FAST-PT/gamma_funcs.py at master · Michalychforever/FAST-PT · GitHub

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''' 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) )

	# to higher order
	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) +1./1260*(1./asym_plus**5 - 1./asym_minus**5) )

	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