view release on metacpan or  search on metacpan

libmd/igami.c  view on Meta::CPAN

/*							igami()
 *
 *      Inverse of complemented imcomplete md_gamma integral
 *
 *
 *
 * SYNOPSIS:
 *
 * double a, x, p, igami();
 *
 * x = igami( a, p );
 *
 * DESCRIPTION:
 *
 * Given p, the function finds x such that
 *
 * It is valid in the right-hand-tail of the distribution, p < 0.5.
 *  igamc( a, x ) = p.
 *
 * Starting with the approximate value
 *
 *         3
 *  x = a t
 *
 *  where
 *
 *  t = 1 - d - ndtri(p) sqrt(d)
 * 
 * and
 *
 *  d = 1/9a,
 *
 * the routine performs up to 10 Newton iterations to find the
 * root of igamc(a,x) - p = 0.
 *
 * ACCURACY:
 *
 * Tested at random a, p in the intervals indicated.
 *
 *                a        p                      Relative error:
 * arithmetic   domain   domain     # trials      peak         rms
 *    IEEE     0.5,100   0,0.5       100000       1.0e-14     1.7e-15
 *    IEEE     0.01,0.5  0,0.5       100000       9.0e-14     3.4e-15
 *    IEEE    0.5,10000  0,0.5        20000       2.3e-13     3.8e-14
 */

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1987, 1995, 2000 by Stephen L. Moshier
*/

#include "mconf.h"

extern double MACHEP, MAXNUM, MAXLOG, MINLOG;
#ifdef ANSIPROT
extern double igamc ( double, double );
extern double ndtri ( double );
extern double md_exp ( double );
extern double md_fabs ( double );
extern double md_log ( double );
extern double sqrt ( double );
extern double lgam ( double );
#else
double igamc(), ndtri(), md_exp(), md_fabs(), md_log(), sqrt(), lgam();
#endif

double igami( a, md_y0 )
double a, md_y0;
{
double x0, x1, x, yl, yh, y, d, lgm, dithresh;
int i, dir;

if( md_y0 > 0.5)
    mtherr( "igami", PLOSS);

/* bound the solution */
x0 = MAXNUM;
yl = 0;
x1 = 0;
yh = 1.0;
dithresh = 5.0 * MACHEP;

/* approximation to inverse function */
d = 1.0/(9.0*a);
y = ( 1.0 - d - ndtri(md_y0) * sqrt(d) );
x = a * y * y * y;

lgm = lgam(a);

for( i=0; i<10; i++ )
	{
	if( x > x0 || x < x1 )
		goto ihalve;