logmvnpdf.m

function [logp] = logmvnpdf(x,mu,Sigma)
% outputs log likelihood array for observations x  where x_n ~ N(mu,Sigma)
% x is NxD, mu is 1xD, Sigma is DxD
% obtained from:
% http://uk.mathworks.com/matlabcentral/fileexchange/34064-log-multivariate-normal-distribution-function

[N,D] = size(x);
const = -0.5 * D * log(2*pi);

xc = bsxfun(@minus,x,mu);

term1 = -0.5 * sum((xc / Sigma) .* xc, 2); % N x 1
term2 = const - 0.5 * logdet(Sigma);    % scalar
logp = term1' + term2;

end

function y = logdet(A)

U = chol(A);
y = 2*sum(log(diag(U)));

end

% Copyright (c) 2011, Benjamin Dichter
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