import math
import torch
# from .optimizer import Optimizer


class Nadam(torch.optim.Optimizer):
    '''
    Implements Nadam algorithm. (Modified Adam from PyTorch_)

    It has been proposed in `Incorporating Nesterov Momentum into Adam`_.

    Arguments:
        * ``params`` (iterable): iterable of parameters to optimize or dicts defining parameter groups.
        * ``lr`` (``float``, optional): learning rate (default: 1e-3).
        * ``betas`` (Tuple[``float``, ``float``], optional): coefficients used for computing
          running averages of gradient and its square (default: (0.9, 0.999)).
        * ``eps`` (``float``, optional): term added to the denominator to improve
          numerical stability (default: 1e-8). 
        * ``weight_decay`` (``float``, optional): weight decay (L2 penalty) (default: 0).
        * ``amsgrad`` (``boolean``, optional): whether to use the AMSGrad variant of this
          algorithm from the paper `On the Convergence of Adam and Beyond`_
          (default: False).
    
    .. _PyTorch:
        https://pytorch.org/docs/stable/_modules/torch/optim/adam.html#Adam
    .. _Incorporating Nesterov Momentum into Adam:
        https://openreview.net/pdf?id=OM0jvwB8jIp57ZJjtNEZ
    .. _On the Convergence of Adam and Beyond:
        https://openreview.net/forum?id=ryQu7f-RZ
    '''

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, amsgrad=False):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        if not 0.0 <= eps:
            raise ValueError("Invalid epsilon value: {}".format(eps))
        if not 0.0 <= betas[0] < 1.0:
            raise ValueError("Invalid beta parameter at index 0: {}".format(betas[0]))
        if not 0.0 <= betas[1] < 1.0:
            raise ValueError("Invalid beta parameter at index 1: {}".format(betas[1]))
        defaults = dict(lr=lr, betas=betas, eps=eps,
                        weight_decay=weight_decay, amsgrad=amsgrad)
        super(Nadam, self).__init__(params, defaults)

    def __setstate__(self, state):
        super(Nadam, self).__setstate__(state)
        for group in self.param_groups:
            group.setdefault('amsgrad', False)

    def step(self, closure=None):
        '''
        Performs a single optimization step.

        Arguments:
            * ``closure`` (callable, optional): A closure that reevaluates the model
                and returns the loss.
        '''
        loss = None
        if closure is not None:
            loss = closure()

        for group in self.param_groups:
            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                amsgrad = group['amsgrad']

                state = self.state[p]

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    # Exponential moving average of gradient values
                    state['exp_avg'] = torch.zeros_like(p.data)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p.data)
                    if amsgrad:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state['max_exp_avg_sq'] = torch.zeros_like(p.data)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                if amsgrad:
                    max_exp_avg_sq = state['max_exp_avg_sq']
                beta1, beta2 = group['betas']

                state['step'] += 1

                if group['weight_decay'] != 0:
                    grad.add_(group['weight_decay'], p.data)

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(1 - beta1, grad)
                exp_avg_sq.mul_(beta2).addcmul_(1 - beta2, grad, grad)
                if amsgrad:
                    # Maintains the maximum of all 2nd moment running avg. till now
                    torch.max(max_exp_avg_sq, exp_avg_sq, out=max_exp_avg_sq)
                    # Use the max. for normalizing running avg. of gradient
                    denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                else:
                    denom = exp_avg_sq.sqrt().add_(group['eps'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']
                step_size = group['lr'] * math.sqrt(bias_correction2) / bias_correction1


                # only change is here
                # p.data.addcdiv_(-step_size, exp_avg, denom)

                p.data.addcdiv_(-step_size, beta1 * exp_avg + (1-beta1) * grad, denom)

        return loss