function [X] = cov2data(SigmaX, n, dist)
%cov2data Creates a data set from a covariance matrix.
%
% USE:
% [data] = cov2data(covX, n, dist)
%
% INPUTS:
% covX = the covariance matrix.
% n = sample size.
% dist = a string specifying the distribution from which data are crated.
%        See the help file on random.  Default is Normal (or Gaussian).
% 
% Output:
% data = realizations of variables with the specified distribution.
%
% As of 2/18/2002, only normal distribution is supported.

% Tomo Eguchi
% 18 February 2002

if nargin >= 2,
   dist = 'norm';
end

[nrS, ncS] = size(SigmaX);
numVar = nrS;

% spectral decomposition of SigmaX and order eigenvalues and eigenvectors:
[U, lambda] = eigOrder(SigmaX);
Y = zeros(n, numVar);          % initialize the Y matrix

% Y contains random variables with means 0 and variances = eigenvalues. 
for i = 1:numVar,
   Y(:, i) = random(dist, 0, sqrt(lambda(i,i)), n, 1);
end

% create X, i.e., observables according to the covariance matrix of X.
X = Y * U';