wolffd@0: function p = gaussian_prob(x, m, C, use_log)
wolffd@0: % GAUSSIAN_PROB Evaluate a multivariate Gaussian density.
wolffd@0: % p = gaussian_prob(X, m, C)
wolffd@0: % p(i) = N(X(:,i), m, C) where C = covariance matrix and each COLUMN of x is a datavector
wolffd@0: 
wolffd@0: % p = gaussian_prob(X, m, C, 1) returns log N(X(:,i), m, C) (to prevents underflow).
wolffd@0: %
wolffd@0: % If X has size dxN, then p has size Nx1, where N = number of examples
wolffd@0: 
wolffd@0: if nargin < 4, use_log = 0; end
wolffd@0: 
wolffd@0: if length(m)==1 % scalar
wolffd@0:   x = x(:)';
wolffd@0: end
wolffd@0: [d N] = size(x);
wolffd@0: %assert(length(m)==d); % slow
wolffd@0: m = m(:);
wolffd@0: M = m*ones(1,N); % replicate the mean across columns
wolffd@0: denom = (2*pi)^(d/2)*sqrt(abs(det(C)));
wolffd@0: mahal = sum(((x-M)'*inv(C)).*(x-M)',2);   % Chris Bregler's trick
wolffd@0: if any(mahal<0)
wolffd@0:   warning('mahal < 0 => C is not psd')
wolffd@0: end
wolffd@0: if use_log
wolffd@0:   p = -0.5*mahal - log(denom);
wolffd@0: else
wolffd@0:   p = exp(-0.5*mahal) / (denom+eps);
wolffd@0: end