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/* igamif()
*
* Inverse of complemented imcomplete gamma integral
*
*
*
* SYNOPSIS:
*
* float a, x, y, igamif();
*
* x = igamif( a, y );
*
*
*
* DESCRIPTION:
*
* Given y, the function finds x such that
*
* igamc( a, x ) = y.
*
* Starting with the approximate value
*
* 3
* x = a t
*
* where
*
* t = 1 - d - ndtri(y) sqrt(d)
*
* and
*
* d = 1/9a,
*
* the routine performs up to 10 Newton iterations to find the
* root of igamc(a,x) - y = 0.
*
*
* ACCURACY:
*
* Tested for a ranging from 0 to 100 and x from 0 to 1.
*
* Relative error:
* arithmetic domain # trials peak rms
* IEEE 0,100 5000 1.0e-5 1.5e-6
*
*/
/*
Cephes Math Library Release 2.2: July, 1992
Copyright 1984, 1987, 1992 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/
#include <math.h>
extern float MACHEPF, MAXLOGF;
#define fabsf(x) ( (x) < 0 ? -(x) : (x) )
#ifdef ANSIC
float igamcf(float, float);
float ndtrif(float), expf(float), logf(float), sqrtf(float), lgamf(float);
#else
float igamcf();
float ndtrif(), expf(), logf(), sqrtf(), lgamf();
#endif
float igamif( float aa, float yy0 )
{
float a, y0, d, y, x0, lgm;
int i;
a = aa;
y0 = yy0;
/* approximation to inverse function */
d = 1.0/(9.0*a);
y = ( 1.0 - d - ndtrif(y0) * sqrtf(d) );
x0 = a * y * y * y;
lgm = lgamf(a);
for( i=0; i<10; i++ )
{
if( x0 <= 0.0 )
{
mtherr( "igamif", UNDERFLOW );
return(0.0);
}
y = igamcf(a,x0);
/* compute the derivative of the function at this point */
d = (a - 1.0) * logf(x0) - x0 - lgm;
if( d < -MAXLOGF )
{
mtherr( "igamif", UNDERFLOW );
goto done;
}
d = -expf(d);
/* compute the step to the next approximation of x */
if( d == 0.0 )
goto done;
d = (y - y0)/d;
x0 = x0 - d;
if( i < 3 )
continue;
if( fabsf(d/x0) < (2.0 * MACHEPF) )
goto done;
}
done:
return( x0 );
}
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