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Module « scipy.special »

Fonction loggamma - module scipy.special

Signature de la fonction loggamma

def loggamma(*args, **kwargs) 

Description

help(scipy.special.loggamma)

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


    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 plane at which to compute ``loggamma``
    out : ndarray, optional
        Output array for computed values of ``loggamma``

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

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

    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]_.

    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.
    

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