Module « scipy.special »

Fonction multigammaln - module scipy.special

Signature de la fonction multigammaln

def multigammaln(a, d) 

Description

multigammaln.__doc__

Returns the log of multivariate gamma, also sometimes called the
    generalized gamma.

    Parameters
    ----------
    a : ndarray
        The multivariate gamma is computed for each item of `a`.
    d : int
        The dimension of the space of integration.

    Returns
    -------
    res : ndarray
        The values of the log multivariate gamma at the given points `a`.

    Notes
    -----
    The formal definition of the multivariate gamma of dimension d for a real
    `a` is

    .. math::

        \Gamma_d(a) = \int_{A>0} e^{-tr(A)} |A|^{a - (d+1)/2} dA

    with the condition :math:`a > (d-1)/2`, and :math:`A > 0` being the set of
    all the positive definite matrices of dimension `d`.  Note that `a` is a
    scalar: the integrand only is multivariate, the argument is not (the
    function is defined over a subset of the real set).

    This can be proven to be equal to the much friendlier equation

    .. math::

        \Gamma_d(a) = \pi^{d(d-1)/4} \prod_{i=1}^{d} \Gamma(a - (i-1)/2).

    References
    ----------
    R. J. Muirhead, Aspects of multivariate statistical theory (Wiley Series in
    probability and mathematical statistics).