def rgamma(self, alpha, lam, lngamalpha=False, \
xmax=float('inf'), pmax=1.0, \
tolf=FOURMACHEPS, itmax=128):
"""
The gamma distribution
f = lam * exp(-lam*x) * (lam*x)**(alpha-1) / gamma(alpha)
The cdf is the integral = the incomplete gamma ratio.
x, lam, alpha >= 0
NB It is possible to provide the value of the natural logarithm of the
complete gamma function lngamma(alpha) as a pre-computed input (may be
computed using numlib.specfunc.lngamma) instead of the default "False",
a feature that will make rgamma 50 % faster!
tolf and itmax are the numerical control parameters of igamma
and cgamma.
"""
assert xmax >= 0.0, "xmax must be a non-negative float in rgamma!"
self._checkpmax(pmax, 'rgamma')
pmx = pmax
if xmax < float('inf'): \
pmx = min(pmax, cgamma(alpha, lam, xmax, lngamalpha, tolf, itmax))
p = pmx * self.runif01()
x = igamma(p, alpha, lam, lngamalpha, tolf, itmax)
return x
def _fifi2fid(x):
x = kept_within(0.0, x)
cdf = cgamma(alpha, lam, x, lngalpha, tolf, itmax)
pdf = dgamma(alpha, lam, x, lngalpha)
fi = cdf - prob
if pdf <= 0.0:
if fi == 0.0: fi2fid = 1.0
else: fi2fid = MAXFLOAT
else:
fi2fid = fi/pdf
return fi, fi2fid
