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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 _pre_train(self, stop_param_updates, num_epochs, updates_epoch):
 """Set parameters and constants before training."""

        # Calculate the total number of updates given early stopping.
        updates = {k: stop_param_updates.get(k, num_epochs) * updates_epoch
                   for k, v in self.params.items()}

        # Calculate the value of a single step given the number of allowed
        # updates.
        single_steps = {k: np.exp(-((1.0 - (1.0 / v)))
                        * self.params[k]['factor'])
                        for k, v in updates.items()}

        # Calculate the factor given the true factor and the value of a
        # single step.
        constants = {k: np.exp(-self.params[k]['factor']) / v
                     for k, v in single_steps.items()}

        return constants