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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 map_query(self, init_iter=1000, later_iter=20, dual_threshold=0.0002, integrality_gap_threshold=0.0002, tighten_triplet=True, max_triplets=5, max_iterations=100, prolong=False):
 """ MAP query method using Max Product LP method. This returns the best assignment of the nodes in the form of a dictionary. Parameters init_iter: integer Number of maximum iterations that we want MPLP to run for the first time. later_iter: integer Number of maximum iterations that we want MPLP to run for later iterations dual_threshold: double This sets the minimum width between the dual objective decrements. If the decrement is lesser than the threshold, then that means we have stuck on a local minima. integrality_gap_threshold: double This sets the threshold for the integrality gap below which we say that the solution is satisfactory. tighten_triplet: bool set whether to use triplets as clusters or not. max_triplets: integer Set the maximum number of triplets that can be added at once. max_iterations: integer Maximum number of times we tighten the relaxation. Used only when tighten_triplet is set True. prolong: bool If set False: The moment we exhaust of all the triplets the tightening stops. If set True: The tightening will be performed max_iterations number of times irrespective of the triplets. Reference: Section 3.3: The Dual Algorithm; Tightening LP Relaxation for MAP using Message Passing (2008) By Sontag Et al. Examples -------- {'B': 0.93894, 'C': 1.121, 'A': 1.8323, 'F': 1.5093, 'D': 1.7765, 'E': 2.12239} """


        self.dual_threshold = dual_threshold
        self.integrality_gap_threshold = integrality_gap_threshold
        # Run MPLP initially for a maximum of init_iter times.
        self._run_mplp(init_iter)
        # If triplets are to be used for the tightening, we proceed as follows
        if tighten_triplet:
            self._tighten_triplet(max_iterations, later_iter, max_triplets, prolong)
        # Get the best result from the best assignment
        self.best_decoded_result = {factor.scope()[0]: factor.values[self.best_assignment[frozenset(factor.scope())]]
                                    for factor in self.model.factors if len(factor.scope()) == 1}
        return self.best_decoded_result