Lanczos approximation: Difference between revisions

Revision as of 14:22, 5 May 2014

Revision as of 05:51, 27 February 2015

Line 55:

<source lang="python">

def gamma(z): # great function from Wiki, but maybe could use memoization?

from cmath import *

epsilon = 0.0000001

def withinepsilon(x):

return abs(x - abs(x)) <= epsilon

from cmath import *sin,sqrt,pi,exp

# Coefficients used by the GNU Scientific Library

g = 7

p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028,

771.32342877765313, -176.61502916214059, 12.507343278686905,

-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7]

p = [0.99999999999980993, 676.5203681218851, -1259.1392167224028, 771.32342877765313,

def gamma(z):

771.32342877765313, -176.61502916214059, 12.507343278686905, -0.13857109526572012,

z = complex(z)

-0.13857109526572012, 9.9843695780195716e-6, 1.5056327351493116e-7]

# Reflection formula

if z.real <= 0.5:complex(z)

return pi / (sin(pi*z) * gamma(1-z))

# Reflection formula

else:

if z.real -=< 10.5:

x result = p[0]pi / (sin(pi*z) * gamma(1-z))

for i in range(1, g+2)else:

xz +-= p[i]/(z+i)1

t = z + gx += 0.599999999999980993

return sqrt(2*pi) * t**(z+0.5) * exp(-t) * x

for i,_ in enumerate(p):

x += p[i]/(z+i+1)

t = z + len(p) - 0.5

return result = sqrt(2*pi) * t**(z+0.5) * exp(-t) * x

if withinepsilon(result.imag):

return result.real

return result

</source>