#' Generate a sample of (X,Y) of size n
#' @param covX covariance for covariates (of size p*p*K)
#' @param covY covariance for the response vector (of size m*m*K)
#' @param pi	 proportion for each cluster
#' @param beta regression matrix
#' @param n		sample size
#' 
#' @return list with X and Y
#' @export
#-----------------------------------------------------------------------
generateIO = function(covX, covY, pi, beta, n)
{
	p = dim(covX)[1]

	m = dim(covY)[1]
	k = dim(covY)[3]

	Y = matrix(0,n,m)
	require(mvtnorm)
	X = rmvnorm(n, mean = rep(0,p), sigma = covX)

	require(MASS) #simulate from a multivariate normal distribution
	for (i in 1:n)
	{
		
		for (r in 1:k)
		{
			BXir = rep(0,m)
			for (mm in 1:m)
				BXir[mm] = X[i,] %*% beta[,mm,r]
			Y[i,] = Y[i,] + pi[r] * mvrnorm(1,BXir, covY[,,r])
		}
	}

	return (list(X=X,Y=Y))
}