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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_rng.h>
#include <gsl/gsl_randist.h>
#include "DLTmath.h"
#include "statistics.h"
#include "lognormal_dist.h"
double
lognormal_dev(const double zeta, const double sigma, const gsl_rng *r2)
{
double u, v, rr2, normal, z;
do
{
/* choose x,y in uniform square (-1,-1) to (+1,+1) */
u = -1.0 + 2.0 * gsl_rng_uniform(r2);
v = -1.0 + 2.0 * gsl_rng_uniform(r2);
/* see if it is in the unit circle */
rr2 = u*u + v*v;
}
while (rr2 > 1.0 || rr2 == 0.0);
normal = u * sqrt(-2.0 * log(rr2) / rr2);
z = exp(sigma * normal + zeta);
return (z);
}
double
lognormal_pdf(const double x, const double zeta, const double sigma)
{
double u;
if (x <= 0.0)
{
return (0.0);
}
else
{
u = (log(x) - zeta) / sigma;
return (exp(-0.5*u*u) / (x * fabs(sigma) * sqrt(2.0 * MY_PI)));
}
}
double
lognormal_lnpdf(const double x, const double zeta, const double sigma)
{
double u, p;
u = (log(x) - zeta) / sigma;
p = -log(x * fabs(sigma)) - (log(2.0 * MY_PI) / 2.0) - (mysquare(u) / 2.0);
return (p);
}
double
lognormal_cdf(const double x, const double zeta, const double sigma)
{
if (x <= 0.0)
return (0.0);
else
return (0.5 * (1.0 + erf((log(x) - zeta) / (sigma * sqrt(2.0)))));
}
double
lognormal_sdf(const double x, const double zeta, const double sigma)
{
if (x <= 0.0)
return (1.0);
else
return (1.0 - lognormal_cdf(x, zeta, sigma));
}
double
lognormal_int(const double x, const double y, const double zeta, const double sigma)
{
if (x <= 0.0)
return (lognormal_cdf(y, zeta, sigma));
else
return (lognormal_cdf(y, zeta, sigma) - lognormal_cdf(x, zeta, sigma));
}
/* correct */
double
lognormal_logL(const double zeta, const double sigma)
{
return (-(zeta + 0.5 * log(2.0 * MY_PI * MY_E * mysquare(sigma))));
}
/* fit a lognormal distribution by maximum likelihood */
double
lognormal_fit(const double *data, const int num, double *zeta, double *sigma, double *prob)
{
double ave, avesqr, var, x;
int i;
ave = avesqr = 0.0;
for (i = 0; i < num; ++i)
{
if (data[i] == 0.0)
continue;
else if (data[i] < 0.0)
{
fprintf(stderr, "\n ERROR345: lognormal data must be > 0.0 ");
return(-1.0);
}
else
{
x = log(data[i]);
ave += x;
avesqr += (x*x);
}
}
ave /= (double) num;
avesqr /= (double) num;
/* m = exp(ave); */ /* this is the scale parameter */
var = 0.0;
for (i = 0; i < num; ++i)
{
if (data[i] == 0.0)
var += mysquare(ave);
else
var += mysquare(log(data[i]) - ave);
}
var /= (double) num - 1;
*zeta = ave;
*sigma = sqrt(var);
return(chi_sqr_adapt(data, num, 0, prob, *zeta, *sigma, lognormal_pdf, lognormal_lnpdf, lognormal_int));
}
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