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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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