def cov_matrix(y1, y2):
    cov1 = np.cov(y1)
    cov2 = np.cov(y2)

    [L1, U1] = np.linalg.eig(cov1)
    [L2, U2] = np.linalg.eig(cov2)
    U1 = U1.real
    U2 = U2.real
    L1 = L1.real
    L1 = L1.real
    L1 = np.diag(L1)
    L2 = np.diag(L2)
    R1 = np.dot(U1, L1)
    R1 = np.dot(R1, U1.T)
    R2 = np.dot(U2, L2)
    R2 = np.dot(R2, U2.T)
    return R1, R2

def PDF(x, u, R):
    [col] = u.shape
    a = np.power(2*np.pi, col)
    b = np.linalg.det(R)
    den = np.dot(a, b)
    den = np.sqrt(den, 2)

    a = u - x
    b = np.power(R, -1)
    c = np.dot(a.T, b)
    esp = -np.dot(c, a)/2

    F = (exp(esp))/den

    return F