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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 <stdlib.h>
#include <gsl/gsl_sf_gamma.h>
#include <gsl/gsl_sf_psi.h>
//#include "DLTmath.h"
#include "statistics.h"
#include "gamma_dist.h" /* gamma_dev() */
#include "chisqrgen_dist.h"
/* The chi^2 distribution has the form
p(x) dx = (1/(2^(n/2) * Gamma(nu/2))) * x^((nu - 2)/2) * exp(-x/2)) dx
0 <= x < +inf
nu > 0
*/
double
chisqrgen_dev(const double nu, const double lambda, const gsl_rng *r2)
{
return(lambda * 2.0 * gamma_dev(1.0, 0.5*nu, r2));
}
double
chisqrgen_pdf(const double x, const double nu, const double lambda)
{
double p, nu2;
if (x <= 0.0)
{
return(0.0);
}
else
{
nu2 = 0.5*nu;
p = (nu2-1.0)*log(x/lambda) - 0.5*x/lambda - nu2*log(2.0) - lgamma(nu2);
return(exp(p)/lambda);
}
}
double
chisqrgen_lnpdf(const double x, const double nu, const double lambda)
{
double nu2 = 0.5*nu;
return((nu2-1.0)*log(x/lambda) - 0.5*x/lambda - nu2*log(2.0) - lgamma(nu2) - log(lambda));
}
double
chisqrgen_cdf(const double x, const double nu, const double lambda)
{
if (x <= 0.0)
return(0.0);
else
{
/* printf("\n****** %f %f %f", */
/* gsl_sf_gamma_inc_P(0.5*nu, 0.5*x/lambda), */
/* IncompleteGamma(0.5*nu, 0.5*x/lambda), */
/* 1.0 - IncompleteGamma(0.5*nu, 0.5*x/lambda)/tgamma(0.5*x/lambda)); */
return(gsl_sf_gamma_inc_P(0.5*nu, 0.5*x/lambda));
}
}
double
chisqrgen_sdf(const double x, const double nu, const double lambda)
{
if (x <= 0.0)
return(1.0);
else
return(1.0 - chisqrgen_cdf(x, nu, lambda));
}
double
chisqrgen_int(const double x, const double y, const double nu, const double lambda)
{
if (x <= 0.0)
return(chisqrgen_cdf(y, nu, lambda));
else
return(chisqrgen_cdf(y, nu, lambda) - chisqrgen_cdf(x, nu, lambda));
}
/* This is from Cover and Thomas (_Elements of Information Theory_),
but it is wrong. Something's wrong.
I even did the integration myself and got the same answer. Weird.
*/
/* double */
/* chisqrgen_logL(const double nu, const double lambda) */
/* { */
/* double logL, nu2; */
/* */
/* nu2 = nu / 2.0; */
/* */
/* logL = -log(2.0 * tgamma(nu2)) - (1.0 - nu2) * gsl_sf_psi(nu2) - nu2; */
/* */
/* return(logL); */
/* } */
double
chisqrgen_logL(const double nu, const double lambda)
{
double nu2 = 0.5*nu;
/* printf("\nchisqrgen logL: %f %f %f %f %f\n", */
/* (nu2 - 1.0)*gsl_sf_psi(nu2), - log(2.0), - nu2, - lgammav, */
/* (nu2 - 1.0)*gsl_sf_psi(nu2) - log(2.0) - nu2 - lgammav); */
return((nu2 - 1.0)*gsl_sf_psi(nu2) - log(2.0) - nu2 - lgamma(nu2));
}
/* For the maximum likelihood fit we nust find the root of:
F1 = (1/N)\Sum{log(x)} - log(2 lambda) - digamma{nu/2} = 0
where the first derivative with repect to nu (dF1/dnu) is:
F1' = -trigamma(nu/2)/2 = 0
*/
static void
evalchisqrgenML(const double logterm, const double nu, const double lambda, double *fx, double *dfx)
{
*fx = logterm - gsl_sf_psi(0.5*nu) - log(2.0 * lambda);
*dfx = -0.5*gsl_sf_psi_1(0.5*nu);
}
/* fit a chisqrgen distribution by maxinum likelihood */
double
chisqrgen_fit(const double *data, const int num, double *nu, double *lambda, double *prob)
{
double ave, var, logterm, fx, dfx, guess_nu;
int i;
double iter = 100;
double tol = 1e-8;
ave = 0.0;
for (i = 0; i < num; ++i)
{
if (data[i] < 0.0)
{
fprintf(stderr, "\n ERROR345: chi^2 distributed data must be >= 0.0 ");
return(-1.0);
}
else
{
ave += data[i];
}
}
ave /= (double) num;
var = 0.0;
for (i = 0; i < num; ++i)
var += (data[i] - ave) * (data[i] - ave);
var /= (double) num;
guess_nu = *nu = 2.0 * ave * ave / var;
*lambda = 0.5 * var / ave;
logterm = 0.0;
for (i = 0; i < num; ++i)
{
if(data[i] == 0.0)
continue;
logterm += log(data[i]);
}
logterm /= (double) num;
for (i = 0; i < iter; ++i)
{
evalchisqrgenML(logterm, *nu, *lambda, &fx, &dfx);
if (fabs(fx) < tol)
break; /* success */
*nu -= (fx / dfx); /* Newton-Raphson correction */
if (*nu <= 0.0)
*nu = tol;
*lambda = ave / *nu;
/* printf("\n chi^2 gen -- nu: %f lambda: %f ", *nu, *lambda); */
/* fflush(NULL); */
}
if (i == iter)
*nu = guess_nu;
/* chisqrgen_logL(*nu, 0.0); */
return(chi_sqr_adapt(data, num, 0, prob, *nu, *lambda, chisqrgen_pdf, chisqrgen_lnpdf, chisqrgen_int));
}
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