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Solve the following problem using Python, implementing the functions described below, one line at a time
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Description:
 def minimal_rotation(R, t, iterations=2):
 """Adjust frame so that there is no rotation about z' axis The output of this function is a frame that rotates the z axis onto the same z' axis as the input frame, but with minimal rotation about that axis. This is done by pre-composing the input rotation with a rotation about the z axis through an angle gamma, where dgamma/dt = 2*(dR/dt * z * R.conjugate()).w This ensures that the angular velocity has no component along the z' axis. Note that this condition becomes easier to impose the closer the input rotation is to a minimally rotating frame, which means that repeated application of this function improves its accuracy. By default, this function is iterated twice, though a few more iterations may be called for. Parameters ========== R: quaternion array Time series describing rotation t: float array Corresponding times at which R is measured iterations: int [defaults to 2] Repeat the minimization to refine the result """

    from scipy.interpolate import InterpolatedUnivariateSpline as spline
    if iterations == 0:
        return R
    R = quaternion.as_float_array(R)
    Rdot = np.empty_like(R)
    for i in range(4):
        Rdot[:, i] = spline(t, R[:, i]).derivative()(t)
    R = quaternion.from_float_array(R)
    Rdot = quaternion.from_float_array(Rdot)
    halfgammadot = quaternion.as_float_array(Rdot * quaternion.z * R.conjugate())[:, 0]
    halfgamma = spline(t, halfgammadot).antiderivative()(t)
    Rgamma = np.exp(quaternion.z * halfgamma)
    return minimal_rotation(R * Rgamma, t, iterations=iterations-1)