&]\c@`sTdZddlmZmZmZddlZddlmZ dgZ dZ dS(sVSome more special functions which may be useful for multivariate statistical analysis.i(tdivisiontprint_functiontabsolute_importN(tgammalnt multigammalncC`stj|}tj| s4tj||krCtdntj|d|dkrtd|d|dfn||ddtjtj}|tjt gt d|dD]}||dd^qdd 7}|S( sReturns 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). s*d should be a positive integer (dimension)g?is+condition a (%f) > 0.5 * (d-1) (%f) not metg?g?itaxisi( tnptasarraytisscalartfloort ValueErrortanytlogtpitsumtloggamtrange(tatdtrestj((s8lib/python2.7/site-packages/scipy/special/spfun_stats.pyR,s*%"K( t__doc__t __future__RRRtnumpyRt scipy.specialRRt__all__R(((s8lib/python2.7/site-packages/scipy/special/spfun_stats.pyt!s