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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 sample(self, model, num_samples, epsilon, lmin=1, lmax=1, thin=1, burn=0, session=None, initialize=True, anchor=True, logprobs=True):
 """ A straight-forward HMC implementation. The mass matrix is assumed to be the identity. The gpflow model must implement `build_objective` method to build `f` function (tensor) which in turn based on model's internal trainable parameters `x`. f(x) = E(x) we then generate samples from the distribution pi(x) = exp(-E(x))/Z The total number of iterations is given by: burn + thin * num_samples The leafrog (Verlet) integrator works by picking a random number of steps uniformly between lmin and lmax, and taking steps of length epsilon. :param model: gpflow model with `build_objective` method implementation. :param num_samples: number of samples to generate. :param epsilon: HMC tuning parameter - stepsize. :param lmin: HMC tuning parameter - lowest integer `a` of uniform `[a, b]` distribution used for drawing number of leapfrog iterations. :param lmax: HMC tuning parameter - largest integer `b` from uniform `[a, b]` distribution used for drawing number of leapfrog iterations. :param thin: an integer which specifies the thinning interval. :param burn: an integer which specifies how many initial samples to discard. :param session: TensorFlow session. The default session or cached GPflow session will be used if it is none. :param initialize: indication either TensorFlow initialization is required or not. :param anchor: dump live trainable values computed within specified TensorFlow session to actual parameters (in python scope). :param logprobs: indicates either logprob values shall be included in output or not. :return: data frame with `num_samples` traces, where columns are full names of trainable parameters except last column, which is `logprobs`. Trainable parameters are represented as constrained values in output. :raises: ValueError exception in case when wrong parameter ranges were passed. """


        if lmax <= 0 or lmin <= 0:
            raise ValueError('The lmin and lmax parameters must be greater zero.')
        if thin <= 0:
            raise ValueError('The thin parameter must be greater zero.')
        if burn < 0:
            raise ValueError('The burn parameter must be equal or greater zero.')

        lmax += 1
        session = model.enquire_session(session)

        model.initialize(session=session, force=initialize)

        with tf.name_scope('hmc'):
            params = list(model.trainable_parameters)
            xs = list(model.trainable_tensors)

            def logprob_grads():
                logprob = tf.negative(model.build_objective())
                grads = tf.gradients(logprob, xs)
                return logprob, grads

            thin_args = [logprob_grads, xs, thin, epsilon, lmin, lmax]

            if burn > 0:
                burn_op = _burning(burn, *thin_args)
                session.run(burn_op, feed_dict=model.feeds)

            xs_dtypes = _map(lambda x: x.dtype, xs)
            logprob_dtype = model.objective.dtype
            dtypes = _flat(xs_dtypes, [logprob_dtype])
            indices = np.arange(num_samples)

            def map_body(_):
                xs_sample, logprob_sample = _thinning(*thin_args)
                return _flat(xs_sample, [logprob_sample])

            hmc_output = tf.map_fn(map_body, indices, dtype=dtypes,
                                   back_prop=False, parallel_iterations=1)
            with tf.control_dependencies(hmc_output):
                unconstrained_trace, logprob_trace = hmc_output[:-1], hmc_output[-1]
                constrained_trace = _map(lambda x, param: param.transform.forward_tensor(x),
                                         unconstrained_trace, params)
                hmc_output = constrained_trace + [logprob_trace]

        names = [param.pathname for param in params]
        raw_traces = session.run(hmc_output, feed_dict=model.feeds)

        if anchor:
            model.anchor(session)

        traces = dict(zip(names, map(list, raw_traces[:-1])))
        if logprobs:
            traces.update({'logprobs': raw_traces[-1]})
        return pd.DataFrame(traces)