<SYSTEM_TASK:>
Solve the following problem using Python, implementing the functions described below, one line at a time
<END_TASK>
<USER_TASK:>
Description:
 def check_treedepth(fit, verbose=True, per_chain=False):
 """Check for transitions that ended prematurely due to maximum tree depth limit Parameters fit : StanFit4Model object verbose : bool or int, optional If ``verbose`` is ``False`` or a nonpositive integer, no diagnostic messages are printed, and only the return value of the function conveys diagnostic information. If it is ``True`` (the default) or an integer greater than zero, then a diagnostic message is printed only if there are transitions that ended ended prematurely due to maximum tree depth limit. If it is an integer greater than 2, then extra diagnostic messages are printed. per_chain : bool, optional Print the number of prematurely ending transitions in each chain Returns ------- bool ``True`` if there are no problems with tree depth and ``False`` otherwise. Raises ------ ValueError If ``fit`` has no information about tree depth. This could happen if ``fit`` was generated from a sampler other than NUTS. """


    verbosity = int(verbose)

    sampler_params = fit.get_sampler_params(inc_warmup=False)

    try:
        depths = np.column_stack([y['treedepth__'].astype(int) for y in sampler_params])
    except:
        raise ValueError('Cannot access tree depth information from fit object')

    try:
        max_treedepth = int(fit.stan_args[0]['ctrl']['sampling']['max_treedepth'])
    except:
        raise ValueError('Cannot obtain value of max_treedepth from fit object')

    n_for_chains =  (depths >= max_treedepth).sum(axis=0)

    n = n_for_chains.sum()

    if n > 0:
        if verbosity > 0:
            N = depths.size
            logger.warning(('{} of {} iterations saturated the maximum tree depth of {}'
                                + ' ({:.3g} %)').format(n, N, max_treedepth, 100 * n / N))

            if per_chain:
                chain_len, num_chains = depths.shape

                for chain_num in range(num_chains):
                    if n_for_chains[chain_num] > 0:
                        logger.warning('Chain {}: {} of {} saturated '.format(chain_num + 1,
                                                                              n_for_chains[chain_num],
                                                                              chain_len) +
                                       'the maximum tree depth of {} ({:.3g} %).'.format(max_treedepth,
                                                                                    100 * n_for_chains[chain_num] /
                                                                                    chain_len))

            logger.warning('Run again with max_treedepth larger than {}'.format(max_treedepth) +
                           ' to avoid saturation')

        return False
    else:
        if verbosity > 2:
            logger.info('No transitions that ended prematurely due to maximum tree depth limit')

        return True