gamma_functions.py

#!/usr/bin/env python

from math import gamma,e

# Continued Fraction Computation
# 6.5.31 Handbook of Mathematical Functions, page 263
#    Recursive implementation
def upper_incomplete_gamma(a,x,d=0,iterations=100):
    if d == iterations:
        if ((d % 2) == 1):
            return 1.0 # end iterations
        else:
            m = d/2
            return x + (m-a)
    if d == 0:
        try:
            result = ((x**a) * (e**(-x)))/upper_incomplete_gamma(a,x,d=d+1)
        except OverflowError:
            result = 0.0
        return result
    elif ((d % 2) == 1):
        m = 1.0+((d-1.0)/2.0)
        return x+ ((m-a)/(upper_incomplete_gamma(a,x,d=d+1)))
    else:
        m = d/2
        return 1+(m/(upper_incomplete_gamma(a,x,d=d+1)))

# 6.5.31 Handbook of Mathematical Functions, page 263
#    Recursive implementation
def upper_incomplete_gamma2(a,x,d=0,iterations=100):
    if d == iterations:
        return 1.0 
    if d == 0:
        result = ((x**a) * (e**(-x)))/upper_incomplete_gamma2(a,x,d=d+1)
        return result
    else:
        m = (d*2)-1
        return (m-a)+x+ ((d*(a-d))/(upper_incomplete_gamma2(a,x,d=d+1)))

def lower_incomplete_gamma(a,x,d=0,iterations=100):
    if d == iterations:
        if ((d % 2) == 1):
            return 1.0 # end iterations
        else:
            m = d/2
            return x + (m-a)
    if d == 0:
        result = ((x**a) * (e**(-x)))/lower_incomplete_gamma(a,x,d=d+1)
        return result
    elif ((d % 2) == 1):
        m = d - 1
        n = (d-1.0)/2.0
        return a + m - (((a+n)*x)/lower_incomplete_gamma(a,x,d=d+1))
    else:
        m = d-1
        n = d/2.0
        return a+m+((n*x)/(lower_incomplete_gamma(a,x,d=d+1)))

def lower_incomplete_gamma2(a,x):
    return gamma(a)-upper_incomplete_gamma2(a,x)

def complimentary_incomplete_gamma(a,x):
    return 1.0-upper_incomplete_gamma(a,x)

# Scipy name mappings
def gammainc(a,x):
    return lower_incomplete_gamma(a,x)/gamma(a)

def gammaincc(a,x):
    return upper_incomplete_gamma(a,x)/gamma(a)