calculate pressure along a Hugoniot throug nonlinear equations
    presented in Jameison 1982

    :param rho: density in g/cm^3
    :param rho0: density at 1 bar in g/cm^3
    :param a: prefactor for nonlinear fit of Hugoniot data
    :param b: prefactor for nonlinear fit of Hugoniot data
    :param c: prefactor for nonlinear fit of Hugoniot data
    :return: pressure along Hugoniot in GPa

def hugoniot_p_nlin(rho, rho0, a, b, c):
    """
    calculate pressure along a Hugoniot throug nonlinear equations
    presented in Jameison 1982

    :param rho: density in g/cm^3
    :param rho0: density at 1 bar in g/cm^3
    :param a: prefactor for nonlinear fit of Hugoniot data
    :param b: prefactor for nonlinear fit of Hugoniot data
    :param c: prefactor for nonlinear fit of Hugoniot data
    :return: pressure along Hugoniot in GPa
    """
    eta = 1. - (rho0 / rho)
    Up = np.zeros_like(eta)
    if isuncertainties([rho, rho0, a, b, c]):
        Up[eta != 0.] = ((b * eta - 1.) + unp.sqrt(
            np.power((1. - b * eta), 2.) - 4. * np.power(eta, 2.) * a * c)) /\
            (-2. * eta * c)
    else:
        Up[eta != 0.] = ((b * eta - 1.) + np.sqrt(
            np.power((1. - b * eta), 2.) - 4. * np.power(eta, 2.) * a * c)) /\
            (-2. * eta * c)
    Us = a + Up * b + Up * Up * c
    Ph = rho0 * Up * Us
    return Ph