Norta3

def fit_NORTA3(EX, CovX, d, F_invs=None, mc_samples=1E6, seed=0, output_flag=0, n_proc=4):
    """
    Computes covariance matrix for NORTA procedure in an exact, non data-driven context
    
    Args:
        EX: expected value of the d-dimensional vectors, assume
        CovX: covariance matrix of the d-dimensional vector
        d (int): dimension of the random vector.
        F_invs (list of func): optional parameter to specify the marginal
            distributions. Each function must support vector operations.
            Default is None, which constructs the marginals from the data.
        mc_samples(int): number of samples used in the Monte Carlo integration.
        seed (int): seed for the random generator in NORTA
        output_flag (int): 0 no output; 1 debug output
        n_proc (int): num of processor to parallelize norta
    Return:
        NORTA_GEN (NORTA): an object that stores the necessary information to
            generate NORTA random vectors.
    """
    global OUTPUT
    global MC_SAMPLES
    OUTPUT = output_flag
    MC_SAMPLES = mc_samples
    assert n_proc > 0, "Number of processors is positive and integer."
    
    if OUTPUT == 1:
        print("Starting NORTA fitting")
        print("Finding %i correlation terms" % (int(d * (d - 1) / 2)))
    C = None  # matrix for NORTA
    
    VarX = np.diag(np.diag(CovX))
    working_pool = mp.Pool(n_proc)
    D = np.eye(d)
    ij_pairs = [(i, j) for i in range(d) for j in range(i + 1, d)]
    mp_data = product(ij_pairs, [F_invs], [CovX], [EX])
    ij_rho_z = working_pool.map(find_rho_z, mp_data)
    for ix, (i, j) in enumerate(ij_pairs):
        D[i, j] = ij_rho_z[ix]
        D[j, i] = D[i, j]        
    # Finds the closest positive definte matrix to the one obtained by NORTA
    D2 = nearestPD(D)
    C = cholesky(D2, lower=True)
    working_pool.terminate()
    NORTA_GEN = NORTA(F_invs, C, seed)
    return NORTA_GEN