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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 get_umbrella_sampling_data( us_trajs, us_centers, us_force_constants, md_trajs=None, kT=None, width=None):
 r""" Wraps umbrella sampling data or a mix of umbrella sampling and and direct molecular dynamics. Parameters us_trajs : list of N arrays, each of shape (T_i, d) List of arrays, each having T_i rows, one for each time step, and d columns where d is the dimension in which umbrella sampling was applied. Often d=1, and thus us_trajs will be a list of 1d-arrays. us_centers : array-like of size N List or array of N center positions. Each position must be a d-dimensional vector. For 1d us_force_constants : float or array-like of float The force constants used in the umbrellas, unit-less (e.g. kT per length unit). If different force constants were used for different umbrellas, a list or array of N force constants can be given. For multidimensional umbrella sampling, the force matrix must be used. md_trajs : list of M arrays, each of shape (T_i, d), optional, default=None Unbiased molecular dynamics simulations. Format like umbrella_trajs. kT : float (optinal) Use this attribute if the supplied force constants are NOT unit-less. width : array-like of float, optional, default=None Specify periodicity for individual us_traj dimensions. Each positive entry will make the corresponding feature periodic and use the given value as width. None/zero values will be treated as non-periodic. Returns ------- ttrajs : list of N+M int arrays, each of shape (T_i,) are in at any time. btrajs : list of N+M float arrays, each of shape (T_i, K) The floats are the reduced bias energies for each thermodynamic state and configuration. umbrella_centers : float array of shape (K, d) The individual umbrella centers labelled accordingly to ttrajs. force_constants : float array of shape (K, d, d) The individual force matrices labelled accordingly to ttrajs. unbiased_state : int or None Index of the unbiased thermodynamic state (if present). """

    ttrajs, umbrella_centers, force_constants, unbiased_state = _get_umbrella_sampling_parameters(
        us_trajs, us_centers, us_force_constants, md_trajs=md_trajs, kT=kT)
    if md_trajs is None:
        md_trajs = []
    if width is None:
        width = _np.zeros(shape=(umbrella_centers.shape[1],), dtype=_np.float64)
    else:
        width = _np.asarray(
            map(lambda w: w if w is not None and w > 0.0 else 0.0, width),
            dtype=_np.float64)
    if width.shape[0] != umbrella_centers.shape[1]:
        raise ValueError('Unmatching number of width components.')
    btrajs = _get_umbrella_bias_sequences(
        us_trajs + md_trajs, umbrella_centers, force_constants, width)
    return ttrajs, btrajs, umbrella_centers, force_constants, unbiased_state