import math

import torch
from torch.optim.optimizer import Optimizer


class Nadam(Optimizer):
    """Implements Nadam algorithm (a variant of Adam based on Nesterov momentum).

    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: 2e-3)
        betas (Tuple[float, float], optional): coefficients used for computing
            running averages of gradient and its square
        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)
        schedule_decay (float, optional): momentum schedule decay (default: 4e-3)

    __ http://cs229.stanford.edu/proj2015/054_report.pdf
    __ http://www.cs.toronto.edu/~fritz/absps/momentum.pdf

        Originally taken from: https://github.com/pytorch/pytorch/pull/1408
        NOTE: Has potential issues but does work well on some problems.
    """

    def __init__(self, params, lr=2e-3, betas=(0.9, 0.999), eps=1e-8,
                 weight_decay=0, schedule_decay=4e-3):
        if not 0.0 <= lr:
            raise ValueError("Invalid learning rate: {}".format(lr))
        defaults = dict(
            lr=lr,
            betas=betas,
            eps=eps,
            weight_decay=weight_decay,
            schedule_decay=schedule_decay,
        )
        super(Nadam, self).__init__(params, defaults)

    @torch.no_grad()
    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:
            with torch.enable_grad():
                loss = closure()

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

                # State initialization
                if len(state) == 0:
                    state['step'] = 0
                    state['m_schedule'] = 1.
                    state['exp_avg'] = torch.zeros_like(p)
                    state['exp_avg_sq'] = torch.zeros_like(p)

                # Warming momentum schedule
                m_schedule = state['m_schedule']
                schedule_decay = group['schedule_decay']
                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                beta1, beta2 = group['betas']
                eps = group['eps']
                state['step'] += 1
                t = state['step']
                bias_correction2 = 1 - beta2 ** t

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

                momentum_cache_t = beta1 * (1. - 0.5 * (0.96 ** (t * schedule_decay)))
                momentum_cache_t_1 = beta1 * (1. - 0.5 * (0.96 ** ((t + 1) * schedule_decay)))
                m_schedule_new = m_schedule * momentum_cache_t
                m_schedule_next = m_schedule * momentum_cache_t * momentum_cache_t_1
                state['m_schedule'] = m_schedule_new

                # Decay the first and second moment running average coefficient
                exp_avg.mul_(beta1).add_(grad, alpha=1. - beta1)
                exp_avg_sq.mul_(beta2).addcmul_(grad, grad, value=1. - beta2)

                denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(eps)
                p.addcdiv_(grad, denom, value=-group['lr'] * (1. - momentum_cache_t) / (1. - m_schedule_new))
                p.addcdiv_(exp_avg, denom, value=-group['lr'] * momentum_cache_t_1 / (1. - m_schedule_next))

        return loss
