import math
import torch
from torch.optim import Optimizer
__all__ = ['Adam']


def _default_c_hook_lr(g: dict, n: int) -> float:
    return g['lr']


def _default_c_hook_beta(g: dict, n: int) -> float:
    return g['betas'][0]

class GWDC (Optimizer):
    r"""Implements Adam algorithm.
        It has been proposed in `Adam: A Method for Stochastic Optimization`_.
        The implementation of the L2 penalty follows changes proposed in
        `Decoupled Weight Decay Regularization`_.
        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)
        .. _Adam\: A Method for Stochastic Optimization:
            https://arxiv.org/abs/1412.6980
        .. _Decoupled Weight Decay Regularization:
            https://arxiv.org/abs/1711.05101
        .. _On the Convergence of Adam and Beyond:
            https://openreview.net/forum?id=ryQu7f-RZ
        """

    def __init__(self, params, lr=1e-2, betas=(0.9, 0.999), eps=1e-8, weight_decay=0, amsgrad=False,
                 beta3=1e-4) -> None:
        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]))
        if not 0.0 <= weight_decay:
            raise ValueError ("Invalid weight_decay value: {}".format (weight_decay))
        if not 0.0 <= beta3:
            raise ValueError ("Invalid a value: {}".format (beta3))
        self.c_hook_lr = _default_c_hook_lr
        self.c_hook_beta = _default_c_hook_beta
        defaults = dict (lr=lr, betas=betas, eps=eps,
                         weight_decay=weight_decay, amsgrad=amsgrad, beta3=beta3)
        super (GWDC, self).__init__ (params, defaults)

    def __setstate__(self, state):
        super (GWDC, self).__setstate__ (state)
        for group in self.param_groups:
            group.setdefault ('amsgrad', False)
            group.setdefalut ('beta3', 1e-4)

    @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
                if grad.is_sparse:
                    raise RuntimeError ('GWDC does not support sparse gradients, please consider SparseAdam instead')
                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, memory_format=torch.preserve_format)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    # eta_hat value
                    state['eta_hat'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    # eta value
                    state['eta'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    # V value
                    state['v'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    state['n'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    state['u'] = torch.zeros_like (p, memory_format=torch.preserve_format)
                    if amsgrad:
                        # Maintains max of all exp. moving avg. of sq. grad. values
                        state['max_exp_avg_sq'] = torch.zeros_like (p, memory_format=torch.preserve_format)

                exp_avg, exp_avg_sq = state['exp_avg'], state['exp_avg_sq']
                eta_hat, eta, n, u = state['eta_hat'], state['eta'], state['n'], state['u']
                if amsgrad:
                    max_exp_avg_sq = state['max_exp_avg_sq']
                else:
                    max_exp_avg_sq = None
                beta1, beta2 = group['betas']
                state['step'] += 1

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

                # beta_1,t = beta1t*e^{-beta_3*t}
                beta1 = 0.9 * math.exp (-group['beta3'] * state['step'])

                # 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)

                n = 0.1 - 0.1 / (1 - beta2) / state['step']
                u = 0.1 + 0.1 / (1 - beta2) / state['step']

                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)
                    eta_hat = torch.clamp (group['lr'] / max_exp_avg_sq, min=n, max=u)
                    eta = eta_hat / math.sqrt (state['step'])
                    # Use the max. for normalizing running avg. of gradient
                    # denom = (max_exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
                    # denom = max_exp_avg_sq.sqrt().add_(group['eps'])
                    # step_size = group['lr']
                else:
                    # bias_correction1 = 1 - beta1 ** state['step']
                    # bias_correction2 = 1 - beta2 ** state['step']
                    eta_hat = torch.clamp (group['lr'] / exp_avg_sq, min=n, max=u)
                    eta = eta_hat / math.sqrt (state['step'])
                    # denom = (exp_avg_sq.sqrt() / math.sqrt(bias_correction2)).add_(group['eps'])
                    # step_size = group['lr'] / bias_correction1

                # p.addcdiv_(exp_avg, denom, value=-step_size)
                p.addcmul_ (exp_avg, eta, value=-1)

        return loss
