''' This is the file that we keep all our Gamma function routines in.
J.E. McEwen
'''
import numpy as np
from numpy import exp, pi, sin, cos, log, sqrt
from scipy.special import gamma
def log_gamma(z):
z=gamma(z)
w=log(z)
x=np.real(w)
y=np.imag(w)
return x,y
def g_m_vals(mu,q):
imag_q= np.imag(q)
g_m=np.zeros(q.size, dtype=complex)
cut =200
asym_q=q[np.absolute(imag_q) >cut]
asym_plus=(mu+1+asym_q)/2.
asym_minus=(mu+1-asym_q)/2.
q_good=q[ (np.absolute(imag_q) <=cut) & (q!=mu + 1 + 0.0j)]
alpha_plus=(mu+1+q_good)/2.
alpha_minus=(mu+1-q_good)/2.
g_m[(np.absolute(imag_q) <=cut) & (q!= mu + 1 + 0.0j)] =gamma(alpha_plus)/gamma(alpha_minus)
#g_m[np.absolute(imag_q)>cut] = exp( (asym_plus-0.5)*log(asym_plus) - (asym_minus-0.5)*log(asym_minus) - asym_q )
g_m[np.absolute(imag_q)>cut] = exp( (asym_plus-0.5)*log(asym_plus) - (asym_minus-0.5)*log(asym_minus) - asym_q \
+1./12 *(1./asym_plus - 1./asym_minus) +1./360.*(1./asym_minus**3 - 1./asym_plus**3) )
g_m[np.where(q==mu+1+0.0j)[0]] = 0.+0.0j
return g_m
def gamsn(z):
z=np.asarray(z, dtype=complex)
result=sqrt(pi) /2. * 2**z *g_m_vals(0.5, z-0.5)
return result