def make_invcovmatrix(sigma_x, sigma_y, rho=0):
    """ create inverse covariance matrix from given standard deviations and normalised correlation rho, vectorized """
    F = 1.0 / (sigma_x ** 2 * sigma_y ** 2 * (1 - rho ** 2))
    return (F * sigma_y ** 2, F * -rho * sigma_x * sigma_y), (F * -rho *
        sigma_x * sigma_y, F * sigma_x ** 2)
