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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, initial_pos, num_samples, stepsize=None, return_type='dataframe'):
 """ Method to return samples using No U Turn Sampler Parameters initial_pos: A 1d array like object Vector representing values of parameter position, the starting state in markov chain. num_samples: int Number of samples to be generated stepsize: float , defaults to None The stepsize for proposing new values of position and momentum in simulate_dynamics If None, then will be choosen suitably return_type: string (dataframe | recarray) Return type for samples, either of 'dataframe' or 'recarray'. Defaults to 'dataframe' Returns ------- sampled: A pandas.DataFrame or a numpy.recarray object depending upon return_type argument Examples --------- x y z 0 1.000000 1.000000 1.000000 1 1.760756 0.271543 -0.613309 2 1.883387 0.990745 -0.611720 3 0.980812 0.340336 -0.916283 4 0.781338 0.647220 -0.948640 5 0.040308 -1.391406 0.412201 6 1.179549 -1.450552 1.105216 7 1.100320 -1.313926 1.207815 8 1.484520 -1.349247 0.768599 9 0.934942 -1.894589 0.471772 """

        initial_pos = _check_1d_array_object(initial_pos, 'initial_pos')
        _check_length_equal(initial_pos, self.model.variables, 'initial_pos', 'model.variables')

        if stepsize is None:
            stepsize = self._find_reasonable_stepsize(initial_pos)

        types = [(var_name, 'float') for var_name in self.model.variables]
        samples = np.zeros(num_samples, dtype=types).view(np.recarray)

        samples[0] = tuple(initial_pos)
        position_m = initial_pos

        for i in range(1, num_samples):
            # Genrating sample
            position_m = self._sample(position_m, stepsize)
            samples[i] = tuple(position_m)

        return _return_samples(return_type, samples)