prob_distribution.h

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/* 
 * This file is part of biomcmc-lib, a low-level library for phylogenomic analysis.
 * Copyright (C) 2019-today  Leonardo de Oliveira Martins [ leomrtns at gmail.com;  http://www.leomartins.org ]
 *
 * biomcmc 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 (file "COPYING" or http://www.gnu.org/copyleft/gpl.html).
 */

#ifndef _biomcmc_prob_distribution_h_
#define _biomcmc_prob_distribution_h_

#include "lowlevel.h"
#include "random_number.h"

typedef struct discrete_sample_struct* discrete_sample;

/* \brief sampling from a discrete distribution in O(1) time (from GSL based on Walker's algorithm) */
struct discrete_sample_struct
{
  size_t K; /* note that here we DO NOT use int, but size_t (which limits somehow the largest vector size, but practical) */
  size_t *A;
  double *F;
};

// reminder: gamma is in E[x] = a/b , but poisson is E[x] = lambda (since lambda is related to alpha, not beta) */

void biomcmc_discrete_gamma (double alpha, double beta, double *rate, int nrates);

double biomcmc_dexp_dt (double d, double lambda, double m, bool log_p);
double biomcmc_pexp_dt (double d, double lambda, double m, bool log_p);
double biomcmc_qexp_dt (double p, double lambda, double m, bool log_p);

double biomcmc_dgamma (double x, double alpha, double beta, bool log_p);
double biomcmc_qgamma (double p, double alpha, double beta, bool log_p);
double biomcmc_pgamma (double x, double alpha, double beta, bool log_p);

double biomcmc_dnorm (double x, double mu, double sigma, bool log_p);
double biomcmc_qnorm (double p, double mu, double sigma, bool log_p);
double biomcmc_pnorm (double x, double mu, double sigma, bool log_p);

double biomcmc_dlnorm (double x, double meanlog, double sdlog, bool log_p);
double biomcmc_qlnorm (double p, double meanlog, double sdlog, bool log_p);
double biomcmc_plnorm (double x, double meanlog, double sdlog, bool log_p);

double biomcmc_dpois (double x, double lambda, bool log_p);
/*The quantile function of the Poisson distribution. */
double biomcmc_qpois (double p, double lambda, bool log_p);
double biomcmc_ppois (double x, double lambda, bool log_p);

double biomcmc_rng_gamma (double alpha, double beta);
double biomcmc_rng_norm (double mu, double sigma);
double biomcmc_rng_lnorm (double meanlog, double sdlog);
double biomcmc_rng_pois (double mu);


/* Calculates log|gamma(x)| and returns the sign of the gamma function in sgn if *sgn is not NULL. */
double biomcmc_lgammafn (double x, int *sgn);
/*  This function computes the value of the gamma function. */
double biomcmc_gammafn (double x);

double biomcmc_log1p (double x);
double biomcmc_log1pmx (double x);
double biomcmc_expm1 (double x);

/* create the struct for sampling from an arbitrary empirical frequency vector */
discrete_sample new_discrete_sample_from_frequencies (double *prob, size_t size);
/* free discrete_sample_struct */
void del_discrete_sample (discrete_sample g);
/* sample index from empirical discrete distribution (between zero and g->K which is the original vector size) */
size_t biomcmc_rng_discrete (discrete_sample g);
/* density from empirical frequency vector (that is, original values from vector) */
double biomcmc_discrete_sample_pdf (discrete_sample g, size_t k);

/* Compute log (exp (logx) + exp (logy)) without overflow and without loss of accuracy. */
double biomcmc_logspace_add (double logx, double logy);
/* Compute log (exp (logx) - exp (logy)) without overflow and without loss of accuracy. */
double biomcmc_logspace_sub (double logx, double logy);
bool biomcmc_isfinite(double x);

#endif