trajectory.py 文件源码

def temporal_derived_power_series(z, C, up_to_order, series_termination_index, spatial_der_order=0):
    """
    compute the temporal derivatives
    q^{(n)}(z) = \sum_{k=0}^{series_termination_index} C[k][n,:] z^k / k!
    from n=0 to n=up_to_order
    :param z: scalar
    :param C:
    :param up_to_order:
    :param series_termination_index:
    :param spatial_der_order:
    :return: Q = np.array( [q^{(0)}, ... , q^{(up_to_order)}] )
    """

    if not isinstance(z, Number):
        raise TypeError
    if any([C[i].shape[0] - 1 < up_to_order for i in range(series_termination_index+1)]):
        raise ValueError

    len_t = C[0].shape[1]
    Q = np.nan*np.zeros((up_to_order+1, len_t))

    for i in range(up_to_order+1):
        sum_Q = np.zeros(len_t)
        for j in range(series_termination_index+1-spatial_der_order):
            sum_Q += C[j+spatial_der_order][i, :]*z**(j)/sm.factorial(j)
        Q[i, :] = sum_Q

    return Q