| Server IP : 217.160.0.135 / Your IP : 216.73.217.25 Web Server : Apache System : Linux www 6.18.52-i1-ampere #1203 SMP Mon Sep 14 18:29:59 CEST 2026 aarch64 User : sws1074145052 ( 1074145052) PHP Version : 8.3.32 Disable Function : NONE MySQL : OFF | cURL : ON | WGET : ON | Perl : ON | Python : OFF | Sudo : OFF | Pkexec : OFF Directory : /usr/lib/python3/dist-packages/scipy/special/__pycache__/ |
Upload File : |
�
d�c� � �* � d Z ddlZddlmZ dgZd� ZdS )zVSome more special functions which may be useful for multivariate statistical
analysis.� N)�gammaln� multigammalnc �� � � t j � � � � t j |� � rt j |� � |k rt d� � �t j � d|dz
z k � � rt d� d|dz
z fz � � �||dz
z dz t j t j � � z }|t j t � fd�t d|dz � � D � � � � d�� � z
}|S ) 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).
Examples
--------
>>> import numpy as np
>>> from scipy.special import multigammaln, gammaln
>>> a = 23.5
>>> d = 10
>>> multigammaln(a, d)
454.1488605074416
Verify that the result agrees with the logarithm of the equation
shown above:
>>> d*(d-1)/4*np.log(np.pi) + gammaln(a - 0.5*np.arange(0, d)).sum()
454.1488605074416
z*d should be a positive integer (dimension)g �?� z+condition a (%f) > 0.5 * (d-1) (%f) not metg �?c �& �� g | ]
}�|d z
dz z
��S )g �?� � )�.0�j�as ��</usr/lib/python3/dist-packages/scipy/special/_spfun_stats.py�
<listcomp>z multigammaln.<locals>.<listcomp>j s% �� �B�B�B�q�1��B���z�>�B�B�B� r )�axis) �np�asarray�isscalar�floor�
ValueError�any�log�pi�sum�loggam�range)r �d�ress ` r
r r * s� �� �p �
�1�
�
�A�
�;�q�>�>� G�b�h�q�k�k�Q� .� .��E�F�F�F� �v�a�3�!�a�%�=� �!�!� -��F� �s�a��c�{�+�,� -� -� -�
��!��9�t� �r�v�b�e�}�}�
,�C��2�6�&�B�B�B�B�E�!�Q�q�S�M�M�B�B�B�C�C�!� L� L� L�L�C� �Jr )�__doc__�numpyr �
scipy.specialr r �__all__r r r r
�<module>r" sX ��@
�
� � � � � +� +� +� +� +� +� �
��A� A� A� A� Ar