# publicscipy/scipy

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 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 #! /usr/bin/env python# Last Change: Sat Mar 21 02:00 PM 2009 J# Copyright (c) 2001, 2002 Enthought, Inc.## All rights reserved.## Redistribution and use in source and binary forms, with or without# modification, are permitted provided that the following conditions are met:## a. Redistributions of source code must retain the above copyright notice,# this list of conditions and the following disclaimer.# b. Redistributions in binary form must reproduce the above copyright# notice, this list of conditions and the following disclaimer in the# documentation and/or other materials provided with the distribution.# c. Neither the name of the Enthought nor the names of its contributors# may be used to endorse or promote products derived from this software# without specific prior written permission.### THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"# AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE# IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE# ARE DISCLAIMED. IN NO EVENT SHALL THE REGENTS OR CONTRIBUTORS BE LIABLE FOR# ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL# DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR# SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY# OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH# DAMAGE."""Some more special functions which may be useful for multivariate statisticalanalysis."""import numpy as npfrom scipy.special import gammaln as loggam__all__ = ['multigammln']def multigammaln(a, d):    """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:: \Gamma_d(a) = \int_{A>0}{e^{-tr(A)\cdot{|A|}^{a - (m+1)/2}dA}} with the condition a > (d-1)/2, and A>0 being the set of all the positive definite matrices of dimension s. 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:: \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). """    a = np.asarray(a)    if not np.isscalar(d) or (np.floor(d) != d):        raise ValueError("d should be a positive integer (dimension)")    if np.any(a <= 0.5 * (d - 1)):        raise ValueError("condition a (%f) > 0.5 * (d-1) (%f) not met" \                         % (a, 0.5 * (d-1)))    res = (d * (d-1) * 0.25) * np.log(np.pi)    if a.size == 1:        axis = -1    else:        axis = 0    res += np.sum(loggam([(a - (j - 1.)/2) for j in range(1, d+1)]), axis)    return res
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