Module « scipy.special »

Fonction loggamma - module scipy.special

Signature de la fonction loggamma

Description

loggamma.__doc__

loggamma(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

loggamma(z, out=None)

Principal branch of the logarithm of the gamma function.

Defined to be :math:`\log(\Gamma(x))` for :math:`x > 0` and
extended to the complex plane by analytic continuation. The
function has a single branch cut on the negative real axis.

.. versionadded:: 0.18.0

Parameters
----------
z : array-like
    Values in the complex plain at which to compute ``loggamma``
out : ndarray, optional
    Output array for computed values of ``loggamma``

Returns
-------
loggamma : ndarray
    Values of ``loggamma`` at z.

Notes
-----
It is not generally true that :math:`\log\Gamma(z) =
\log(\Gamma(z))`, though the real parts of the functions do
agree. The benefit of not defining `loggamma` as
:math:`\log(\Gamma(z))` is that the latter function has a
complicated branch cut structure whereas `loggamma` is analytic
except for on the negative real axis.

The identities

.. math::
  \exp(\log\Gamma(z)) &= \Gamma(z) \\
  \log\Gamma(z + 1) &= \log(z) + \log\Gamma(z)

make `loggamma` useful for working in complex logspace.

On the real line `loggamma` is related to `gammaln` via
``exp(loggamma(x + 0j)) = gammasgn(x)*exp(gammaln(x))``, up to
rounding error.

The implementation here is based on [hare1997]_.

See also
--------
gammaln : logarithm of the absolute value of the gamma function
gammasgn : sign of the gamma function

References
----------
.. [hare1997] D.E.G. Hare,
  *Computing the Principal Branch of log-Gamma*,
  Journal of Algorithms, Volume 25, Issue 2, November 1997, pages 221-236.