave += wts[i] * x[i];
wtsum += wts[i];
}
ave /= wtsum;
variance = 0.0;
for (i = 0; i < n; ++i)
{
tmp = (x[i] - ave);
variance += wts[i] * tmp * tmp;
}
variance /= wtsum;
*mean = ave;
*var = variance;
return(1.0);
}
void
normal_init_mix_params(const double *x, const int n, const int mixn, double *mean,
double *var)
{
int j;
double imean, ivar, ilogL;
normal_fit(x, n, &imean, &ivar, &ilogL);
for (j = 0; j < mixn; ++j)
{
mean[j] = imean - (2.0 * sqrt(ivar)) + (4.0 * sqrt(ivar) * (j + 1.0) / (1.0 + mixn));
var[j] = ivar / mixn;
}
}
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