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function y = mtpdf(x,xm,C,v,constIx)
% y = mtpdf(x,xm,C,v)
% The pdf value for multivariate Student t distribution
%
% x: p-by-draws matrix of values evaluated at where p=size(x,1) is # of variables
% xm: p-by-draws matrix of the mean of x
% C: p-by-p Choleski square root of PDS S, which is the covariance matrix
% in the normal case so that S = C*C'
% v (>0): scaler -- the degrees of freedom
% constIx: index for the constant. 1: constant (normalized); 0: no constant (unnormalized)
%----------
% y: p-by-draws matrix of pdf's for multivariate Student t distribution with v degrees of freedom
%
% Christian P. Robert, "The Bayesian Choice," Springer-Verlag, New York, 1994,
% p. 382.
%
% December 1998 by Tao Zha
%
% Copyright (C) 1997-2012 Tao Zha
%
% This free software: you can redistribute it and/or modify
% it under the terms of the GNU General Public License as published by
% the Free Software Foundation, either version 3 of the License, or
% (at your option) any later version.
%
% It is distributed in the hope that it will be useful,
% but WITHOUT ANY WARRANTY; without even the implied warranty of
% MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
% GNU General Public License for more details.
%
% If you did not received a copy of the GNU General Public License
% with this software, see <http://www.gnu.org/licenses/>.
%
[p,nx]=size(x);
z = C\(x-xm);
if constIx
dSh=sum(log(diag(C))); % (detSigma)^(1/2)
%* Use gammaln function to avoid overflows.
term = exp(gammaln((v + p) / 2) - gammaln(v/2) - dSh);
y = (term*(v*pi)^(-p/2)) * (1 + sum(z.*z,1)/v).^(-(v + p)/2);
y = y';
else
y = (1 + sum(z.*z,1)/v).^(-(v + p)/2);
y = y';
end
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