function p = gaussian_prob(x, m, C, use_log)% GAUSSIAN_PROB Evaluate a multivariate Gaussian density.% p = gaussian_prob(X, m, C, use_log)%% p(i) = N(X(:,i), m, C) if use_log = 0 (default)% p(i) = log N(X(:,i), m, C) if use_log = 1. This prevents underflow.%% If X has size dxN, then p has size Nx1, where N = number of examplesif nargin < 4, use_log = 0; endif length(m)==1 % scalar  x = x(:)';end[d N] = size(x);%assert(length(m)==d); % slowm = m(:);M = m*ones(1,N); % replicate the mean across columnsdenom = (2*pi)^(d/2)*sqrt(abs(det(C)));mahal = sum(((x-M)'*inv(C)).*(x-M)',2);   % Chris Bregler's trickif any(mahal<0)  warning('mahal < 0 => C is not psd')endif use_log  p = -0.5*mahal - log(denom);else  p = exp(-0.5*mahal) / (denom+eps);end