/*
 *  Mathlib : A C Library of Special Functions
 *  Copyright (C) 2003	      The R Foundation
 *
 *  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, 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.
 *
 *  A copy of the GNU General Public License is available via WWW at
 *  http://www.gnu.org/copyleft/gpl.html.  You can also obtain it by
 *  writing to the Free Software Foundation, Inc., 59 Temple Place,
 *  Suite 330, Boston, MA  02111-1307  USA.
 *
 *
 *  SYNOPSIS
 *
 *	#include <Rmath.h>
 *	void rmultinom(int n, double* prob, int K, int* rN);
 *
 *  DESCRIPTION
 *
 *	Random Vector from the multinomial distribution.
 *             ~~~~~~
 *  NOTE
 *	Because we generate random _vectors_ this doesn't fit easily
 *	into the do_random[1-4](.) framework setup in ../main/random.c
 *	as that is used only for the univariate random generators.
 *      Multivariate distributions typically have too complex parameter spaces
 *	to be treated uniformly.
 *	=> Hence also can have  int arguments.
 */

#include "nmath.h"
#include <stdlib.h>

#ifdef MATHLIB_STANDALONE
#define ML_ERR_ret_NAN(_k_) {ML_ERROR(ME_DOMAIN); rN[_k_]=-1; return;}
#else
#define ML_ERR_ret_NAN(_k_) {ML_ERROR(ME_DOMAIN); rN[_k_]=NA_INTEGER; return;}
#endif

void rmultinom(int n, double* prob, int K, int* rN)
/* `Return' vector  rN[1:K] {K := length(prob)}
 *  where rN[j] ~ Bin(n, prob[j]) ,  sum_j rN[j] == n,  sum_j prob[j] == 1,
 */
{
    int k;
    double pp, p_tot = 0.;

#ifdef MATHLIB_STANDALONE
    if (K < 1) { ML_ERROR(ME_DOMAIN); return;}
    if (n < 0)  ML_ERR_ret_NAN(0);
#else
    if (K == NA_INTEGER || K < 1) { ML_ERROR(ME_DOMAIN); return;}
    if (n == NA_INTEGER || n < 0)  ML_ERR_ret_NAN(0);
#endif

    /* Note: prob[K] is only used here for checking  sum_k prob[k] = 1 ;
     *       Could make loop one shorter and drop that check !
     */
    for(k = 0; k < K; k++) {
	pp = prob[k];
	if (!R_FINITE(pp) || pp < 0. || pp > 1.) ML_ERR_ret_NAN(k);
	p_tot += pp;
	rN[k] = 0;
    }
    if(fabs(p_tot - 1.) > 1e-7)
	MATHLIB_ERROR("rbinom: probability sum should be 1, but is %g", p_tot);
    if (n == 0) return;
    if (K == 1 && p_tot == 0.) return;/* trivial border case: do as rbinom */

    /* Generate the first K-1 obs. via binomials */

    for(k = 0; k < K-1; k++) { /* (p_tot, n) are for "remaining binomial" */
	if(prob[k]) {
	    pp = prob[k] / p_tot;
	    rN[k] = ((pp < 1.) ? (int) rbinom((double) n,  pp) :
		     /*>= 1; > 1 happens because of rounding */
		     n);
	    n -= rN[k];
	}
	else rN[k] = 0;
	if(n <= 0) /* we have all*/ return;
	p_tot -= prob[k]; /* i.e. = sum(prob[(k+1):K]) */
    }
    rN[K-1] = n;
    return;
}
#undef ML_ERR_ret_NAN
