src/nmath/dgamma.c

/*
 *  AUTHOR
 *    Catherine Loader, catherine@research.bell-labs.com.
 *    October 23, 2000.
 *
 *  Merge in to R:
 *	Copyright (C) 2000-2019 The R Core Team
 *	Copyright (C) 2004-2019 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 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, a copy is available at
 *  https://www.R-project.org/Licenses/
 *
 *
 * DESCRIPTION
 *
 *   Computes the density of the gamma distribution,
 *
 *                   1/s (x/s)^{a-1} exp(-x/s)
 *        p(x;a,s) = -----------------------
 *                            (a-1)!
 *
 *   where 's' is the scale (= 1/lambda in other parametrizations)
 *     and 'a' is the shape parameter ( = alpha in other contexts).
 *
 * The old (R 1.1.1) version of the code is available via '#define D_non_pois'
 */

#include "nmath.h"
#include "dpq.h"

double dgamma(double x, double shape, double scale, int give_log)
{
    double pr;
#ifdef IEEE_754
    if (ISNAN(x) || ISNAN(shape) || ISNAN(scale))
        return x + shape + scale;
#endif
    if (shape < 0 || scale <= 0) ML_ERR_return_NAN;
    if (x < 0)
	return R_D__0;
    if (shape == 0) /* point mass at 0 */
	return (x == 0)? ML_POSINF : R_D__0;
    if (x == 0) {
	if (shape < 1) return ML_POSINF;
	if (shape > 1) return R_D__0;
	/* else */
	return give_log ? -log(scale) : 1 / scale;
    }

    if (shape < 1) {
	pr = dpois_raw(shape, x/scale, give_log);
	return (
	    give_log/* NB: currently *always*  shape/x > 0  if shape < 1:
		     * -- overflow to Inf happens, but underflow to 0 does NOT : */
	    ? pr + (R_FINITE(shape/x)
		    ? log(shape/x)
		    : /* shape/x overflows to +Inf */ log(shape) - log(x))
	    : pr*shape / x);
    }
    /* else  shape >= 1 */
    pr = dpois_raw(shape-1, x/scale, give_log);
    return give_log ? pr - log(scale) : pr/scale;
}