class NoamOpt:
    "Optim wrapper that implements rate."

    def __init__(self, model_size, factor, warmup, optimizer):
        self.optimizer = optimizer
        self._step = 0
        self.warmup = warmup
        self.factor = factor
        self.model_size = model_size
        self._rate = 0

    def step(self):
        "Update parameters and rate"
        self._step += 1
        rate = self.rate()
        for p in self.optimizer.param_groups:
            p['lr'] = rate
        self._rate = rate
        self.optimizer.step()

    def rate(self, step=None):
        "Implement `lrate` above"
        if step is None:
            step = self._step
        return self.factor * \
            (self.model_size ** (-0.5) *
             min(step ** (-0.5), step * self.warmup ** (-1.5)))

    def save_state_dict(self):
        return {
            'inner_optimizer_state_dict': self.optimizer.state_dict(),
            'step': self._step,
            'warmup': self.warmup,
            'factor': self.factor,
            'model_size': self.model_size,
            'rate': self._rate
        }

    def load_state_dict(self, state_dict):
        self._rate = state_dict['rate']
        self._step = state_dict['step']
        self.optimizer.load_state_dict(state_dict['inner_optimizer_state_dict'])