% [alpha, mu, sigma, ll ] = gmm(data, k, nres, sig, prevsing, maxstep, prec)
%
% INPUT:
%    data    : n by d data points (n points of dimensionality d).
%    k       : number of desired clusters.
%    nres    : number of random restarts. 
%    sig     : d*d matrix of 0's and 1's used to cancel unwanted elements
%              in sigma matrices (for forced decoupling).
%   prevsing : d*1 vector of minimal diagonal values allowed in sigmas. 
%   maxstep  : maximum number of allowed iteration in a single run.
%              100 is fine (mostly converges in 10-30, depending on prec)
%   prec     : required precision. 1e-3 is typically fine, after that it 
%              slows down at no extra accuracy gain. Corresponds roughly to 
%              number of significant digits.
%
% OUTPUT:
%    alpha : weights of components (k by 1).
%    mu    : mean for each component (k by d).
%    sigma : covariance matrix for each comp. (d by d by k).
%    ll    : best log-likelihood.
%
% NOTES:
%    This is a .mex file and is much faster than the counterpart .m file.
%    On some simple problems it was ~4 times faster than the (efficient) 
%    .m file. The program has hard-coded k-means and doesn't rely on any
%    outside functions. If convergence is not established in maxstep, it
%    returns the last available value. However, if k-means breaks its 
%    maximum number of iterations, it will produce an error (this will 
%    never, ever happen, but just in case...).
%
%                   by Igor Cadez 01/23/99