Lanczos approximation: Difference between revisions

Revision as of 15:48, 28 March 2017

Revision as of 20:17, 4 April 2017

Line 50:

<source lang="python">

from cmath import sin, sqrt, pi, exp

def gamma(z):

epsilon = 0.0000001

def withinepsilon(x):

return abs(x) <= epsilon

p = [676.5203681218851

from cmath import sin,sqrt,pi,exp

,-1259.1392167224028

,771.32342877765313

,-176.61502916214059

,12.507343278686905

,-0.13857109526572012

,9.9843695780195716e-6, 1.5056327351493116e-7]

,1.5056327351493116e-7

]

EPSILON = 1e-07

p = [ 676.5203681218851, -1259.1392167224028, 771.32342877765313,

def drop_imag(z):

-176.61502916214059, 12.507343278686905, -0.13857109526572012,

if abs(z.imag) <= EPSILON:

9.9843695780195716e-6, 1.5056327351493116e-7]

returnz result= z.real

return resultz

def gamma(z):

z = complex(z)

# Reflection formula (edit: this use of reflection (thus the if-else structure) seems unnecessary and just adds more code to execute. it calls itself again, so it still needs to execute the same "for" loop yet has an extra calculation at the end)

if z.real < 0.5:

resulty = pi / (sin(pi*z) * gamma(1-z)) ### Reflection formula

else:

z -= 1

x = 0.99999999999980993

for (i, pval) in enumerate(p):

x += pval / (z+i+1)

t = z + len(p) - 0.5

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

return drop_imag(y)

"""

if withinepsilon(result.imag):

The above use of the reflection (thus the if-else structure) seems unnecessary

return result.real

and just adds more code to execute. It calls itself again, so it still needs

return result

to execute the same "for" loop yet has an extra calculation at the end)

"""

print gamma(1)

print gamma(5)

print gamma(0.5)

</source>