import math

import torch

from torch.optim.optimizer import Optimizer

class AdamW(Optimizer):

    r"""Implements AdamW algorithm.

    The original Adam algorithm was proposed in `Adam: A Method for Stochastic Optimization`_.

    The AdamW variant was 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 coefficient (default: 1e-2)

        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-3, betas=(0.9, 0.999), eps=1e-8,

                 weight_decay=1e-2, 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(AdamW, self).__init__(params, defaults)

    def __setstate__(self, state):

        super(AdamW, 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

                # Perform stepweight decay

                p.data.mul_(1 - group['lr'] * group['weight_decay'])

                # Perform optimization step

                grad = p.grad.data

                if grad.is_sparse:

                    raise RuntimeError('Adam 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.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

                # 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

                p.data.addcdiv_(-step_size, exp_avg, denom)

        return loss

class Nadam(Optimizer):

    def __init__(self, params, lr=1e-3, betas=(0.9, 0.999), eps=1e-8,

                 schedule_decay=0.004,amsgrad=False):

        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,

                        amsgrad=amsgrad,schedule_decay=schedule_decay)

        super(Nadam, self).__init__(params, defaults)

    def step(self, closure=None):

        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

                if grad.is_sparse:

                    raise RuntimeError('Nadam 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.data)

                    # Exponential moving average of squared gradient values

                    state['exp_avg_sq'] = torch.zeros_like(p.data)

                    state['m_schedule'] = 1

                    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

                momentum_cache_t = beta1 * (

                        1. - 0.5 * math.pow(0.96, state['step'] * group['schedule_decay'] ))

                momentum_cache_t_1 = beta1 * (

                        1. - 0.5 * math.pow(0.96, (state['step']+1) * group['schedule_decay'] ))

                state['m_schedule'] = state['m_schedule'] * momentum_cache_t

                exp_avg.mul_(beta1).add_(1 - beta1, grad)

                m_t_prime = exp_avg/(1 - state['m_schedule'] * momentum_cache_t_1)

                g_prime = grad.div(1 - state['m_schedule'])

                m_t_bar = (1. - momentum_cache_t) * g_prime + momentum_cache_t_1 * m_t_prime

                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

                    v_t_prime = max_exp_avg_sq/(1 - beta2 ** state['step'])

                else:

                    v_t_prime = exp_avg_sq / (1 - beta2 ** state['step'])

                denom = v_t_prime.sqrt().add_(group['eps'])

                p.data.addcdiv_(-group['lr'], m_t_bar , denom)

        return loss