[SciPy-dev] Definition of gammaln(x) for negative x

[G-J van Rooyen]

Hey everyone

Ticket #737 refers:

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Gamma in negative for negative x whose floor value is odd. As such,
gammaln does not make sense for those values (while staying in the
real domain, at least). scipy.special.gammaln returns bogus values:

import numpy as np
from scipy.special import gamma, gammaln
print np.log(gamma(-0.5))
print gammaln(-0.5)

Returns nan in the first case (expected) and 1.26551212348 in the
second (totally meaningless value).

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The info line for gammaln reads:
*  gammaln      -- Log of the absolute value of the gamma function.

With this definition of gammaln, the function actually works fine,
since np.log(abs(gamma(-0.5))) is in fact 1.2655. However, this seems
to be an unusual definition for gammaln. What is the best way to fix
it? Options:

1) Keep it as it is, with gammaln(x) = ln|gamma(x)|
2) Change it so that it returns NaN for negative values of gamma(x)
(i.e. negative x whose floor value is odd)
3) Change it to always give NaN for negative values of x (Matlab's approach)
4) Have it return complex values for negative logarithms

Which is best?

G-J