igami

Inverse of complemented incomplete gamma integral.

SYNOPSIS:

double a, x, p, igami();
x = igami(a, p);

DESCRIPTION:

Given p, the function finds x such that

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