# scipy/scipy

### Subversion checkout URL

You can clone with HTTPS or Subversion.

Fetching contributors…

Cannot retrieve contributors at this time

98 lines (78 sloc) 3.553 kb
 #! /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 statistical analysis.""" from __future__ import division, print_function, absolute_import import numpy as np from scipy.special import gammaln as loggam __all__ = ['multigammaln'] 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
Something went wrong with that request. Please try again.