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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, position, stepsize):
 """ Returns a sample using a single iteration of NUTS """


        # Re-sampling momentum
        momentum = np.random.normal(0, 1, len(position))

        # Initializations
        depth = 0
        position_backward, position_forward = position, position
        momentum_backward, momentum_forward = momentum, momentum
        candidate_set_size = accept_set_bool = 1
        _, log_pdf = self.grad_log_pdf(position, self.model).get_gradient_log_pdf()

        # Resample slice variable `u`
        slice_var = np.random.uniform(0, np.exp(log_pdf - 0.5 * np.dot(momentum, momentum)))

        while accept_set_bool == 1:
            direction = np.random.choice([-1, 1], p=[0.5, 0.5])
            if direction == -1:
                # Build a tree in backward direction
                (position_backward, momentum_backward, _, _, position_bar,
                 candidate_set_size2, accept_set_bool2) = self._build_tree(position_backward, momentum_backward,
                                                                           slice_var, direction, depth, stepsize)
            else:
                # Build tree in forward direction
                (_, _, position_forward, momentum_forward, position_bar,
                 candidate_set_size2, accept_set_bool2) = self._build_tree(position_forward, momentum_forward,
                                                                           slice_var, direction, depth, stepsize)
            if accept_set_bool2 == 1:
                if np.random.rand() < candidate_set_size2 / candidate_set_size:
                    position = position_bar.copy()

            accept_set_bool, candidate_set_size = self._update_acceptance_criteria(position_forward, position_backward,
                                                                                   momentum_forward, momentum_backward,
                                                                                   accept_set_bool2, candidate_set_size,
                                                                                   candidate_set_size2)
            depth += 1

        return position