random mv gaussian

# 30D gaussian data set with the following properties:
# anisotropic (covariance not scaled identity)
# non-axis aligned (rotated)
# non-centered (translated)

n = 300                                                                                                                                            
d = 30                                                                                                                                             
                                                                                                                                                   
Sigma = eye(d)                                                                                                                                     
Sigma[1,1] = 20                                                                                                                                    
Sigma[10,10] = 25                                                                                                                                  
Sigma[11,11] = 15                                                                                                                                  
Sigma[19,19] = 10                                                                                                                                  
Sigma[20,20] = 30                                                                                                                                  
                                                                                                                                                   
Sigma_decomp = chol(Sigma)                                                                                                                         
                                                                                                                                                   
mu = ones(d,1)*10                                                                                                                                  
                                                                                                                                                   
X = (Sigma_decomp * randn(d,n))                                                                                                
                                                                                                                                                   
# random rotation:                                                                                                                                 
# since Q is an orthonormal matrix, it is a d-dimensional rotation matrix.                                                                         
Q,R = qr(randn(d,d))                                                                                                                               
                                                                                                                                                   
X = Q * X                                                                                                                                          

X = (mu * ones(1,n)) .+ X
                                                                                                                                              
X = X' # expecting n x d matrix