def _do_step(x, y, z, tau, kappa, d_x, d_y, d_z, d_tau, d_kappa, alpha):
    """
    An implementation of [1] Equation 8.9

    References
    ----------
    .. [1] Andersen, Erling D., and Knud D. Andersen. "The MOSEK interior point
           optimizer for linear programming: an implementation of the
           homogeneous algorithm." High performance optimization. Springer US,
           2000. 197-232.

    """
    x = x + alpha * d_x
    tau = tau + alpha * d_tau
    z = z + alpha * d_z
    kappa = kappa + alpha * d_kappa
    y = y + alpha * d_y
    return x, y, z, tau, kappa