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File Content: `spfun_stats.cpython-35.pyc`



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������������������@���sW���d��Z��d�d�l�m�Z�m�Z�m�Z�d�d�l�Z�d�d�l�m�Z	�d�g�Z
�d�d����Z�d�S)zVSome more special functions which may be useful for multivariate statistical
analysis.�����)�division�print_function�absolute_importN)�gammaln�multigammalnc����������������s����t��j���������t��j�|���s4�t��j�|���|�k�r@�t�d�����t��j����d�|�d�k���r{�t�d����d�|�d�f�����|�|�d�d�t��j�t��j���}�|�t��j�t	����f�d�d����t
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a���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).

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Name	Size	Permission
__init__.cpython-35.opt-1.pyc	23337 bytes	0644
__init__.cpython-35.pyc	23337 bytes	0644
_ellip_harm.cpython-35.opt-1.pyc	5949 bytes	0644
_ellip_harm.cpython-35.pyc	5949 bytes	0644
_mptestutils.cpython-35.opt-1.pyc	13427 bytes	0644
_mptestutils.cpython-35.pyc	13427 bytes	0644
_spherical_bessel.cpython-35.opt-1.pyc	5467 bytes	0644
_spherical_bessel.cpython-35.pyc	5467 bytes	0644
_testutils.cpython-35.opt-1.pyc	10670 bytes	0644
_testutils.cpython-35.pyc	10670 bytes	0644
add_newdocs.cpython-35.opt-1.pyc	132479 bytes	0644
add_newdocs.cpython-35.pyc	132479 bytes	0644
basic.cpython-35.opt-1.pyc	72955 bytes	0644
basic.cpython-35.pyc	72955 bytes	0644
generate_ufuncs.cpython-35.opt-1.pyc	41799 bytes	0644
generate_ufuncs.cpython-35.pyc	41799 bytes	0644
lambertw.cpython-35.opt-1.pyc	3191 bytes	0644
lambertw.cpython-35.pyc	3191 bytes	0644
orthogonal.cpython-35.opt-1.pyc	54319 bytes	0644
orthogonal.cpython-35.pyc	54319 bytes	0644
setup.cpython-35.opt-1.pyc	3206 bytes	0644
setup.cpython-35.pyc	3206 bytes	0644
spfun_stats.cpython-35.opt-1.pyc	2299 bytes	0644
spfun_stats.cpython-35.pyc	2299 bytes	0644

File Content: spfun_stats.cpython-35.pyc

File Content: `spfun_stats.cpython-35.pyc`