DBL chdtri(DBL df, DBL y)
{
DBL x;
if ((y < 0.0) || (y > 1.0) || (df < 1.0))
throw POV_EXCEPTION_STRING("Illegal values in chdtri().");
x = igami(0.5 * df, y);
return (2.0 * x);
}
double chdtri (double df, double y)
{
double x;
if (y < 0.0 || y > 1.0 || df < 1.0) {
mtherr("chdtri", CEPHES_DOMAIN);
return 0.0;
}
x = igami(0.5 * df, y);
return 2.0 * x;
}
double pdtri( int k, double y )
{
double v;
if( (k < 0) || (y < 0.0) || (y >= 1.0) )
{
mtherr( "pdtri", DOMAIN );
return( 0.0 );
}
v = k+1;
v = igami( v, y );
return( v );
}
double
gammaincinv(double a, double y)
{
double lo = 0.0, hi;
double flo = -y, fhi = 0.25 - y;
double params[2];
double best_x, best_f, errest;
fsolve_result_t r;
if (a <= 0.0 || y <= 0.0 || y >= 0.25) {
return igami(a, 1-y);
}
/* Note: flo and fhi must have different signs (and be != 0),
* otherwise fsolve terminates with an error.
*/
params[0] = a;
params[1] = y;
hi = igami(a, 0.75);
/* I found Newton to be unreliable. Also, after we generate a small
interval by bisection above, false position will do a large step
from an interval of width ~1e-4 to ~1e-14 in one step (a=10, x=0.05,
but similiar for other values).
*/
r = false_position(&lo, &flo, &hi, &fhi,
(objective_function)gammainc, params,
2*MACHEP, 2*MACHEP, 1e-2*a,
&best_x, &best_f, &errest);
if (!(r == FSOLVE_CONVERGED || r == FSOLVE_EXACT) &&
errest > ALLOWED_ATOL + ALLOWED_RTOL*fabs(best_x)) {
best_x = GAMMAINCINV_NaN;
}
return best_x;
}
double igamci(double a, double q)
{
int i;
double x, fac, f_fp, fpp_fp;
if (npy_isnan(a) || npy_isnan(q)) {
return NPY_NAN;
}
else if ((a < 0.0) || (q < 0.0) || (q > 1.0)) {
mtherr("gammainccinv", DOMAIN);
}
else if (q == 0.0) {
return NPY_INFINITY;
}
else if (q == 1.0) {
return 0.0;
}
else if (q > 0.9) {
return igami(a, 1 - q);
}
x = find_inverse_gamma(a, 1 - q, q);
for (i = 0; i < 3; i++) {
fac = igam_fac(a, x);
if (fac == 0.0) {
return x;
}
f_fp = (igamc(a, x) - q) * x / (-fac);
fpp_fp = -1.0 + (a - 1) / x;
if (npy_isinf(fpp_fp)) {
x = x - f_fp;
}
else {
x = x - f_fp / (1.0 - 0.5 * f_fp * fpp_fp);
}
}
return x;
}
