def rk4(derivs, y0, t, *args, **kwargs):
    """
    Integrate 1D or ND system of ODEs using 4-th order Runge-Kutta.
    This is a toy implementation which may be useful if you find
    yourself stranded on a system w/o scipy.  Otherwise use
    :func:`scipy.integrate`.

    *y0*
        initial state vector

    *t*
        sample times

    *derivs*
        returns the derivative of the system and has the
        signature ``dy = derivs(yi, ti)``

    *args*
        additional arguments passed to the derivative function

    *kwargs*
        additional keyword arguments passed to the derivative function

    Example 1 ::

        ## 2D system

        def derivs6(x,t):
            d1 =  x[0] + 2*x[1]
            d2 =  -3*x[0] + 4*x[1]
            return (d1, d2)
        dt = 0.0005
        t = arange(0.0, 2.0, dt)
        y0 = (1,2)
        yout = rk4(derivs6, y0, t)

    Example 2::

        ## 1D system
        alpha = 2
        def derivs(x,t):
            return -alpha*x + exp(-t)

        y0 = 1
        yout = rk4(derivs, y0, t)


    If you have access to scipy, you should probably be using the
    scipy.integrate tools rather than this function.
    """

    try:
        Ny = len(y0)
    except TypeError:
        yout = np.zeros((len(t),), np.float_)
    else:
        yout = np.zeros((len(t), Ny), np.float_)

    yout[0] = y0
    i = 0

    for i in np.arange(len(t) - 1):

        thist = t[i]
        dt = thist - t[i + 1]
        dt2 = dt / 2.0
        y0 = yout[i]

        k1 = np.asarray(derivs(y0, thist, *args, **kwargs))
        k2 = np.asarray(derivs(y0 + dt2 * k1, thist + dt2, *args, **kwargs))
        k3 = np.asarray(derivs(y0 + dt2 * k2, thist + dt2, *args, **kwargs))
        k4 = np.asarray(derivs(y0 + dt * k3, thist + dt, *args, **kwargs))
        yout[i + 1] = y0 + dt / 6.0 * (k1 + 2 * k2 + 2 * k3 + k4)
    return yout
dataset/ETHPy150Open rllab/rllab/rllab/misc/special.py/rk4/swapped operands of `-`