inline long double gamma_p(long double x, long double y)
{
#ifdef BOOST_MSVC
return igam((double)x, (double)y);
#else
return igaml(x, y);
#endif
}
double chdtr (double df, double x)
{
if (x < 0.0 || df < 1.0) {
mtherr("chdtr", CEPHES_DOMAIN);
return 0.0;
}
return igam(df/2.0, x/2.0);
}
double pdtrc( int k, double m )
{
double v;
if( (k < 0) || (m <= 0.0) )
{
mtherr( "pdtrc", DOMAIN );
return( 0.0 );
}
v = k+1;
return( igam( v, m ) );
}
double igami(double a, double p)
{
int i;
double x, fac, f_fp, fpp_fp;
if (npy_isnan(a) || npy_isnan(p)) {
return NPY_NAN;
}
else if ((a < 0) || (p < 0) || (p > 1)) {
mtherr("gammaincinv", DOMAIN);
}
else if (p == 0.0) {
return 0.0;
}
else if (p == 1.0) {
return NPY_INFINITY;
}
else if (p > 0.9) {
return igamci(a, 1 - p);
}
x = find_inverse_gamma(a, p, 1 - p);
/* Halley's method */
for (i = 0; i < 3; i++) {
fac = igam_fac(a, x);
if (fac == 0.0) {
return x;
}
f_fp = (igam(a, x) - p) * x / fac;
/* The ratio of the first and second derivatives simplifies */
fpp_fp = -1.0 + (a - 1) / x;
if (npy_isinf(fpp_fp)) {
/* Resort to Newton's method in the case of overflow */
x = x - f_fp;
}
else {
x = x - f_fp / (1.0 - 0.5 * f_fp * fpp_fp);
}
}
return x;
}
inline double gamma_p(double x, double y)
{ return igam(x, y); }
static DBL igamc(DBL a, DBL x)
{
DBL ans, c, yc, ax, y, z;
DBL pk, pkm1, pkm2, qk, qkm1, qkm2;
DBL r, t;
int sgngam = 0;
if ((x <= 0) || (a <= 0))
{
return (1.0);
}
if ((x < 1.0) || (x < a))
{
return (1.0 - igam(a, x));
}
ax = a * log(x) - x - lgam(a, &sgngam);
if (ax < -MAXLOG)
{
/*
mtherr("igamc", UNDERFLOW);
*/
return (0.0);
}
ax = exp(ax);
/* continued fraction */
y = 1.0 - a;
z = x + y + 1.0;
c = 0.0;
pkm2 = 1.0;
qkm2 = x;
pkm1 = x + 1.0;
qkm1 = z * x;
ans = pkm1 / qkm1;
do
{
c += 1.0;
y += 1.0;
z += 2.0;
yc = y * c;
pk = pkm1 * z - pkm2 * yc;
qk = qkm1 * z - qkm2 * yc;
if (qk != 0)
{
r = pk / qk;
t = fabs((ans - r) / r);
ans = r;
}
else
{
t = 1.0;
}
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if (fabs(pk) > BIG)
{
pkm2 /= BIG;
pkm1 /= BIG;
qkm2 /= BIG;
qkm1 /= BIG;
}
}
while (t > MACHEP);
return (ans * ax);
}
double igamc( double a, double x )
{
double ans, ax, c, yc, r, t, y, z;
double pk, pkm1, pkm2, qk, qkm1, qkm2;
if( (x <= 0) || ( a <= 0) )
return( 1.0 );
if( (x < 1.0) || (x < a) )
return( 1.0 - igam(a,x) );
ax = a * log(x) - x - lgam(a);
if( ax < -MAXLOG )
{
mtherr( "igamc", UNDERFLOW );
return( 0.0 );
}
ax = exp(ax);
/* continued fraction */
y = 1.0 - a;
z = x + y + 1.0;
c = 0.0;
pkm2 = 1.0;
qkm2 = x;
pkm1 = x + 1.0;
qkm1 = z * x;
ans = pkm1/qkm1;
do
{
c += 1.0;
y += 1.0;
z += 2.0;
yc = y * c;
pk = pkm1 * z - pkm2 * yc;
qk = qkm1 * z - qkm2 * yc;
if( qk != 0 )
{
r = pk/qk;
t = fabs( (ans - r)/r );
ans = r;
}
else
t = 1.0;
pkm2 = pkm1;
pkm1 = pk;
qkm2 = qkm1;
qkm1 = qk;
if( fabs(pk) > big )
{
pkm2 *= biginv;
pkm1 *= biginv;
qkm2 *= biginv;
qkm1 *= biginv;
}
}
while( t > MACHEP );
return( ans * ax );
}
static double
gammainc(double x, double params[2])
{
return /*cephes_*/igam(params[0], x) - params[1];
}
