import math

import torch
from torch.optim.optimizer import Optimizer

from .types import Betas2, OptFloat, OptLossClosure, Params

__all__ = ('DiffGrad',)


class DiffGrad(Optimizer):
    r"""Implements DiffGrad algorithm.

    It has been proposed in `DiffGrad: An Optimization Method for
    Convolutional Neural Networks`__.

    Arguments:
        params: iterable of parameters to optimize or dicts defining
            parameter groups
        lr: learning rate (default: 1e-3)
        betas: coefficients used for computing
            running averages of gradient and its square (default: (0.9, 0.999))
        eps: term added to the denominator to improve
            numerical stability (default: 1e-8)
        weight_decay: weight decay (L2 penalty) (default: 0)

    Example:
        >>> import torch_optimizer as optim
        >>> optimizer = optim.DiffGrad(model.parameters(), lr=0.1)
        >>> optimizer.zero_grad()
        >>> loss_fn(model(input), target).backward()
        >>> optimizer.step()

    __ https://arxiv.org/abs/1909.11015

    Note:
        Reference code: https://github.com/shivram1987/diffGrad
    """

    def __init__(
        self,
        params: Params,
        lr: float = 1e-3,
        betas: Betas2 = (0.9, 0.999),
        eps: float = 1e-8,
        weight_decay: float = 0.0,
    ) -> None:
        if lr <= 0.0:
            raise ValueError('Invalid learning rate: {}'.format(lr))
        if eps < 0.0:
            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 weight_decay < 0.0:
            raise ValueError(
                'Invalid weight_decay value: {}'.format(weight_decay)
            )

        defaults = dict(lr=lr, betas=betas, eps=eps, weight_decay=weight_decay)
        super(DiffGrad, self).__init__(params, defaults)

    def step(self, closure: OptLossClosure = None) -> OptFloat:
        r"""Performs a single optimization step.

        Arguments:
            closure: 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:
            beta1, beta2 = group['betas']

            for p in group['params']:
                if p.grad is None:
                    continue
                grad = p.grad.data
                if grad.is_sparse:
                    msg = (
                        'DiffGrad does not support sparse gradients, '
                        'please consider SparseAdam instead'
                    )
                    raise RuntimeError(msg)

                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)
                    # Exponential moving average of squared gradient values
                    state['exp_avg_sq'] = torch.zeros_like(p)
                    # Previous gradient
                    state['previous_grad'] = torch.zeros_like(p)

                exp_avg, exp_avg_sq, previous_grad = (
                    state['exp_avg'],
                    state['exp_avg_sq'],
                    state['previous_grad'],
                )

                state['step'] += 1

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

                # 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().add_(group['eps'])

                bias_correction1 = 1 - beta1 ** state['step']
                bias_correction2 = 1 - beta2 ** state['step']

                # compute diffgrad coefficient (dfc)
                diff = torch.abs(previous_grad - grad)
                dfc = torch.div(1.0, (1.0 + torch.exp(-diff)))
                state['previous_grad'] = grad.clone()

                # update momentum with dfc
                exp_avg1 = exp_avg * dfc

                step_size = (
                    group['lr']
                    * math.sqrt(bias_correction2)
                    / bias_correction1
                )

                p.data.addcdiv_(exp_avg1, denom, value=-step_size)

        return loss