function y = fn_mtpdf(x,xm,C,v,covIx,constIx)
% y = mtpdf(x,xm,C,v,covIx,constIx)
%    The pdf value for multivariate Student t distribution allowing many values (draws) stored in columns.
%
% 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'.  That is, C=chol(S)' (notice the transpose ' here).
% v (>0):  A scalar value for the degrees of freedom.
% covIx: An index for a decomposition of the covariance matrix.  If 1, C=chol(S)' (notice the transpose ');
%               if 0, C=chol(inv(S)) (note that there is no transpose here).
% constIx:  An 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.
%
% Tao Zha, December 1998; Revised, January 2002.

[p,nx]=size(x);
if covIx
   z = C\(x-xm);
else
   z = C*(x-xm);
end


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